id	sid	tid	token	lemma	pos
ap-3488	1	1	acta	acta	PROPN
ap-3488	1	2	polytechnica	polytechnica	PROPN
ap-3488	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3488	1	4	/	/	SYM
ap-3488	1	5	app.2016.56.0001	app.2016.56.0001	PROPN
ap-3488	1	6	acta	acta	PROPN
ap-3488	1	7	polytechnica	polytechnica	PROPN
ap-3488	1	8	56(1):1–9	56(1):1–9	PROPN
ap-3488	1	9	,	,	PUNCT
ap-3488	1	10	2016	2016	NUM
ap-3488	1	11	©	©	PROPN
ap-3488	1	12	czech	czech	PROPN
ap-3488	1	13	technical	technical	PROPN
ap-3488	1	14	university	university	PROPN
ap-3488	1	15	in	in	ADP
ap-3488	1	16	prague	prague	PROPN
ap-3488	1	17	,	,	PUNCT
ap-3488	1	18	2016	2016	NUM
ap-3488	1	19	available	available	ADJ
ap-3488	1	20	online	online	ADV
ap-3488	1	21	at	at	ADP
ap-3488	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3488	1	23	formation	formation	NOUN
ap-3488	1	24	control	control	NOUN
ap-3488	1	25	of	of	ADP
ap-3488	1	26	multiple	multiple	ADJ
ap-3488	1	27	unicycle	unicycle	NOUN
ap-3488	1	28	-	-	PUNCT
ap-3488	1	29	type	type	NOUN
ap-3488	1	30	robots	robot	NOUN
ap-3488	1	31	using	use	VERB
ap-3488	1	32	lie	lie	NOUN
ap-3488	1	33	group	group	NOUN
ap-3488	1	34	youwei	youwei	NOUN
ap-3488	1	35	dong∗	dong∗	PROPN
ap-3488	1	36	,	,	PUNCT
ap-3488	1	37	ahmed	ahmed	PROPN
ap-3488	1	38	rahmani	rahmani	PROPN
ap-3488	1	39	ecole	ecole	PROPN
ap-3488	1	40	centrale	centrale	PROPN
ap-3488	1	41	de	de	X
ap-3488	1	42	lille	lille	PROPN
ap-3488	1	43	,	,	PUNCT
ap-3488	1	44	cité	cité	PROPN
ap-3488	1	45	scientifique	scientifique	PROPN
ap-3488	1	46	–	–	PUNCT
ap-3488	1	47	cs20048	cs20048	PROPN
ap-3488	1	48	,	,	PUNCT
ap-3488	1	49	59651	59651	NUM
ap-3488	1	50	villeneuve	villeneuve	PROPN
ap-3488	1	51	d’ascq	d’ascq	PROPN
ap-3488	1	52	cedex	cedex	NOUN
ap-3488	1	53	,	,	PUNCT
ap-3488	1	54	france	france	PROPN
ap-3488	1	55	∗	∗	NOUN
ap-3488	1	56	corresponding	correspond	VERB
ap-3488	1	57	author	author	NOUN
ap-3488	1	58	:	:	PUNCT
ap-3488	1	59	youwei.dong@ec-lille.fr	youwei.dong@ec-lille.fr	X
ap-3488	2	1	abstract	abstract	ADJ
ap-3488	2	2	.	.	PUNCT
ap-3488	3	1	in	in	ADP
ap-3488	3	2	this	this	DET
ap-3488	3	3	paper	paper	NOUN
ap-3488	3	4	the	the	DET
ap-3488	3	5	formation	formation	NOUN
ap-3488	3	6	control	control	NOUN
ap-3488	3	7	of	of	ADP
ap-3488	3	8	a	a	DET
ap-3488	3	9	multi	multi	ADJ
ap-3488	3	10	-	-	ADJ
ap-3488	3	11	robots	robots	ADJ
ap-3488	3	12	system	system	NOUN
ap-3488	3	13	is	be	AUX
ap-3488	3	14	investigated	investigate	VERB
ap-3488	3	15	.	.	PUNCT
ap-3488	4	1	the	the	DET
ap-3488	4	2	proposed	propose	VERB
ap-3488	4	3	control	control	NOUN
ap-3488	4	4	law	law	PROPN
ap-3488	4	5	,	,	PUNCT
ap-3488	4	6	based	base	VERB
ap-3488	4	7	on	on	ADP
ap-3488	4	8	lie	lie	PROPN
ap-3488	4	9	group	group	NOUN
ap-3488	4	10	theory	theory	NOUN
ap-3488	4	11	,	,	PUNCT
ap-3488	4	12	is	be	AUX
ap-3488	4	13	applied	apply	VERB
ap-3488	4	14	to	to	PART
ap-3488	4	15	control	control	VERB
ap-3488	4	16	the	the	DET
ap-3488	4	17	formation	formation	NOUN
ap-3488	4	18	of	of	ADP
ap-3488	4	19	a	a	DET
ap-3488	4	20	group	group	NOUN
ap-3488	4	21	of	of	ADP
ap-3488	4	22	unicycle	unicycle	NOUN
ap-3488	4	23	-	-	PUNCT
ap-3488	4	24	type	type	NOUN
ap-3488	4	25	robots	robot	NOUN
ap-3488	4	26	.	.	PUNCT
ap-3488	5	1	the	the	DET
ap-3488	5	2	communication	communication	NOUN
ap-3488	5	3	topology	topology	NOUN
ap-3488	5	4	is	be	AUX
ap-3488	5	5	supposed	suppose	VERB
ap-3488	5	6	to	to	PART
ap-3488	5	7	be	be	AUX
ap-3488	5	8	a	a	DET
ap-3488	5	9	rooted	rooted	ADJ
ap-3488	5	10	directed	direct	VERB
ap-3488	5	11	acyclic	acyclic	ADJ
ap-3488	5	12	graph	graph	NOUN
ap-3488	5	13	and	and	CCONJ
ap-3488	5	14	fixed	fix	VERB
ap-3488	5	15	.	.	PUNCT
ap-3488	6	1	some	some	DET
ap-3488	6	2	numerical	numerical	ADJ
ap-3488	6	3	simulations	simulation	NOUN
ap-3488	6	4	using	use	VERB
ap-3488	6	5	matlab	matlab	PROPN
ap-3488	6	6	are	be	AUX
ap-3488	6	7	made	make	VERB
ap-3488	6	8	to	to	PART
ap-3488	6	9	validate	validate	VERB
ap-3488	6	10	our	our	PRON
ap-3488	6	11	results	result	NOUN
ap-3488	6	12	.	.	PUNCT
ap-3488	7	1	keywords	keyword	NOUN
ap-3488	7	2	:	:	PUNCT
ap-3488	7	3	formation	formation	NOUN
ap-3488	7	4	control	control	NOUN
ap-3488	7	5	;	;	PUNCT
ap-3488	7	6	multi	multi	ADJ
ap-3488	7	7	-	-	ADJ
ap-3488	7	8	robot	robot	ADJ
ap-3488	7	9	system	system	NOUN
ap-3488	7	10	;	;	PUNCT
ap-3488	7	11	unicycle	unicycle	NOUN
ap-3488	7	12	-	-	PUNCT
ap-3488	7	13	type	type	NOUN
ap-3488	7	14	robot	robot	NOUN
ap-3488	7	15	;	;	PUNCT
ap-3488	7	16	lie	lie	NOUN
ap-3488	7	17	group	group	NOUN
ap-3488	7	18	;	;	PUNCT
ap-3488	7	19	lie	lie	NOUN
ap-3488	7	20	algebra	algebra	NOUN
ap-3488	7	21	.	.	PUNCT
ap-3488	8	1	1	1	X
ap-3488	8	2	.	.	X
ap-3488	8	3	introduction	introduction	NOUN
ap-3488	8	4	the	the	DET
ap-3488	8	5	various	various	ADJ
ap-3488	8	6	ways	way	NOUN
ap-3488	8	7	to	to	PART
ap-3488	8	8	control	control	VERB
ap-3488	8	9	and	and	CCONJ
ap-3488	8	10	coordinate	coordinate	VERB
ap-3488	8	11	a	a	DET
ap-3488	8	12	group	group	NOUN
ap-3488	8	13	of	of	ADP
ap-3488	8	14	mobile	mobile	ADJ
ap-3488	8	15	robots	robot	NOUN
ap-3488	8	16	widely	widely	ADV
ap-3488	8	17	have	have	AUX
ap-3488	8	18	been	be	AUX
ap-3488	8	19	studied	study	VERB
ap-3488	8	20	in	in	ADP
ap-3488	8	21	recent	recent	ADJ
ap-3488	8	22	years	year	NOUN
ap-3488	8	23	.	.	PUNCT
ap-3488	9	1	this	this	PRON
ap-3488	9	2	has	have	AUX
ap-3488	9	3	brought	bring	VERB
ap-3488	9	4	a	a	DET
ap-3488	9	5	breadth	breadth	NOUN
ap-3488	9	6	of	of	ADP
ap-3488	9	7	innovation	innovation	NOUN
ap-3488	9	8	,	,	PUNCT
ap-3488	9	9	providing	provide	VERB
ap-3488	9	10	considerable	considerable	ADJ
ap-3488	9	11	attention	attention	NOUN
ap-3488	9	12	for	for	ADP
ap-3488	9	13	the	the	DET
ap-3488	9	14	potential	potential	ADJ
ap-3488	9	15	applications	application	NOUN
ap-3488	9	16	,	,	PUNCT
ap-3488	9	17	such	such	ADJ
ap-3488	9	18	as	as	ADP
ap-3488	9	19	flocking	flock	VERB
ap-3488	9	20	systems	system	NOUN
ap-3488	9	21	control	control	NOUN
ap-3488	9	22	,	,	PUNCT
ap-3488	9	23	surveillance	surveillance	NOUN
ap-3488	9	24	,	,	PUNCT
ap-3488	9	25	search	search	NOUN
ap-3488	9	26	and	and	CCONJ
ap-3488	9	27	rescue	rescue	NOUN
ap-3488	9	28	,	,	PUNCT
ap-3488	9	29	cooperative	cooperative	ADJ
ap-3488	9	30	construction	construction	NOUN
ap-3488	9	31	,	,	PUNCT
ap-3488	9	32	distributed	distribute	VERB
ap-3488	9	33	sensor	sensor	NOUN
ap-3488	9	34	fusion	fusion	NOUN
ap-3488	9	35	,	,	PUNCT
ap-3488	9	36	etc	etc	X
ap-3488	9	37	.	.	X
ap-3488	9	38	when	when	SCONJ
ap-3488	9	39	comparing	compare	VERB
ap-3488	9	40	the	the	DET
ap-3488	9	41	mission	mission	NOUN
ap-3488	9	42	outcome	outcome	NOUN
ap-3488	9	43	of	of	ADP
ap-3488	9	44	a	a	DET
ap-3488	9	45	multi	multi	ADJ
ap-3488	9	46	-	-	ADJ
ap-3488	9	47	robot	robot	ADJ
ap-3488	9	48	system	system	NOUN
ap-3488	9	49	(	(	PUNCT
ap-3488	9	50	mrs	mrs	PROPN
ap-3488	9	51	)	)	PUNCT
ap-3488	9	52	to	to	ADP
ap-3488	9	53	that	that	PRON
ap-3488	9	54	of	of	ADP
ap-3488	9	55	a	a	DET
ap-3488	9	56	single	single	ADJ
ap-3488	9	57	robot	robot	NOUN
ap-3488	9	58	,	,	PUNCT
ap-3488	9	59	it	it	PRON
ap-3488	9	60	is	be	AUX
ap-3488	9	61	clear	clear	ADJ
ap-3488	9	62	that	that	SCONJ
ap-3488	9	63	cooperation	cooperation	NOUN
ap-3488	9	64	among	among	ADP
ap-3488	9	65	multiple	multiple	ADJ
ap-3488	9	66	robots	robot	NOUN
ap-3488	9	67	can	can	AUX
ap-3488	9	68	perform	perform	VERB
ap-3488	9	69	complex	complex	ADJ
ap-3488	9	70	tasks	task	NOUN
ap-3488	9	71	that	that	SCONJ
ap-3488	9	72	it	it	PRON
ap-3488	9	73	would	would	AUX
ap-3488	9	74	otherwise	otherwise	ADV
ap-3488	9	75	be	be	AUX
ap-3488	9	76	impossible	impossible	ADJ
ap-3488	9	77	for	for	SCONJ
ap-3488	9	78	a	a	DET
ap-3488	9	79	single	single	ADJ
ap-3488	9	80	powerful	powerful	ADJ
ap-3488	9	81	robot	robot	NOUN
ap-3488	9	82	to	to	PART
ap-3488	9	83	accomplish	accomplish	VERB
ap-3488	9	84	.	.	PUNCT
ap-3488	10	1	the	the	DET
ap-3488	10	2	fundamental	fundamental	ADJ
ap-3488	10	3	idea	idea	NOUN
ap-3488	10	4	behind	behind	ADP
ap-3488	10	5	multirobotics	multirobotic	NOUN
ap-3488	10	6	is	be	AUX
ap-3488	10	7	to	to	PART
ap-3488	10	8	allow	allow	VERB
ap-3488	10	9	the	the	DET
ap-3488	10	10	individuals	individual	NOUN
ap-3488	10	11	to	to	PART
ap-3488	10	12	interact	interact	VERB
ap-3488	10	13	with	with	ADP
ap-3488	10	14	each	each	DET
ap-3488	10	15	other	other	ADJ
ap-3488	10	16	to	to	PART
ap-3488	10	17	find	find	VERB
ap-3488	10	18	solutions	solution	NOUN
ap-3488	10	19	of	of	ADP
ap-3488	10	20	complex	complex	ADJ
ap-3488	10	21	problems	problem	NOUN
ap-3488	10	22	.	.	PUNCT
ap-3488	11	1	each	each	PRON
ap-3488	11	2	of	of	ADP
ap-3488	11	3	them	they	PRON
ap-3488	11	4	senses	sense	VERB
ap-3488	11	5	the	the	DET
ap-3488	11	6	relative	relative	ADJ
ap-3488	11	7	positions	position	NOUN
ap-3488	11	8	of	of	ADP
ap-3488	11	9	his	his	PRON
ap-3488	11	10	neighbors	neighbor	NOUN
ap-3488	11	11	,	,	PUNCT
ap-3488	11	12	and	and	CCONJ
ap-3488	11	13	achieves	achieve	VERB
ap-3488	11	14	the	the	DET
ap-3488	11	15	desired	desire	VERB
ap-3488	11	16	formation	formation	NOUN
ap-3488	11	17	by	by	ADP
ap-3488	11	18	controlling	control	VERB
ap-3488	11	19	the	the	DET
ap-3488	11	20	relative	relative	ADJ
ap-3488	11	21	positions	position	NOUN
ap-3488	11	22	[	[	X
ap-3488	11	23	1–3	1–3	NOUN
ap-3488	11	24	]	]	X
ap-3488	11	25	.	.	PUNCT
ap-3488	12	1	in	in	ADP
ap-3488	12	2	formation	formation	NOUN
ap-3488	12	3	control	control	NOUN
ap-3488	12	4	,	,	PUNCT
ap-3488	12	5	various	various	ADJ
ap-3488	12	6	control	control	NOUN
ap-3488	12	7	topologies	topology	NOUN
ap-3488	12	8	can	can	AUX
ap-3488	12	9	be	be	AUX
ap-3488	12	10	adopted	adopt	VERB
ap-3488	12	11	,	,	PUNCT
ap-3488	12	12	depending	depend	VERB
ap-3488	12	13	on	on	ADP
ap-3488	12	14	the	the	DET
ap-3488	12	15	specific	specific	ADJ
ap-3488	12	16	environment	environment	NOUN
ap-3488	12	17	and	and	CCONJ
ap-3488	12	18	tasks	task	NOUN
ap-3488	12	19	.	.	PUNCT
ap-3488	13	1	theoretical	theoretical	ADJ
ap-3488	13	2	views	view	NOUN
ap-3488	13	3	of	of	ADP
ap-3488	13	4	mrs	mrs	PROPN
ap-3488	13	5	behavior	behavior	NOUN
ap-3488	13	6	are	be	AUX
ap-3488	13	7	divided	divide	VERB
ap-3488	13	8	into	into	ADP
ap-3488	13	9	centralized	centralized	ADJ
ap-3488	13	10	and	and	CCONJ
ap-3488	13	11	decentralized	decentralized	ADJ
ap-3488	13	12	systems	system	NOUN
ap-3488	13	13	.	.	PUNCT
ap-3488	14	1	in	in	ADP
ap-3488	14	2	a	a	DET
ap-3488	14	3	centralized	centralized	ADJ
ap-3488	14	4	system	system	NOUN
ap-3488	14	5	,	,	PUNCT
ap-3488	14	6	a	a	DET
ap-3488	14	7	powerful	powerful	ADJ
ap-3488	14	8	core	core	NOUN
ap-3488	14	9	unit	unit	NOUN
ap-3488	14	10	makes	make	VERB
ap-3488	14	11	decisions	decision	NOUN
ap-3488	14	12	and	and	CCONJ
ap-3488	14	13	communicates	communicate	VERB
ap-3488	14	14	with	with	ADP
ap-3488	14	15	the	the	DET
ap-3488	14	16	others	other	NOUN
ap-3488	14	17	.	.	PUNCT
ap-3488	15	1	in	in	ADP
ap-3488	15	2	the	the	DET
ap-3488	15	3	decentralized	decentralize	VERB
ap-3488	15	4	approach	approach	NOUN
ap-3488	15	5	,	,	PUNCT
ap-3488	15	6	the	the	DET
ap-3488	15	7	robots	robot	NOUN
ap-3488	15	8	can	can	AUX
ap-3488	15	9	communicate	communicate	VERB
ap-3488	15	10	and	and	CCONJ
ap-3488	15	11	share	share	VERB
ap-3488	15	12	information	information	NOUN
ap-3488	15	13	with	with	ADP
ap-3488	15	14	each	each	DET
ap-3488	15	15	other	other	ADJ
ap-3488	15	16	[	[	X
ap-3488	15	17	4	4	NUM
ap-3488	15	18	]	]	PUNCT
ap-3488	15	19	.	.	PUNCT
ap-3488	16	1	we	we	PRON
ap-3488	16	2	will	will	AUX
ap-3488	16	3	focus	focus	VERB
ap-3488	16	4	on	on	ADP
ap-3488	16	5	distributed	distribute	VERB
ap-3488	16	6	system	system	NOUN
ap-3488	16	7	control	control	NOUN
ap-3488	16	8	due	due	ADP
ap-3488	16	9	to	to	ADP
ap-3488	16	10	its	its	PRON
ap-3488	16	11	advantages	advantage	NOUN
ap-3488	16	12	,	,	PUNCT
ap-3488	16	13	such	such	ADJ
ap-3488	16	14	as	as	ADP
ap-3488	16	15	feasibility	feasibility	NOUN
ap-3488	16	16	,	,	PUNCT
ap-3488	16	17	accuracy	accuracy	NOUN
ap-3488	16	18	,	,	PUNCT
ap-3488	16	19	robustness	robustness	NOUN
ap-3488	16	20	,	,	PUNCT
ap-3488	16	21	cost	cost	NOUN
ap-3488	16	22	,	,	PUNCT
ap-3488	16	23	and	and	CCONJ
ap-3488	16	24	so	so	ADV
ap-3488	16	25	on	on	ADV
ap-3488	16	26	.	.	PUNCT
ap-3488	17	1	many	many	ADJ
ap-3488	17	2	studies	study	NOUN
ap-3488	17	3	have	have	AUX
ap-3488	17	4	been	be	AUX
ap-3488	17	5	devoted	devote	VERB
ap-3488	17	6	to	to	ADP
ap-3488	17	7	the	the	DET
ap-3488	17	8	control	control	NOUN
ap-3488	17	9	and	and	CCONJ
ap-3488	17	10	coordination	coordination	NOUN
ap-3488	17	11	of	of	ADP
ap-3488	17	12	multi	multi	ADJ
ap-3488	17	13	-	-	ADJ
ap-3488	17	14	agent	agent	ADJ
ap-3488	17	15	systems	system	NOUN
ap-3488	17	16	and	and	CCONJ
ap-3488	17	17	multi	multi	ADJ
ap-3488	17	18	-	-	ADJ
ap-3488	17	19	robot	robot	ADJ
ap-3488	17	20	systems	system	NOUN
ap-3488	17	21	(	(	PUNCT
ap-3488	17	22	e.g.	e.g.	ADV
ap-3488	17	23	[	[	X
ap-3488	17	24	1	1	NUM
ap-3488	17	25	,	,	PUNCT
ap-3488	17	26	4–9	4–9	NOUN
ap-3488	17	27	]	]	X
ap-3488	17	28	)	)	PUNCT
ap-3488	17	29	.	.	PUNCT
ap-3488	18	1	some	some	PRON
ap-3488	18	2	of	of	ADP
ap-3488	18	3	these	these	DET
ap-3488	18	4	results	result	NOUN
ap-3488	18	5	have	have	AUX
ap-3488	18	6	been	be	AUX
ap-3488	18	7	used	use	VERB
ap-3488	18	8	to	to	PART
ap-3488	18	9	control	control	VERB
ap-3488	18	10	vehicles	vehicle	NOUN
ap-3488	18	11	(	(	PUNCT
ap-3488	18	12	holonomic	holonomic	ADJ
ap-3488	18	13	,	,	PUNCT
ap-3488	18	14	nonholonomic	nonholonomic	ADJ
ap-3488	18	15	mobile	mobile	ADJ
ap-3488	18	16	robots	robot	NOUN
ap-3488	18	17	,	,	PUNCT
ap-3488	18	18	etc	etc	X
ap-3488	18	19	.	.	X
ap-3488	18	20	)	)	PUNCT
ap-3488	18	21	.	.	PUNCT
ap-3488	19	1	in	in	ADP
ap-3488	19	2	this	this	DET
ap-3488	19	3	paper	paper	NOUN
ap-3488	19	4	,	,	PUNCT
ap-3488	19	5	our	our	PRON
ap-3488	19	6	goal	goal	NOUN
ap-3488	19	7	is	be	AUX
ap-3488	19	8	to	to	PART
ap-3488	19	9	control	control	VERB
ap-3488	19	10	a	a	DET
ap-3488	19	11	group	group	NOUN
ap-3488	19	12	of	of	ADP
ap-3488	19	13	unicycle	unicycle	NOUN
ap-3488	19	14	robots	robot	NOUN
ap-3488	19	15	to	to	PART
ap-3488	19	16	achieve	achieve	VERB
ap-3488	19	17	a	a	DET
ap-3488	19	18	desired	desire	VERB
ap-3488	19	19	formation	formation	NOUN
ap-3488	19	20	.	.	PUNCT
ap-3488	20	1	motivated	motivate	VERB
ap-3488	20	2	by	by	ADP
ap-3488	20	3	references	reference	NOUN
ap-3488	20	4	[	[	X
ap-3488	20	5	10–14	10–14	NUM
ap-3488	20	6	]	]	PUNCT
ap-3488	20	7	,	,	PUNCT
ap-3488	20	8	we	we	PRON
ap-3488	20	9	focus	focus	VERB
ap-3488	20	10	on	on	ADP
ap-3488	20	11	a	a	DET
ap-3488	20	12	rigid	rigid	ADJ
ap-3488	20	13	body	body	NOUN
ap-3488	20	14	with	with	ADP
ap-3488	20	15	kinematics	kinematic	NOUN
ap-3488	20	16	evolving	evolve	VERB
ap-3488	20	17	on	on	ADP
ap-3488	20	18	lie	lie	NOUN
ap-3488	20	19	groups	group	NOUN
ap-3488	20	20	.	.	PUNCT
ap-3488	21	1	this	this	PRON
ap-3488	21	2	is	be	AUX
ap-3488	21	3	based	base	VERB
ap-3488	21	4	on	on	ADP
ap-3488	21	5	regarding	regard	VERB
ap-3488	21	6	the	the	DET
ap-3488	21	7	set	set	NOUN
ap-3488	21	8	of	of	ADP
ap-3488	21	9	rigid	rigid	ADJ
ap-3488	21	10	body	body	NOUN
ap-3488	21	11	posture	posture	NOUN
ap-3488	21	12	as	as	ADP
ap-3488	21	13	the	the	DET
ap-3488	21	14	lie	lie	NOUN
ap-3488	21	15	group	group	NOUN
ap-3488	21	16	se(2	se(2	PROPN
ap-3488	21	17	)	)	PUNCT
ap-3488	21	18	,	,	PUNCT
ap-3488	21	19	which	which	PRON
ap-3488	21	20	leads	lead	VERB
ap-3488	21	21	to	to	ADP
ap-3488	21	22	a	a	DET
ap-3488	21	23	set	set	NOUN
ap-3488	21	24	of	of	ADP
ap-3488	21	25	kinematic	kinematic	ADJ
ap-3488	21	26	equations	equation	NOUN
ap-3488	21	27	.	.	PUNCT
ap-3488	22	1	these	these	DET
ap-3488	22	2	equations	equation	NOUN
ap-3488	22	3	are	be	AUX
ap-3488	22	4	expressed	express	VERB
ap-3488	22	5	in	in	ADP
ap-3488	22	6	terms	term	NOUN
ap-3488	22	7	of	of	ADP
ap-3488	22	8	standard	standard	ADJ
ap-3488	22	9	coordinated	coordinate	VERB
ap-3488	22	10	invariant	invariant	ADJ
ap-3488	22	11	linear	linear	ADJ
ap-3488	22	12	operators	operator	NOUN
ap-3488	22	13	on	on	ADP
ap-3488	22	14	the	the	DET
ap-3488	22	15	lie	lie	NOUN
ap-3488	22	16	algebra	algebra	PROPN
ap-3488	22	17	se(2	se(2	NOUN
ap-3488	22	18	)	)	PUNCT
ap-3488	22	19	.	.	PUNCT
ap-3488	23	1	this	this	DET
ap-3488	23	2	approach	approach	NOUN
ap-3488	23	3	allows	allow	VERB
ap-3488	23	4	a	a	DET
ap-3488	23	5	global	global	ADJ
ap-3488	23	6	description	description	NOUN
ap-3488	23	7	of	of	ADP
ap-3488	23	8	rigid	rigid	ADJ
ap-3488	23	9	body	body	NOUN
ap-3488	23	10	motion	motion	NOUN
ap-3488	23	11	which	which	PRON
ap-3488	23	12	does	do	AUX
ap-3488	23	13	not	not	PART
ap-3488	23	14	suffer	suffer	VERB
ap-3488	23	15	from	from	ADP
ap-3488	23	16	singularities	singularity	NOUN
ap-3488	23	17	.	.	PUNCT
ap-3488	24	1	it	it	PRON
ap-3488	24	2	provides	provide	VERB
ap-3488	24	3	a	a	DET
ap-3488	24	4	geometric	geometric	ADJ
ap-3488	24	5	description	description	NOUN
ap-3488	24	6	of	of	ADP
ap-3488	24	7	rigid	rigid	ADJ
ap-3488	24	8	motion	motion	NOUN
ap-3488	24	9	which	which	PRON
ap-3488	24	10	greatly	greatly	ADV
ap-3488	24	11	simplifies	simplify	VERB
ap-3488	24	12	an	an	DET
ap-3488	24	13	analysis	analysis	NOUN
ap-3488	24	14	of	of	ADP
ap-3488	24	15	the	the	DET
ap-3488	24	16	mechanisms	mechanism	NOUN
ap-3488	24	17	[	[	X
ap-3488	24	18	10	10	NUM
ap-3488	24	19	]	]	PUNCT
ap-3488	24	20	.	.	PUNCT
ap-3488	25	1	paper	paper	NOUN
ap-3488	26	1	[	[	X
ap-3488	26	2	1	1	X
ap-3488	26	3	]	]	PUNCT
ap-3488	26	4	proposed	propose	VERB
ap-3488	26	5	an	an	DET
ap-3488	26	6	elegant	elegant	ADJ
ap-3488	26	7	control	control	NOUN
ap-3488	26	8	law	law	NOUN
ap-3488	26	9	based	base	VERB
ap-3488	26	10	on	on	ADP
ap-3488	26	11	lie	lie	NOUN
ap-3488	26	12	algebra	algebra	NOUN
ap-3488	26	13	theory	theory	NOUN
ap-3488	26	14	for	for	ADP
ap-3488	26	15	consensus	consensus	NOUN
ap-3488	26	16	of	of	ADP
ap-3488	26	17	a	a	DET
ap-3488	26	18	multi	multi	ADJ
ap-3488	26	19	-	-	ADJ
ap-3488	26	20	agent	agent	ADJ
ap-3488	26	21	system	system	NOUN
ap-3488	26	22	.	.	PUNCT
ap-3488	27	1	it	it	PRON
ap-3488	27	2	has	have	VERB
ap-3488	27	3	the	the	DET
ap-3488	27	4	holonomic	holonomic	ADJ
ap-3488	27	5	constraints	constraint	NOUN
ap-3488	27	6	,	,	PUNCT
ap-3488	27	7	while	while	SCONJ
ap-3488	27	8	nonholonomic	nonholonomic	ADJ
ap-3488	27	9	constraints	constraint	NOUN
ap-3488	27	10	are	be	AUX
ap-3488	27	11	not	not	PART
ap-3488	27	12	considered	consider	VERB
ap-3488	27	13	.	.	PUNCT
ap-3488	28	1	in	in	ADP
ap-3488	28	2	[	[	X
ap-3488	28	3	12	12	NUM
ap-3488	28	4	]	]	PUNCT
ap-3488	28	5	,	,	PUNCT
ap-3488	28	6	lie	lie	NOUN
ap-3488	28	7	algebra	algebra	NOUN
ap-3488	28	8	is	be	AUX
ap-3488	28	9	used	use	VERB
ap-3488	28	10	to	to	PART
ap-3488	28	11	study	study	VERB
ap-3488	28	12	the	the	DET
ap-3488	28	13	path	path	NOUN
ap-3488	28	14	following	follow	VERB
ap-3488	28	15	control	control	NOUN
ap-3488	28	16	of	of	ADP
ap-3488	28	17	one	one	NUM
ap-3488	28	18	mobile	mobile	ADJ
ap-3488	28	19	robot	robot	NOUN
ap-3488	28	20	.	.	PUNCT
ap-3488	29	1	in	in	ADP
ap-3488	29	2	[	[	X
ap-3488	29	3	15	15	NUM
ap-3488	29	4	]	]	PUNCT
ap-3488	29	5	,	,	PUNCT
ap-3488	29	6	distributed	distribute	VERB
ap-3488	29	7	formation	formation	NOUN
ap-3488	29	8	control	control	NOUN
ap-3488	29	9	of	of	ADP
ap-3488	29	10	multi	multi	ADJ
ap-3488	29	11	-	-	ADJ
ap-3488	29	12	nonholonomic	nonholonomic	ADJ
ap-3488	29	13	robots	robot	NOUN
ap-3488	29	14	is	be	AUX
ap-3488	29	15	studied	study	VERB
ap-3488	29	16	.	.	PUNCT
ap-3488	30	1	however	however	ADV
ap-3488	30	2	the	the	DET
ap-3488	30	3	the	the	DET
ap-3488	30	4	control	control	NOUN
ap-3488	30	5	law	law	NOUN
ap-3488	30	6	is	be	AUX
ap-3488	30	7	a	a	DET
ap-3488	30	8	leader	leader	NOUN
ap-3488	30	9	-	-	PUNCT
ap-3488	30	10	follower	follower	NOUN
ap-3488	30	11	approach	approach	NOUN
ap-3488	30	12	,	,	PUNCT
ap-3488	30	13	and	and	CCONJ
ap-3488	30	14	the	the	DET
ap-3488	30	15	multi	multi	ADJ
ap-3488	30	16	-	-	ADJ
ap-3488	30	17	leader	leader	ADJ
ap-3488	30	18	case	case	NOUN
ap-3488	30	19	is	be	AUX
ap-3488	30	20	not	not	PART
ap-3488	30	21	considered	consider	VERB
ap-3488	30	22	.	.	PUNCT
ap-3488	31	1	in	in	ADP
ap-3488	31	2	this	this	DET
ap-3488	31	3	paper	paper	NOUN
ap-3488	31	4	,	,	PUNCT
ap-3488	31	5	a	a	DET
ap-3488	31	6	lie	lie	NOUN
ap-3488	31	7	group	group	NOUN
ap-3488	31	8	method	method	NOUN
ap-3488	31	9	is	be	AUX
ap-3488	31	10	used	use	VERB
ap-3488	31	11	to	to	PART
ap-3488	31	12	control	control	VERB
ap-3488	31	13	multiple	multiple	ADJ
ap-3488	31	14	unicycletype	unicycletype	NOUN
ap-3488	31	15	robots	robot	NOUN
ap-3488	31	16	.	.	PUNCT
ap-3488	32	1	the	the	DET
ap-3488	32	2	communication	communication	NOUN
ap-3488	32	3	topology	topology	NOUN
ap-3488	32	4	is	be	AUX
ap-3488	32	5	defined	define	VERB
ap-3488	32	6	as	as	ADP
ap-3488	32	7	a	a	DET
ap-3488	32	8	rooted	rooted	ADJ
ap-3488	32	9	directed	direct	VERB
ap-3488	32	10	acyclic	acyclic	ADJ
ap-3488	32	11	graph	graph	NOUN
ap-3488	32	12	(	(	PUNCT
ap-3488	32	13	dag	dag	PROPN
ap-3488	32	14	)	)	PUNCT
ap-3488	32	15	.	.	PUNCT
ap-3488	33	1	due	due	ADP
ap-3488	33	2	to	to	ADP
ap-3488	33	3	the	the	DET
ap-3488	33	4	nonholonomic	nonholonomic	ADJ
ap-3488	33	5	property	property	NOUN
ap-3488	33	6	of	of	ADP
ap-3488	33	7	this	this	DET
ap-3488	33	8	type	type	NOUN
ap-3488	33	9	of	of	ADP
ap-3488	33	10	robot	robot	NOUN
ap-3488	33	11	,	,	PUNCT
ap-3488	33	12	a	a	DET
ap-3488	33	13	new	new	ADJ
ap-3488	33	14	local	local	ADJ
ap-3488	33	15	control	control	NOUN
ap-3488	33	16	law	law	NOUN
ap-3488	33	17	is	be	AUX
ap-3488	33	18	proposed	propose	VERB
ap-3488	33	19	to	to	PART
ap-3488	33	20	make	make	VERB
ap-3488	33	21	the	the	DET
ap-3488	33	22	nonlinear	nonlinear	ADJ
ap-3488	33	23	system	system	NOUN
ap-3488	33	24	converge	converge	VERB
ap-3488	33	25	to	to	ADP
ap-3488	33	26	the	the	DET
ap-3488	33	27	desired	desire	VERB
ap-3488	33	28	formation	formation	NOUN
ap-3488	33	29	.	.	PUNCT
ap-3488	34	1	the	the	DET
ap-3488	34	2	outline	outline	NOUN
ap-3488	34	3	of	of	ADP
ap-3488	34	4	this	this	DET
ap-3488	34	5	paper	paper	NOUN
ap-3488	34	6	is	be	AUX
ap-3488	34	7	as	as	SCONJ
ap-3488	34	8	follows	follow	VERB
ap-3488	34	9	.	.	PUNCT
ap-3488	35	1	in	in	ADP
ap-3488	35	2	section	section	NOUN
ap-3488	35	3	2	2	NUM
ap-3488	35	4	,	,	PUNCT
ap-3488	35	5	some	some	DET
ap-3488	35	6	preliminary	preliminary	ADJ
ap-3488	35	7	results	result	NOUN
ap-3488	35	8	are	be	AUX
ap-3488	35	9	summarized	summarize	VERB
ap-3488	35	10	and	and	CCONJ
ap-3488	35	11	the	the	DET
ap-3488	35	12	formation	formation	NOUN
ap-3488	35	13	control	control	NOUN
ap-3488	35	14	problem	problem	NOUN
ap-3488	35	15	for	for	ADP
ap-3488	35	16	a	a	DET
ap-3488	35	17	group	group	NOUN
ap-3488	35	18	of	of	ADP
ap-3488	35	19	unicycle	unicycle	NOUN
ap-3488	35	20	-	-	PUNCT
ap-3488	35	21	type	type	NOUN
ap-3488	35	22	robots	robot	NOUN
ap-3488	35	23	is	be	AUX
ap-3488	35	24	stated	state	VERB
ap-3488	35	25	.	.	PUNCT
ap-3488	36	1	in	in	ADP
ap-3488	36	2	section	section	NOUN
ap-3488	36	3	3	3	NUM
ap-3488	36	4	,	,	PUNCT
ap-3488	36	5	a	a	DET
ap-3488	36	6	formation	formation	NOUN
ap-3488	36	7	control	control	NOUN
ap-3488	36	8	strategy	strategy	NOUN
ap-3488	36	9	is	be	AUX
ap-3488	36	10	proposed	propose	VERB
ap-3488	36	11	and	and	CCONJ
ap-3488	36	12	the	the	DET
ap-3488	36	13	stability	stability	NOUN
ap-3488	36	14	is	be	AUX
ap-3488	36	15	analyzed	analyze	VERB
ap-3488	36	16	.	.	PUNCT
ap-3488	37	1	the	the	DET
ap-3488	37	2	simulation	simulation	NOUN
ap-3488	37	3	and	and	CCONJ
ap-3488	37	4	results	result	NOUN
ap-3488	37	5	are	be	AUX
ap-3488	37	6	given	give	VERB
ap-3488	37	7	in	in	ADP
ap-3488	37	8	section	section	NOUN
ap-3488	37	9	4	4	NUM
ap-3488	37	10	.	.	PUNCT
ap-3488	37	11	concluding	conclude	VERB
ap-3488	37	12	remarks	remark	NOUN
ap-3488	37	13	are	be	AUX
ap-3488	37	14	finally	finally	ADV
ap-3488	37	15	provided	provide	VERB
ap-3488	37	16	in	in	ADP
ap-3488	37	17	section	section	NOUN
ap-3488	37	18	5	5	NUM
ap-3488	37	19	.	.	NOUN
ap-3488	37	20	2	2	NUM
ap-3488	37	21	.	.	X
ap-3488	37	22	preliminary	preliminary	ADJ
ap-3488	37	23	and	and	CCONJ
ap-3488	37	24	problem	problem	NOUN
ap-3488	37	25	statement	statement	NOUN
ap-3488	37	26	2.1	2.1	NUM
ap-3488	37	27	.	.	PUNCT
ap-3488	38	1	lie	lie	NOUN
ap-3488	38	2	groups	group	NOUN
ap-3488	38	3	definition	definition	NOUN
ap-3488	38	4	1	1	NUM
ap-3488	38	5	[	[	X
ap-3488	38	6	10	10	NUM
ap-3488	38	7	]	]	PUNCT
ap-3488	38	8	.	.	PUNCT
ap-3488	39	1	a	a	DET
ap-3488	39	2	manifold	manifold	NOUN
ap-3488	39	3	of	of	ADP
ap-3488	39	4	dimension	dimension	NOUN
ap-3488	39	5	of	of	ADP
ap-3488	39	6	n	n	PROPN
ap-3488	39	7	is	be	AUX
ap-3488	39	8	a	a	DET
ap-3488	39	9	set	set	NOUN
ap-3488	39	10	m	m	NOUN
ap-3488	39	11	,	,	PUNCT
ap-3488	39	12	which	which	PRON
ap-3488	39	13	is	be	AUX
ap-3488	39	14	locally	locally	ADV
ap-3488	39	15	homeomorphic	homeomorphic	ADJ
ap-3488	39	16	to	to	ADP
ap-3488	39	17	rn	rn	PROPN
ap-3488	39	18	.	.	PUNCT
ap-3488	40	1	a	a	DET
ap-3488	40	2	lie	lie	NOUN
ap-3488	40	3	group	group	NOUN
ap-3488	40	4	is	be	AUX
ap-3488	40	5	a	a	DET
ap-3488	40	6	group	group	NOUN
ap-3488	40	7	g	g	NOUN
ap-3488	40	8	which	which	PRON
ap-3488	40	9	is	be	AUX
ap-3488	40	10	also	also	ADV
ap-3488	40	11	a	a	DET
ap-3488	40	12	smooth	smooth	ADJ
ap-3488	40	13	manifold	manifold	NOUN
ap-3488	40	14	and	and	CCONJ
ap-3488	40	15	for	for	ADP
ap-3488	40	16	which	which	PRON
ap-3488	40	17	the	the	DET
ap-3488	40	18	group	group	NOUN
ap-3488	40	19	operations	operation	NOUN
ap-3488	40	20	(	(	PUNCT
ap-3488	40	21	g	g	NOUN
ap-3488	40	22	,	,	PUNCT
ap-3488	40	23	h	h	NOUN
ap-3488	40	24	)	)	PUNCT
ap-3488	40	25	7→	7→	NUM
ap-3488	40	26	gh	gh	PROPN
ap-3488	40	27	and	and	CCONJ
ap-3488	40	28	g	g	PROPN
ap-3488	40	29	7→	7→	PROPN
ap-3488	40	30	g−1	g−1	PROPN
ap-3488	40	31	are	be	AUX
ap-3488	40	32	smooth	smooth	ADJ
ap-3488	40	33	.	.	PUNCT
ap-3488	41	1	left	leave	VERB
ap-3488	41	2	action	action	NOUN
ap-3488	41	3	of	of	ADP
ap-3488	41	4	g	g	NOUN
ap-3488	41	5	on	on	ADP
ap-3488	41	6	itself	itself	PRON
ap-3488	41	7	lg	lg	NOUN
ap-3488	41	8	:	:	PUNCT
ap-3488	41	9	g→	g→	NOUN
ap-3488	41	10	g	g	NOUN
ap-3488	41	11	is	be	AUX
ap-3488	41	12	defined	define	VERB
ap-3488	41	13	by	by	ADP
ap-3488	41	14	lg(h	lg(h	NOUN
ap-3488	41	15	)	)	PUNCT
ap-3488	42	1	=	=	SYM
ap-3488	42	2	gh	gh	PROPN
ap-3488	42	3	,	,	PUNCT
ap-3488	42	4	and	and	CCONJ
ap-3488	42	5	right	right	ADJ
ap-3488	42	6	action	action	NOUN
ap-3488	42	7	is	be	AUX
ap-3488	42	8	defined	define	VERB
ap-3488	42	9	the	the	DET
ap-3488	42	10	same	same	ADJ
ap-3488	42	11	way	way	NOUN
ap-3488	42	12	.	.	PUNCT
ap-3488	43	1	adjoint	adjoint	NOUN
ap-3488	43	2	action	action	NOUN
ap-3488	43	3	adg	adg	PROPN
ap-3488	43	4	:	:	PUNCT
ap-3488	43	5	g→	g→	PROPN
ap-3488	43	6	g	g	PROPN
ap-3488	43	7	is	be	AUX
ap-3488	43	8	adg(h	adg(h	PROPN
ap-3488	43	9	)	)	PUNCT
ap-3488	43	10	=	=	SYM
ap-3488	44	1	ghg−1	ghg−1	PROPN
ap-3488	44	2	.	.	PUNCT
ap-3488	45	1	here	here	ADV
ap-3488	45	2	are	be	AUX
ap-3488	45	3	two	two	NUM
ap-3488	45	4	examples	example	NOUN
ap-3488	45	5	,	,	PUNCT
ap-3488	45	6	the	the	DET
ap-3488	45	7	special	special	ADJ
ap-3488	45	8	orthogonal	orthogonal	ADJ
ap-3488	45	9	group	group	NOUN
ap-3488	45	10	so(n	so(n	PROPN
ap-3488	45	11	)	)	PUNCT
ap-3488	45	12	=	=	SYM
ap-3488	46	1	{	{	PUNCT
ap-3488	46	2	r	r	NOUN
ap-3488	46	3	∈	∈	NOUN
ap-3488	46	4	gl(n	gl(n	NUM
ap-3488	46	5	,	,	PUNCT
ap-3488	46	6	r	r	NOUN
ap-3488	46	7	)	)	PUNCT
ap-3488	46	8	:	:	PUNCT
ap-3488	46	9	rrt	rrt	NOUN
ap-3488	46	10	=	=	SYM
ap-3488	46	11	i	i	PROPN
ap-3488	46	12	,	,	PUNCT
ap-3488	46	13	detr	detr	PROPN
ap-3488	46	14	=	=	SYM
ap-3488	46	15	+1	+1	PROPN
ap-3488	46	16	}	}	PUNCT
ap-3488	46	17	and	and	CCONJ
ap-3488	46	18	the	the	DET
ap-3488	46	19	special	special	ADJ
ap-3488	46	20	euclidean	euclidean	ADJ
ap-3488	46	21	group	group	NOUN
ap-3488	46	22	se(n	se(n	PROPN
ap-3488	46	23	)	)	PUNCT
ap-3488	46	24	=	=	PRON
ap-3488	46	25	{	{	PUNCT
ap-3488	46	26	(	(	PUNCT
ap-3488	46	27	p	p	X
ap-3488	46	28	,	,	PUNCT
ap-3488	46	29	r	r	NOUN
ap-3488	46	30	)	)	PUNCT
ap-3488	46	31	:	:	PUNCT
ap-3488	46	32	p	p	PROPN
ap-3488	46	33	∈	∈	PROPN
ap-3488	46	34	rn	rn	PROPN
ap-3488	46	35	,	,	PUNCT
ap-3488	46	36	r	r	NOUN
ap-3488	46	37	∈	∈	PROPN
ap-3488	46	38	so(n	so(n	NOUN
ap-3488	46	39	)	)	PUNCT
ap-3488	46	40	}	}	PUNCT
ap-3488	46	41	=	=	PUNCT
ap-3488	46	42	rn	rn	PROPN
ap-3488	46	43	×	×	PROPN
ap-3488	46	44	so(n	so(n	PROPN
ap-3488	46	45	)	)	PUNCT
ap-3488	46	46	.	.	PUNCT
ap-3488	47	1	1	1	NUM
ap-3488	47	2	http://dx.doi.org/10.14311/app.2016.56.0001	http://dx.doi.org/10.14311/app.2016.56.0001	PROPN
ap-3488	47	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3488	47	4	youwei	youwei	NOUN
ap-3488	47	5	dong	dong	PROPN
ap-3488	47	6	,	,	PUNCT
ap-3488	47	7	ahmed	ahmed	PROPN
ap-3488	47	8	rahmani	rahmani	PROPN
ap-3488	47	9	acta	acta	PROPN
ap-3488	47	10	polytechnica	polytechnica	PROPN
ap-3488	47	11	2.2	2.2	NUM
ap-3488	47	12	.	.	PUNCT
ap-3488	48	1	lie	lie	NOUN
ap-3488	48	2	algebra	algebra	PROPN
ap-3488	48	3	associated	associate	VERB
ap-3488	48	4	with	with	ADP
ap-3488	48	5	a	a	DET
ap-3488	48	6	lie	lie	NOUN
ap-3488	48	7	group	group	NOUN
ap-3488	48	8	a	a	DET
ap-3488	48	9	lie	lie	NOUN
ap-3488	48	10	algebra	algebra	VERB
ap-3488	48	11	g	g	NOUN
ap-3488	48	12	over	over	ADP
ap-3488	48	13	r	r	NOUN
ap-3488	48	14	is	be	AUX
ap-3488	48	15	a	a	DET
ap-3488	48	16	real	real	ADJ
ap-3488	48	17	vector	vector	NOUN
ap-3488	48	18	space	space	NOUN
ap-3488	48	19	g	g	NOUN
ap-3488	48	20	together	together	ADV
ap-3488	48	21	with	with	ADP
ap-3488	48	22	a	a	DET
ap-3488	48	23	bilinear	bilinear	NOUN
ap-3488	48	24	operator	operator	NOUN
ap-3488	48	25	[	[	X
ap-3488	48	26	,	,	PUNCT
ap-3488	48	27	]	]	X
ap-3488	48	28	:	:	PUNCT
ap-3488	48	29	g×	g×	X
ap-3488	48	30	g	g	NOUN
ap-3488	48	31	(	(	PUNCT
ap-3488	48	32	called	call	VERB
ap-3488	48	33	the	the	DET
ap-3488	48	34	bracket	bracket	NOUN
ap-3488	48	35	)	)	PUNCT
ap-3488	48	36	such	such	ADJ
ap-3488	48	37	that	that	PRON
ap-3488	48	38	for	for	ADP
ap-3488	48	39	all	all	DET
ap-3488	48	40	x	x	NOUN
ap-3488	48	41	,	,	PUNCT
ap-3488	48	42	y	y	PROPN
ap-3488	48	43	,	,	PUNCT
ap-3488	48	44	z	z	PROPN
ap-3488	48	45	∈	∈	PROPN
ap-3488	48	46	g	g	PROPN
ap-3488	48	47	,	,	PUNCT
ap-3488	48	48	we	we	PRON
ap-3488	48	49	have	have	VERB
ap-3488	48	50	:	:	PUNCT
ap-3488	48	51	•	•	NUM
ap-3488	48	52	anti	anti	ADJ
ap-3488	48	53	-	-	NOUN
ap-3488	48	54	commutativity	commutativity	ADJ
ap-3488	48	55	:	:	PUNCT
ap-3488	48	56	[	[	X
ap-3488	48	57	x	x	X
ap-3488	48	58	,	,	PUNCT
ap-3488	48	59	y	y	PROPN
ap-3488	48	60	]	]	X
ap-3488	48	61	=	=	SYM
ap-3488	48	62	−[y	−[y	NOUN
ap-3488	48	63	,	,	PUNCT
ap-3488	48	64	x	x	X
ap-3488	48	65	]	]	X
ap-3488	48	66	;	;	PUNCT
ap-3488	48	67	•	•	NUM
ap-3488	48	68	jacobi	jacobi	NOUN
ap-3488	48	69	identity	identity	NOUN
ap-3488	48	70	:	:	PUNCT
ap-3488	49	1	[	[	X
ap-3488	49	2	[	[	X
ap-3488	49	3	x	x	X
ap-3488	49	4	,	,	PUNCT
ap-3488	49	5	y	y	PROPN
ap-3488	49	6	]	]	X
ap-3488	49	7	,	,	PUNCT
ap-3488	49	8	z	z	X
ap-3488	49	9	]	]	X
ap-3488	49	10	+	+	CCONJ
ap-3488	50	1	[	[	X
ap-3488	50	2	[	[	X
ap-3488	50	3	y	y	PROPN
ap-3488	50	4	,	,	PUNCT
ap-3488	50	5	z	z	NOUN
ap-3488	50	6	]	]	X
ap-3488	50	7	,	,	PUNCT
ap-3488	50	8	x	x	X
ap-3488	50	9	]	]	X
ap-3488	50	10	+	+	CCONJ
ap-3488	51	1	[	[	X
ap-3488	51	2	[	[	X
ap-3488	51	3	z	z	X
ap-3488	51	4	,	,	PUNCT
ap-3488	51	5	x	x	X
ap-3488	51	6	]	]	X
ap-3488	51	7	,	,	PUNCT
ap-3488	51	8	y	y	X
ap-3488	51	9	]	]	X
ap-3488	51	10	=	=	PUNCT
ap-3488	51	11	0	0	X
ap-3488	51	12	.	.	PUNCT
ap-3488	52	1	a	a	DET
ap-3488	52	2	lie	lie	NOUN
ap-3488	52	3	algebra	algebra	NOUN
ap-3488	52	4	g	g	NOUN
ap-3488	52	5	is	be	AUX
ap-3488	52	6	said	say	VERB
ap-3488	52	7	to	to	PART
ap-3488	52	8	be	be	AUX
ap-3488	52	9	commutative	commutative	ADJ
ap-3488	52	10	(	(	PUNCT
ap-3488	52	11	or	or	CCONJ
ap-3488	52	12	abelian	abelian	ADJ
ap-3488	52	13	)	)	PUNCT
ap-3488	52	14	if	if	SCONJ
ap-3488	52	15	[	[	X
ap-3488	52	16	x	x	X
ap-3488	52	17	,	,	PUNCT
ap-3488	52	18	y	y	PROPN
ap-3488	52	19	]	]	X
ap-3488	52	20	=	=	SYM
ap-3488	52	21	0	0	NUM
ap-3488	52	22	for	for	ADP
ap-3488	52	23	all	all	DET
ap-3488	52	24	x	x	NOUN
ap-3488	52	25	,	,	PUNCT
ap-3488	52	26	y	y	PROPN
ap-3488	52	27	∈	∈	PROPN
ap-3488	52	28	g.	g.	NOUN
ap-3488	52	29	we	we	PRON
ap-3488	52	30	can	can	AUX
ap-3488	52	31	define	define	VERB
ap-3488	52	32	adab	adab	NOUN
ap-3488	52	33	=	=	PUNCT
ap-3488	53	1	[	[	X
ap-3488	53	2	a	a	DET
ap-3488	53	3	,	,	PUNCT
ap-3488	53	4	b	b	NOUN
ap-3488	53	5	]	]	X
ap-3488	53	6	=	=	SYM
ap-3488	53	7	ab	ab	PROPN
ap-3488	53	8	−	−	PROPN
ap-3488	53	9	ba	ba	PROPN
ap-3488	53	10	where	where	SCONJ
ap-3488	53	11	a	a	DET
ap-3488	53	12	,	,	PUNCT
ap-3488	53	13	b	b	NOUN
ap-3488	53	14	∈	∈	NOUN
ap-3488	53	15	gl(n	gl(n	NUM
ap-3488	53	16	,	,	PUNCT
ap-3488	53	17	r	r	NOUN
ap-3488	53	18	)	)	PUNCT
ap-3488	53	19	,	,	PUNCT
ap-3488	53	20	which	which	PRON
ap-3488	53	21	is	be	AUX
ap-3488	53	22	the	the	DET
ap-3488	53	23	vector	vector	NOUN
ap-3488	53	24	space	space	NOUN
ap-3488	53	25	of	of	ADP
ap-3488	53	26	all	all	DET
ap-3488	53	27	n	n	PRON
ap-3488	53	28	×	×	NOUN
ap-3488	53	29	n	n	CCONJ
ap-3488	53	30	real	real	ADJ
ap-3488	53	31	matrices	matrix	NOUN
ap-3488	53	32	,	,	PUNCT
ap-3488	53	33	gl(n	gl(n	X
ap-3488	53	34	,	,	PUNCT
ap-3488	53	35	r	r	NOUN
ap-3488	53	36	)	)	PUNCT
ap-3488	53	37	forms	form	VERB
ap-3488	53	38	a	a	DET
ap-3488	53	39	lie	lie	NOUN
ap-3488	53	40	algebra	algebra	NOUN
ap-3488	53	41	.	.	PUNCT
ap-3488	54	1	clearly	clearly	ADV
ap-3488	54	2	,	,	PUNCT
ap-3488	54	3	we	we	PRON
ap-3488	54	4	have	have	VERB
ap-3488	54	5	[	[	X
ap-3488	54	6	x	x	X
ap-3488	54	7	,	,	PUNCT
ap-3488	54	8	x	x	X
ap-3488	54	9	]	]	X
ap-3488	54	10	=	=	SYM
ap-3488	54	11	0	0	X
ap-3488	54	12	.	.	PUNCT
ap-3488	55	1	the	the	DET
ap-3488	55	2	lie	lie	NOUN
ap-3488	55	3	algebra	algebra	NOUN
ap-3488	55	4	of	of	ADP
ap-3488	55	5	so(2	so(2	NOUN
ap-3488	55	6	)	)	PUNCT
ap-3488	55	7	,	,	PUNCT
ap-3488	55	8	denoted	denote	VERB
ap-3488	55	9	by	by	ADP
ap-3488	55	10	so(2	so(2	NOUN
ap-3488	55	11	)	)	PUNCT
ap-3488	55	12	,	,	PUNCT
ap-3488	55	13	may	may	AUX
ap-3488	55	14	be	be	AUX
ap-3488	55	15	identified	identify	VERB
ap-3488	55	16	with	with	ADP
ap-3488	55	17	a	a	DET
ap-3488	55	18	2×	2×	NUM
ap-3488	55	19	2	2	NUM
ap-3488	55	20	skew	skew	ADJ
ap-3488	55	21	-	-	PUNCT
ap-3488	55	22	symmetric	symmetric	ADJ
ap-3488	55	23	matrix	matrix	NOUN
ap-3488	55	24	of	of	ADP
ap-3488	55	25	the	the	DET
ap-3488	55	26	form	form	NOUN
ap-3488	55	27	ω̂	ω̂	PUNCT
ap-3488	55	28	=	=	PUNCT
ap-3488	56	1	[	[	PUNCT
ap-3488	56	2	0	0	NUM
ap-3488	56	3	−ω	−ω	PROPN
ap-3488	56	4	ω	ω	PROPN
ap-3488	56	5	0	0	NUM
ap-3488	56	6	]	]	PUNCT
ap-3488	56	7	with	with	ADP
ap-3488	56	8	the	the	DET
ap-3488	56	9	bracket	bracket	NOUN
ap-3488	56	10	structure	structure	NOUN
ap-3488	56	11	[	[	X
ap-3488	56	12	ω̂1	ω̂1	ADJ
ap-3488	56	13	,	,	PUNCT
ap-3488	56	14	ω̂2	ω̂2	NOUN
ap-3488	56	15	]	]	X
ap-3488	56	16	=	=	SYM
ap-3488	56	17	ω̂1ω̂2−ω̂2ω̂1	ω̂1ω̂2−ω̂2ω̂1	NOUN
ap-3488	56	18	,	,	PUNCT
ap-3488	56	19	where	where	SCONJ
ap-3488	56	20	ω̂1	ω̂1	ADJ
ap-3488	56	21	,	,	PUNCT
ap-3488	56	22	ω̂2	ω̂2	PUNCT
ap-3488	56	23	∈	∈	PROPN
ap-3488	56	24	so(2	so(2	PROPN
ap-3488	56	25	)	)	PUNCT
ap-3488	56	26	.	.	PUNCT
ap-3488	57	1	the	the	DET
ap-3488	57	2	lie	lie	NOUN
ap-3488	57	3	algebra	algebra	NOUN
ap-3488	57	4	of	of	ADP
ap-3488	57	5	se(2	se(2	PROPN
ap-3488	57	6	)	)	PUNCT
ap-3488	57	7	,	,	PUNCT
ap-3488	57	8	denoted	denote	VERB
ap-3488	57	9	by	by	ADP
ap-3488	57	10	se(2	se(2	PROPN
ap-3488	57	11	)	)	PUNCT
ap-3488	57	12	,	,	PUNCT
ap-3488	57	13	can	can	AUX
ap-3488	57	14	be	be	AUX
ap-3488	57	15	identified	identify	VERB
ap-3488	57	16	with	with	ADP
ap-3488	57	17	a	a	DET
ap-3488	57	18	3	3	NUM
ap-3488	57	19	×	×	NOUN
ap-3488	57	20	3	3	NUM
ap-3488	57	21	matrix	matrix	NOUN
ap-3488	57	22	of	of	ADP
ap-3488	57	23	the	the	DET
ap-3488	57	24	form	form	NOUN
ap-3488	57	25	ξ̂	ξ̂	NOUN
ap-3488	57	26	=	=	SYM
ap-3488	57	27	[	[	PUNCT
ap-3488	57	28	ω̂	ω̂	NUM
ap-3488	57	29	v	v	NOUN
ap-3488	57	30	0	0	NUM
ap-3488	57	31	0	0	NUM
ap-3488	57	32	]	]	PUNCT
ap-3488	57	33	,	,	PUNCT
ap-3488	57	34	where	where	SCONJ
ap-3488	57	35	ω	ω	PROPN
ap-3488	57	36	∈	∈	PROPN
ap-3488	57	37	r	r	NOUN
ap-3488	57	38	,	,	PUNCT
ap-3488	57	39	v	v	NOUN
ap-3488	57	40	∈	∈	NOUN
ap-3488	57	41	r2	r2	NOUN
ap-3488	57	42	,	,	PUNCT
ap-3488	57	43	with	with	ADP
ap-3488	57	44	the	the	DET
ap-3488	57	45	bracket	bracket	NOUN
ap-3488	57	46	[	[	X
ap-3488	57	47	ξ̂1	ξ̂1	NOUN
ap-3488	57	48	,	,	PUNCT
ap-3488	57	49	ξ̂2	ξ̂2	X
ap-3488	57	50	]	]	X
ap-3488	57	51	=	=	PUNCT
ap-3488	58	1	ξ̂1ξ̂2	ξ̂1ξ̂2	PROPN
ap-3488	58	2	−	−	PROPN
ap-3488	58	3	ξ̂2ξ̂1	ξ̂2ξ̂1	PROPN
ap-3488	58	4	.	.	PUNCT
ap-3488	59	1	the	the	DET
ap-3488	59	2	exponential	exponential	ADJ
ap-3488	59	3	map	map	NOUN
ap-3488	59	4	:	:	PUNCT
ap-3488	59	5	exp	exp	NOUN
ap-3488	59	6	:	:	PUNCT
ap-3488	59	7	teg	teg	PROPN
ap-3488	59	8	→	→	SYM
ap-3488	59	9	g	g	PROPN
ap-3488	59	10	is	be	AUX
ap-3488	59	11	a	a	DET
ap-3488	59	12	local	local	ADJ
ap-3488	59	13	diffeomorphism	diffeomorphism	NOUN
ap-3488	59	14	from	from	ADP
ap-3488	59	15	the	the	DET
ap-3488	59	16	neighborhood	neighborhood	NOUN
ap-3488	59	17	of	of	ADP
ap-3488	59	18	zero	zero	NUM
ap-3488	59	19	in	in	ADP
ap-3488	59	20	g	g	NOUN
ap-3488	59	21	onto	onto	ADP
ap-3488	59	22	the	the	DET
ap-3488	59	23	neighborhood	neighborhood	NOUN
ap-3488	59	24	of	of	ADP
ap-3488	59	25	e	e	PROPN
ap-3488	59	26	in	in	ADP
ap-3488	59	27	g.	g.	PROPN
ap-3488	59	28	the	the	DET
ap-3488	59	29	mapping	mapping	PROPN
ap-3488	59	30	t→	t→	SYM
ap-3488	59	31	exp(tξ̂	exp(tξ̂	NOUN
ap-3488	59	32	)	)	PUNCT
ap-3488	59	33	is	be	AUX
ap-3488	59	34	the	the	DET
ap-3488	59	35	unique	unique	ADJ
ap-3488	59	36	one	one	NUM
ap-3488	59	37	-	-	PUNCT
ap-3488	59	38	parameter	parameter	NOUN
ap-3488	59	39	subgroup	subgroup	NOUN
ap-3488	59	40	r→	r→	PROPN
ap-3488	59	41	g	g	PROPN
ap-3488	59	42	with	with	ADP
ap-3488	59	43	tangent	tangent	ADJ
ap-3488	59	44	vector	vector	NOUN
ap-3488	59	45	ξ̂	ξ̂	NOUN
ap-3488	59	46	at	at	ADP
ap-3488	59	47	time	time	NOUN
ap-3488	59	48	0	0	NUM
ap-3488	59	49	.	.	PUNCT
ap-3488	60	1	for	for	ADP
ap-3488	60	2	ω̂	ω̂	PROPN
ap-3488	60	3	∈	∈	PROPN
ap-3488	60	4	so(2	so(2	NOUN
ap-3488	60	5	)	)	PUNCT
ap-3488	60	6	and	and	CCONJ
ap-3488	60	7	ξ̂	ξ̂	NUM
ap-3488	60	8	=	=	SYM
ap-3488	60	9	(	(	PUNCT
ap-3488	60	10	ω̂	ω̂	PROPN
ap-3488	60	11	,	,	PUNCT
ap-3488	60	12	v	v	NOUN
ap-3488	60	13	)	)	PUNCT
ap-3488	60	14	∈	∈	PROPN
ap-3488	60	15	se(2	se(2	NOUN
ap-3488	60	16	)	)	PUNCT
ap-3488	60	17	,	,	PUNCT
ap-3488	60	18	we	we	PRON
ap-3488	60	19	have	have	VERB
ap-3488	60	20	exp	exp	NOUN
ap-3488	60	21	ω̂t	ω̂t	NUM
ap-3488	60	22	=	=	PUNCT
ap-3488	61	1	[	[	PUNCT
ap-3488	61	2	cosωt	cosωt	NOUN
ap-3488	61	3	−	−	PROPN
ap-3488	61	4	sinωt	sinωt	NOUN
ap-3488	61	5	sinωt	sinωt	PROPN
ap-3488	61	6	cosωt	cosωt	PROPN
ap-3488	61	7	]	]	PUNCT
ap-3488	61	8	,	,	PUNCT
ap-3488	61	9	(	(	PUNCT
ap-3488	61	10	1	1	X
ap-3488	61	11	)	)	PUNCT
ap-3488	61	12	exp	exp	NOUN
ap-3488	61	13	ξ̂t	ξ̂t	NUM
ap-3488	61	14	=	=	PUNCT
ap-3488	61	15	[	[	PUNCT
ap-3488	61	16	exp	exp	NOUN
ap-3488	61	17	ω̂t	ω̂t	NUM
ap-3488	61	18	a(ω)v	a(ω)v	PROPN
ap-3488	61	19	0	0	NUM
ap-3488	61	20	1	1	NUM
ap-3488	61	21	]	]	PUNCT
ap-3488	61	22	,	,	PUNCT
ap-3488	61	23	(	(	PUNCT
ap-3488	61	24	2	2	X
ap-3488	61	25	)	)	PUNCT
ap-3488	61	26	where	where	SCONJ
ap-3488	61	27	a(ω	a(ω	NOUN
ap-3488	61	28	)	)	PUNCT
ap-3488	61	29	=	=	SYM
ap-3488	61	30	1	1	NUM
ap-3488	61	31	ω	ω	NOUN
ap-3488	61	32	[	[	PUNCT
ap-3488	61	33	sinωt	sinωt	NOUN
ap-3488	61	34	−(1−	−(1−	VERB
ap-3488	61	35	cosωt	cosωt	NOUN
ap-3488	61	36	)	)	PUNCT
ap-3488	61	37	(	(	PUNCT
ap-3488	61	38	1−	1−	NUM
ap-3488	61	39	cosωt	cosωt	NOUN
ap-3488	61	40	)	)	PUNCT
ap-3488	61	41	sinωt	sinωt	NOUN
ap-3488	61	42	]	]	PUNCT
ap-3488	61	43	.	.	PUNCT
ap-3488	62	1	2.3	2.3	NUM
ap-3488	62	2	.	.	PUNCT
ap-3488	63	1	graph	graph	NOUN
ap-3488	63	2	theory	theory	NOUN
ap-3488	63	3	the	the	DET
ap-3488	63	4	communication	communication	NOUN
ap-3488	63	5	topology	topology	NOUN
ap-3488	63	6	among	among	ADP
ap-3488	63	7	n	n	PRON
ap-3488	63	8	robots	robot	NOUN
ap-3488	63	9	will	will	AUX
ap-3488	63	10	be	be	AUX
ap-3488	63	11	represented	represent	VERB
ap-3488	63	12	by	by	ADP
ap-3488	63	13	a	a	DET
ap-3488	63	14	graph	graph	NOUN
ap-3488	63	15	.	.	PUNCT
ap-3488	64	1	let	let	VERB
ap-3488	64	2	g	g	PROPN
ap-3488	64	3	=	=	SYM
ap-3488	64	4	(	(	PUNCT
ap-3488	64	5	v	v	NOUN
ap-3488	64	6	,	,	PUNCT
ap-3488	64	7	e	e	NOUN
ap-3488	64	8	,	,	PUNCT
ap-3488	64	9	a	a	PRON
ap-3488	64	10	)	)	PUNCT
ap-3488	64	11	be	be	AUX
ap-3488	64	12	a	a	DET
ap-3488	64	13	graph	graph	NOUN
ap-3488	64	14	of	of	ADP
ap-3488	64	15	order	order	NOUN
ap-3488	64	16	n	n	NOUN
ap-3488	64	17	with	with	ADP
ap-3488	64	18	the	the	DET
ap-3488	64	19	finite	finite	PROPN
ap-3488	64	20	nonempty	nonempty	ADV
ap-3488	64	21	set	set	NOUN
ap-3488	64	22	of	of	ADP
ap-3488	64	23	nodes	node	NOUN
ap-3488	64	24	v(g	v(g	ADJ
ap-3488	64	25	)	)	PUNCT
ap-3488	64	26	=	=	SYM
ap-3488	64	27	{	{	PUNCT
ap-3488	64	28	v1	v1	PROPN
ap-3488	64	29	,	,	PUNCT
ap-3488	64	30	.	.	PUNCT
ap-3488	64	31	.	.	PUNCT
ap-3488	65	1	.	.	PUNCT
ap-3488	66	1	,	,	PUNCT
ap-3488	66	2	vn	vn	PROPN
ap-3488	66	3	}	}	PUNCT
ap-3488	66	4	,	,	PUNCT
ap-3488	66	5	the	the	DET
ap-3488	66	6	set	set	NOUN
ap-3488	66	7	of	of	ADP
ap-3488	66	8	edges	edge	NOUN
ap-3488	66	9	e(g	e(g	PROPN
ap-3488	66	10	)	)	PUNCT
ap-3488	67	1	⊂	⊂	PROPN
ap-3488	67	2	v	v	ADP
ap-3488	67	3	×	×	PROPN
ap-3488	67	4	v	v	NOUN
ap-3488	67	5	,	,	PUNCT
ap-3488	67	6	and	and	CCONJ
ap-3488	67	7	an	an	DET
ap-3488	67	8	adjacency	adjacency	NOUN
ap-3488	67	9	matrix	matrix	NOUN
ap-3488	67	10	a	a	DET
ap-3488	67	11	=	=	X
ap-3488	67	12	(	(	PUNCT
ap-3488	67	13	aij)n×n	aij)n×n	NOUN
ap-3488	67	14	.	.	PUNCT
ap-3488	68	1	if	if	SCONJ
ap-3488	68	2	for	for	ADP
ap-3488	68	3	all	all	DET
ap-3488	68	4	(	(	PUNCT
ap-3488	68	5	vi	vi	PROPN
ap-3488	68	6	,	,	PUNCT
ap-3488	68	7	vj	vj	ADJ
ap-3488	68	8	)	)	PUNCT
ap-3488	68	9	∈	∈	PROPN
ap-3488	68	10	e	e	NOUN
ap-3488	68	11	,	,	PUNCT
ap-3488	68	12	(	(	PUNCT
ap-3488	68	13	vj	vj	INTJ
ap-3488	68	14	,	,	PUNCT
ap-3488	68	15	vi	vi	NOUN
ap-3488	68	16	)	)	PUNCT
ap-3488	68	17	∈	∈	NOUN
ap-3488	68	18	e	e	NOUN
ap-3488	68	19	as	as	ADV
ap-3488	68	20	well	well	ADV
ap-3488	68	21	,	,	PUNCT
ap-3488	68	22	the	the	DET
ap-3488	68	23	graph	graph	NOUN
ap-3488	68	24	is	be	AUX
ap-3488	68	25	said	say	VERB
ap-3488	68	26	to	to	PART
ap-3488	68	27	be	be	AUX
ap-3488	68	28	undirected	undirected	ADJ
ap-3488	68	29	,	,	PUNCT
ap-3488	68	30	otherwise	otherwise	ADV
ap-3488	68	31	it	it	PRON
ap-3488	68	32	is	be	AUX
ap-3488	68	33	called	call	VERB
ap-3488	68	34	directed	direct	VERB
ap-3488	68	35	.	.	PUNCT
ap-3488	69	1	here	here	ADV
ap-3488	69	2	,	,	PUNCT
ap-3488	69	3	each	each	DET
ap-3488	69	4	node	node	PROPN
ap-3488	69	5	vi	vi	PROPN
ap-3488	69	6	in	in	ADP
ap-3488	69	7	v	v	NUM
ap-3488	69	8	corresponds	correspond	NOUN
ap-3488	69	9	to	to	ADP
ap-3488	69	10	a	a	DET
ap-3488	69	11	robot	robot	NOUN
ap-3488	69	12	-	-	PUNCT
ap-3488	69	13	i	i	PROPN
ap-3488	69	14	,	,	PUNCT
ap-3488	69	15	and	and	CCONJ
ap-3488	69	16	each	each	DET
ap-3488	69	17	edge	edge	NOUN
ap-3488	69	18	(	(	PUNCT
ap-3488	69	19	vi	vi	NOUN
ap-3488	69	20	,	,	PUNCT
ap-3488	69	21	vj	vj	ADJ
ap-3488	69	22	)	)	PUNCT
ap-3488	69	23	∈	∈	PROPN
ap-3488	69	24	e	e	NOUN
ap-3488	69	25	in	in	ADP
ap-3488	69	26	a	a	DET
ap-3488	69	27	directed	direct	VERB
ap-3488	69	28	graph	graph	NOUN
ap-3488	69	29	corresponds	correspond	VERB
ap-3488	69	30	to	to	ADP
ap-3488	69	31	an	an	DET
ap-3488	69	32	information	information	NOUN
ap-3488	69	33	link	link	NOUN
ap-3488	69	34	from	from	ADP
ap-3488	69	35	robot	robot	NOUN
ap-3488	69	36	-	-	PUNCT
ap-3488	69	37	i	i	PRON
ap-3488	69	38	to	to	ADP
ap-3488	69	39	robot	robot	NOUN
ap-3488	69	40	-	-	PUNCT
ap-3488	69	41	j	j	PROPN
ap-3488	69	42	,	,	PUNCT
ap-3488	69	43	which	which	PRON
ap-3488	69	44	means	mean	VERB
ap-3488	69	45	that	that	SCONJ
ap-3488	69	46	robot	robot	NOUN
ap-3488	69	47	-	-	PUNCT
ap-3488	69	48	j	j	PROPN
ap-3488	69	49	can	can	AUX
ap-3488	69	50	receive	receive	VERB
ap-3488	69	51	information	information	NOUN
ap-3488	69	52	from	from	ADP
ap-3488	69	53	robot	robot	NOUN
ap-3488	69	54	-	-	PUNCT
ap-3488	69	55	i.	i.	NOUN
ap-3488	69	56	in	in	ADP
ap-3488	69	57	contrast	contrast	NOUN
ap-3488	69	58	,	,	PUNCT
ap-3488	69	59	the	the	DET
ap-3488	69	60	pairs	pair	NOUN
ap-3488	69	61	of	of	ADP
ap-3488	69	62	nodes	node	NOUN
ap-3488	69	63	in	in	ADP
ap-3488	69	64	an	an	DET
ap-3488	69	65	undirected	undirected	ADJ
ap-3488	69	66	graph	graph	NOUN
ap-3488	69	67	are	be	AUX
ap-3488	69	68	unordered	unordered	ADJ
ap-3488	69	69	,	,	PUNCT
ap-3488	69	70	where	where	SCONJ
ap-3488	69	71	an	an	DET
ap-3488	69	72	edge	edge	NOUN
ap-3488	69	73	(	(	PUNCT
ap-3488	69	74	vi	vi	NOUN
ap-3488	69	75	,	,	PUNCT
ap-3488	69	76	vj	vj	ADJ
ap-3488	69	77	)	)	PUNCT
ap-3488	69	78	∈	∈	PROPN
ap-3488	69	79	e	e	NOUN
ap-3488	69	80	denotes	denote	VERB
ap-3488	69	81	that	that	SCONJ
ap-3488	69	82	each	each	DET
ap-3488	69	83	robot	robot	NOUN
ap-3488	69	84	can	can	AUX
ap-3488	69	85	communicate	communicate	VERB
ap-3488	69	86	with	with	ADP
ap-3488	69	87	the	the	DET
ap-3488	69	88	other	other	ADJ
ap-3488	69	89	one	one	NUM
ap-3488	69	90	.	.	PUNCT
ap-3488	70	1	the	the	DET
ap-3488	70	2	adjacency	adjacency	PROPN
ap-3488	70	3	matrix	matrix	NOUN
ap-3488	70	4	a	a	PRON
ap-3488	70	5	of	of	ADP
ap-3488	70	6	a	a	DET
ap-3488	70	7	digraph	digraph	NOUN
ap-3488	70	8	g	g	NOUN
ap-3488	70	9	is	be	AUX
ap-3488	70	10	represented	represent	VERB
ap-3488	70	11	as	as	ADP
ap-3488	70	12	a	a	DET
ap-3488	70	13	=	=	SYM
ap-3488	70	14			PROPN
ap-3488	70	15	a11	a11	PROPN
ap-3488	70	16	a12	a12	NOUN
ap-3488	70	17	·	·	PUNCT
ap-3488	70	18	·	·	PUNCT
ap-3488	70	19	·	·	PUNCT
ap-3488	71	1	a1n	a1n	ADP
ap-3488	71	2	a21	a21	PROPN
ap-3488	71	3	a22	a22	PROPN
ap-3488	71	4	·	·	PUNCT
ap-3488	71	5	·	·	PUNCT
ap-3488	71	6	·	·	PUNCT
ap-3488	71	7	a2n	a2n	PROPN
ap-3488	71	8	...	...	PUNCT
ap-3488	71	9	...	...	PUNCT
ap-3488	71	10	.	.	PUNCT
ap-3488	71	11	.	.	PUNCT
ap-3488	71	12	.	.	PUNCT
ap-3488	71	13	...	...	PUNCT
ap-3488	72	1	an1	an1	PROPN
ap-3488	73	1	an2	an2	PROPN
ap-3488	73	2	·	·	PUNCT
ap-3488	73	3	·	·	PUNCT
ap-3488	73	4	·	·	PUNCT
ap-3488	73	5	ann	ann	PROPN
ap-3488	73	6			PROPN
ap-3488	73	7	,	,	PUNCT
ap-3488	73	8	where	where	SCONJ
ap-3488	73	9	aij	aij	PROPN
ap-3488	73	10	is	be	AUX
ap-3488	73	11	the	the	DET
ap-3488	73	12	weight	weight	NOUN
ap-3488	73	13	of	of	ADP
ap-3488	73	14	link	link	NOUN
ap-3488	73	15	(	(	PUNCT
ap-3488	73	16	vi	vi	PROPN
ap-3488	73	17	,	,	PUNCT
ap-3488	73	18	vj	vj	ADJ
ap-3488	73	19	)	)	PUNCT
ap-3488	73	20	and	and	CCONJ
ap-3488	73	21	aii	aii	PROPN
ap-3488	73	22	=	=	SYM
ap-3488	73	23	0	0	NUM
ap-3488	74	1	for	for	ADP
ap-3488	74	2	any	any	DET
ap-3488	74	3	vi	vi	PROPN
ap-3488	74	4	∈	∈	PROPN
ap-3488	74	5	v	v	NOUN
ap-3488	74	6	,	,	PUNCT
ap-3488	74	7	aij	aij	PROPN
ap-3488	74	8	>	>	X
ap-3488	74	9	0	0	PUNCT
ap-3488	75	1	if	if	SCONJ
ap-3488	75	2	(	(	PUNCT
ap-3488	75	3	vi	vi	NOUN
ap-3488	75	4	,	,	PUNCT
ap-3488	75	5	vj	vj	ADJ
ap-3488	75	6	)	)	PUNCT
ap-3488	75	7	∈	∈	PROPN
ap-3488	75	8	e	e	NOUN
ap-3488	75	9	and	and	CCONJ
ap-3488	75	10	aij	aij	PROPN
ap-3488	75	11	=	=	SYM
ap-3488	75	12	0	0	NUM
ap-3488	75	13	otherwise	otherwise	ADV
ap-3488	75	14	.	.	PUNCT
ap-3488	76	1	a	a	PRON
ap-3488	76	2	of	of	ADP
ap-3488	76	3	a	a	DET
ap-3488	76	4	weighted	weight	VERB
ap-3488	76	5	undirected	undirected	ADJ
ap-3488	76	6	graph	graph	NOUN
ap-3488	76	7	is	be	AUX
ap-3488	76	8	defined	define	VERB
ap-3488	76	9	by	by	ADP
ap-3488	76	10	analogy	analogy	NOUN
ap-3488	76	11	,	,	PUNCT
ap-3488	76	12	except	except	SCONJ
ap-3488	76	13	that	that	PRON
ap-3488	76	14	aij	aij	PROPN
ap-3488	76	15	=	=	SYM
ap-3488	76	16	aji,∀i	aji,∀i	PROPN
ap-3488	76	17	6=	6=	PROPN
ap-3488	76	18	j	j	PROPN
ap-3488	77	1	[	[	X
ap-3488	77	2	16	16	NUM
ap-3488	77	3	]	]	PUNCT
ap-3488	77	4	.	.	PUNCT
ap-3488	78	1	a	a	DET
ap-3488	78	2	directed	direct	VERB
ap-3488	78	3	path	path	NOUN
ap-3488	78	4	from	from	ADP
ap-3488	78	5	node	node	PROPN
ap-3488	78	6	vi	vi	PROPN
ap-3488	78	7	to	to	ADP
ap-3488	78	8	vj	vj	PROPN
ap-3488	78	9	is	be	AUX
ap-3488	78	10	a	a	DET
ap-3488	78	11	sequence	sequence	NOUN
ap-3488	78	12	of	of	ADP
ap-3488	78	13	edges	edge	NOUN
ap-3488	78	14	(	(	PUNCT
ap-3488	78	15	vi	vi	ADJ
ap-3488	78	16	,	,	PUNCT
ap-3488	78	17	vj1	vj1	PROPN
ap-3488	78	18	)	)	PUNCT
ap-3488	78	19	,	,	PUNCT
ap-3488	78	20	(	(	PUNCT
ap-3488	78	21	vj1	vj1	PROPN
ap-3488	78	22	,	,	PUNCT
ap-3488	78	23	vj2	vj2	NUM
ap-3488	78	24	)	)	PUNCT
ap-3488	78	25	,	,	PUNCT
ap-3488	78	26	.	.	PUNCT
ap-3488	78	27	.	.	PUNCT
ap-3488	79	1	.	.	PUNCT
ap-3488	80	1	,	,	PUNCT
ap-3488	80	2	(	(	PUNCT
ap-3488	80	3	vjl	vjl	PROPN
ap-3488	80	4	,	,	PUNCT
ap-3488	80	5	vj	vj	INTJ
ap-3488	80	6	)	)	PUNCT
ap-3488	80	7	in	in	ADP
ap-3488	80	8	a	a	DET
ap-3488	80	9	directed	direct	VERB
ap-3488	80	10	graph	graph	NOUN
ap-3488	80	11	g	g	NOUN
ap-3488	80	12	with	with	ADP
ap-3488	80	13	distinct	distinct	ADJ
ap-3488	80	14	nodes	node	NOUN
ap-3488	80	15	vjk	vjk	NOUN
ap-3488	80	16	,	,	PUNCT
ap-3488	80	17	k	k	PROPN
ap-3488	80	18	=	=	SYM
ap-3488	80	19	1	1	NUM
ap-3488	80	20	,	,	PUNCT
ap-3488	80	21	.	.	PUNCT
ap-3488	80	22	.	.	PUNCT
ap-3488	81	1	.	.	PUNCT
ap-3488	82	1	,	,	PUNCT
ap-3488	82	2	l.	l.	PROPN
ap-3488	82	3	a	a	DET
ap-3488	82	4	directed	direct	VERB
ap-3488	82	5	graph	graph	NOUN
ap-3488	82	6	is	be	AUX
ap-3488	82	7	called	call	VERB
ap-3488	82	8	acyclic	acyclic	ADJ
ap-3488	82	9	if	if	SCONJ
ap-3488	82	10	it	it	PRON
ap-3488	82	11	contains	contain	VERB
ap-3488	82	12	no	no	DET
ap-3488	82	13	directed	direct	VERB
ap-3488	82	14	cycle	cycle	NOUN
ap-3488	82	15	.	.	PUNCT
ap-3488	83	1	a	a	DET
ap-3488	83	2	rooted	rooted	ADJ
ap-3488	83	3	graph	graph	NOUN
ap-3488	83	4	is	be	AUX
ap-3488	83	5	a	a	DET
ap-3488	83	6	graph	graph	NOUN
ap-3488	83	7	in	in	ADP
ap-3488	83	8	which	which	PRON
ap-3488	83	9	one	one	NUM
ap-3488	83	10	vertex	vertex	NOUN
ap-3488	83	11	is	be	AUX
ap-3488	83	12	distinguished	distinguish	VERB
ap-3488	83	13	as	as	ADP
ap-3488	83	14	the	the	DET
ap-3488	83	15	root	root	NOUN
ap-3488	83	16	.	.	PUNCT
ap-3488	84	1	2.4	2.4	NUM
ap-3488	84	2	.	.	PUNCT
ap-3488	85	1	problem	problem	NOUN
ap-3488	85	2	statement	statement	NOUN
ap-3488	85	3	a	a	DET
ap-3488	85	4	unicycle	unicycle	NOUN
ap-3488	85	5	-	-	PUNCT
ap-3488	85	6	type	type	NOUN
ap-3488	85	7	mobile	mobile	ADJ
ap-3488	85	8	robot	robot	NOUN
ap-3488	85	9	is	be	AUX
ap-3488	85	10	composed	compose	VERB
ap-3488	85	11	of	of	ADP
ap-3488	85	12	two	two	NUM
ap-3488	85	13	independent	independent	ADJ
ap-3488	85	14	actuated	actuate	VERB
ap-3488	85	15	wheels	wheel	NOUN
ap-3488	85	16	on	on	ADP
ap-3488	85	17	a	a	DET
ap-3488	85	18	common	common	ADJ
ap-3488	85	19	axle	axle	NOUN
ap-3488	85	20	which	which	PRON
ap-3488	85	21	is	be	AUX
ap-3488	85	22	rigidly	rigidly	ADV
ap-3488	85	23	linked	link	VERB
ap-3488	85	24	to	to	ADP
ap-3488	85	25	the	the	DET
ap-3488	85	26	robot	robot	NOUN
ap-3488	85	27	chassis	chassis	NOUN
ap-3488	85	28	.	.	PUNCT
ap-3488	86	1	in	in	ADP
ap-3488	86	2	addition	addition	NOUN
ap-3488	86	3	,	,	PUNCT
ap-3488	86	4	there	there	PRON
ap-3488	86	5	are	be	VERB
ap-3488	86	6	one	one	NUM
ap-3488	86	7	or	or	CCONJ
ap-3488	86	8	several	several	ADJ
ap-3488	86	9	passive	passive	ADJ
ap-3488	86	10	wheels	wheel	NOUN
ap-3488	86	11	(	(	PUNCT
ap-3488	86	12	for	for	ADP
ap-3488	86	13	example	example	NOUN
ap-3488	86	14	,	,	PUNCT
ap-3488	86	15	a	a	DET
ap-3488	86	16	caster	caster	NOUN
ap-3488	86	17	,	,	PUNCT
ap-3488	86	18	swedish	swedish	ADJ
ap-3488	86	19	or	or	CCONJ
ap-3488	86	20	spherical	spherical	ADJ
ap-3488	86	21	wheel	wheel	NOUN
ap-3488	86	22	)	)	PUNCT
ap-3488	86	23	which	which	PRON
ap-3488	86	24	are	be	AUX
ap-3488	86	25	not	not	PART
ap-3488	86	26	controlled	control	VERB
ap-3488	86	27	and	and	CCONJ
ap-3488	86	28	just	just	ADV
ap-3488	86	29	serve	serve	VERB
ap-3488	86	30	for	for	ADP
ap-3488	86	31	sustentation	sustentation	NOUN
ap-3488	86	32	purposes	purpose	NOUN
ap-3488	86	33	[	[	X
ap-3488	86	34	17	17	NUM
ap-3488	86	35	]	]	PUNCT
ap-3488	86	36	.	.	PUNCT
ap-3488	87	1	we	we	PRON
ap-3488	87	2	study	study	VERB
ap-3488	87	3	the	the	DET
ap-3488	87	4	formation	formation	NOUN
ap-3488	87	5	control	control	NOUN
ap-3488	87	6	problem	problem	NOUN
ap-3488	87	7	of	of	ADP
ap-3488	87	8	a	a	DET
ap-3488	87	9	group	group	NOUN
ap-3488	87	10	of	of	ADP
ap-3488	87	11	such	such	ADJ
ap-3488	87	12	robots	robot	NOUN
ap-3488	87	13	and	and	CCONJ
ap-3488	87	14	each	each	DET
ap-3488	87	15	one	one	NOUN
ap-3488	87	16	is	be	AUX
ap-3488	87	17	equipped	equip	VERB
ap-3488	87	18	with	with	ADP
ap-3488	87	19	a	a	DET
ap-3488	87	20	local	local	ADJ
ap-3488	87	21	controller	controller	NOUN
ap-3488	87	22	for	for	ADP
ap-3488	87	23	deciding	decide	VERB
ap-3488	87	24	the	the	DET
ap-3488	87	25	velocities	velocity	NOUN
ap-3488	87	26	.	.	PUNCT
ap-3488	88	1	we	we	PRON
ap-3488	88	2	consider	consider	VERB
ap-3488	88	3	each	each	DET
ap-3488	88	4	robot	robot	NOUN
ap-3488	88	5	as	as	ADP
ap-3488	88	6	a	a	DET
ap-3488	88	7	node	node	NOUN
ap-3488	88	8	of	of	ADP
ap-3488	88	9	a	a	DET
ap-3488	88	10	directed	direct	VERB
ap-3488	88	11	graph	graph	NOUN
ap-3488	88	12	g	g	NOUN
ap-3488	88	13	,	,	PUNCT
ap-3488	88	14	then	then	ADV
ap-3488	88	15	the	the	DET
ap-3488	88	16	communication	communication	NOUN
ap-3488	88	17	topology	topology	NOUN
ap-3488	88	18	of	of	ADP
ap-3488	88	19	a	a	DET
ap-3488	88	20	group	group	NOUN
ap-3488	88	21	of	of	ADP
ap-3488	88	22	n	n	PROPN
ap-3488	88	23	robots	robot	NOUN
ap-3488	88	24	could	could	AUX
ap-3488	88	25	be	be	AUX
ap-3488	88	26	expressed	express	VERB
ap-3488	88	27	by	by	ADP
ap-3488	88	28	an	an	DET
ap-3488	88	29	adjacency	adjacency	NOUN
ap-3488	88	30	matrix	matrix	NOUN
ap-3488	88	31	a	a	DET
ap-3488	88	32	=	=	SYM
ap-3488	88	33	(	(	PUNCT
ap-3488	88	34	aij)n×n	aij)n×n	NOUN
ap-3488	88	35	,	,	PUNCT
ap-3488	88	36	where	where	SCONJ
ap-3488	88	37	aii	aii	PROPN
ap-3488	88	38	=	=	SYM
ap-3488	88	39	0	0	PROPN
ap-3488	88	40	and	and	CCONJ
ap-3488	88	41	aij	aij	PROPN
ap-3488	88	42	=	=	SYM
ap-3488	88	43	1	1	NUM
ap-3488	88	44	if	if	SCONJ
ap-3488	88	45	(	(	PUNCT
ap-3488	88	46	vi	vi	NOUN
ap-3488	88	47	,	,	PUNCT
ap-3488	88	48	vj	vj	ADJ
ap-3488	88	49	)	)	PUNCT
ap-3488	88	50	∈	∈	PROPN
ap-3488	88	51	e	e	NOUN
ap-3488	88	52	or	or	CCONJ
ap-3488	88	53	0	0	NUM
ap-3488	88	54	otherwise	otherwise	ADV
ap-3488	88	55	.	.	PUNCT
ap-3488	89	1	the	the	DET
ap-3488	89	2	purpose	purpose	NOUN
ap-3488	89	3	is	be	AUX
ap-3488	89	4	to	to	PART
ap-3488	89	5	design	design	VERB
ap-3488	89	6	the	the	DET
ap-3488	89	7	strategy	strategy	NOUN
ap-3488	89	8	of	of	ADP
ap-3488	89	9	the	the	DET
ap-3488	89	10	control	control	NOUN
ap-3488	89	11	applied	apply	VERB
ap-3488	89	12	to	to	ADP
ap-3488	89	13	each	each	DET
ap-3488	89	14	robot	robot	NOUN
ap-3488	89	15	in	in	ADP
ap-3488	89	16	order	order	NOUN
ap-3488	89	17	that	that	SCONJ
ap-3488	89	18	this	this	DET
ap-3488	89	19	group	group	NOUN
ap-3488	89	20	of	of	ADP
ap-3488	89	21	mobile	mobile	ADJ
ap-3488	89	22	robots	robot	NOUN
ap-3488	89	23	could	could	AUX
ap-3488	89	24	execute	execute	VERB
ap-3488	89	25	a	a	DET
ap-3488	89	26	predefined	predefine	VERB
ap-3488	89	27	task	task	NOUN
ap-3488	89	28	of	of	ADP
ap-3488	89	29	formation	formation	NOUN
ap-3488	89	30	control	control	NOUN
ap-3488	89	31	.	.	PUNCT
ap-3488	90	1	2.5	2.5	NUM
ap-3488	90	2	.	.	PUNCT
ap-3488	91	1	kinematic	kinematic	ADJ
ap-3488	91	2	model	model	NOUN
ap-3488	91	3	on	on	ADP
ap-3488	91	4	a	a	DET
ap-3488	91	5	lie	lie	NOUN
ap-3488	91	6	group	group	NOUN
ap-3488	91	7	in	in	ADP
ap-3488	91	8	order	order	NOUN
ap-3488	91	9	to	to	PART
ap-3488	91	10	describe	describe	VERB
ap-3488	91	11	the	the	DET
ap-3488	91	12	kinematic	kinematic	ADJ
ap-3488	91	13	properties	property	NOUN
ap-3488	91	14	of	of	ADP
ap-3488	91	15	the	the	DET
ap-3488	91	16	unicycle	unicycle	NOUN
ap-3488	91	17	-	-	PUNCT
ap-3488	91	18	type	type	NOUN
ap-3488	91	19	robot	robot	NOUN
ap-3488	91	20	,	,	PUNCT
ap-3488	91	21	we	we	PRON
ap-3488	91	22	consider	consider	VERB
ap-3488	91	23	a	a	DET
ap-3488	91	24	reference	reference	NOUN
ap-3488	91	25	point	point	NOUN
ap-3488	91	26	or	or	CCONJ
ap-3488	91	27	at	at	ADP
ap-3488	91	28	the	the	DET
ap-3488	91	29	mid	mid	NOUN
ap-3488	91	30	-	-	NOUN
ap-3488	91	31	distance	distance	NOUN
ap-3488	91	32	of	of	ADP
ap-3488	91	33	the	the	DET
ap-3488	91	34	two	two	NUM
ap-3488	91	35	actuated	actuate	VERB
ap-3488	91	36	wheels	wheel	NOUN
ap-3488	91	37	.	.	PUNCT
ap-3488	92	1	then	then	ADV
ap-3488	92	2	we	we	PRON
ap-3488	92	3	define	define	VERB
ap-3488	92	4	two	two	NUM
ap-3488	92	5	frames	frame	NOUN
ap-3488	92	6	:	:	PUNCT
ap-3488	92	7	fi	fi	NOUN
ap-3488	92	8	=	=	PUNCT
ap-3488	92	9	{	{	PUNCT
ap-3488	92	10	o	o	NOUN
ap-3488	92	11	,	,	PUNCT
ap-3488	92	12	x	x	PROPN
ap-3488	92	13	,	,	PUNCT
ap-3488	92	14	y	y	PROPN
ap-3488	92	15	}	}	PUNCT
ap-3488	92	16	and	and	CCONJ
ap-3488	92	17	fr	fr	NOUN
ap-3488	92	18	=	=	PUNCT
ap-3488	92	19	{	{	PUNCT
ap-3488	92	20	or	or	CCONJ
ap-3488	92	21	,	,	PUNCT
ap-3488	92	22	xr	xr	PROPN
ap-3488	92	23	,	,	PUNCT
ap-3488	92	24	yr	yr	NOUN
ap-3488	92	25	}	}	PUNCT
ap-3488	92	26	,	,	PUNCT
ap-3488	92	27	as	as	SCONJ
ap-3488	92	28	shown	show	VERB
ap-3488	92	29	in	in	ADP
ap-3488	92	30	figure	figure	NOUN
ap-3488	92	31	1	1	NUM
ap-3488	92	32	.	.	PUNCT
ap-3488	92	33	fi	fi	NOUN
ap-3488	92	34	=	=	PUNCT
ap-3488	92	35	{	{	PUNCT
ap-3488	92	36	o	o	NOUN
ap-3488	92	37	,	,	PUNCT
ap-3488	92	38	x	x	X
ap-3488	92	39	,	,	PUNCT
ap-3488	92	40	y	y	PROPN
ap-3488	92	41	}	}	PUNCT
ap-3488	92	42	is	be	AUX
ap-3488	92	43	an	an	DET
ap-3488	92	44	arbitrary	arbitrary	ADJ
ap-3488	92	45	inertial	inertial	ADJ
ap-3488	92	46	basis	basis	NOUN
ap-3488	92	47	on	on	ADP
ap-3488	92	48	the	the	DET
ap-3488	92	49	plane	plane	NOUN
ap-3488	92	50	as	as	ADP
ap-3488	92	51	the	the	DET
ap-3488	92	52	global	global	ADJ
ap-3488	92	53	reference	reference	NOUN
ap-3488	92	54	frame	frame	NOUN
ap-3488	92	55	and	and	CCONJ
ap-3488	92	56	fr	fr	NOUN
ap-3488	92	57	=	=	PUNCT
ap-3488	92	58	{	{	PUNCT
ap-3488	92	59	or	or	CCONJ
ap-3488	92	60	,	,	PUNCT
ap-3488	92	61	xr	xr	PROPN
ap-3488	92	62	,	,	PUNCT
ap-3488	92	63	yr	yr	NOUN
ap-3488	92	64	}	}	PUNCT
ap-3488	92	65	is	be	AUX
ap-3488	92	66	a	a	DET
ap-3488	92	67	frame	frame	NOUN
ap-3488	92	68	attached	attach	VERB
ap-3488	92	69	to	to	ADP
ap-3488	92	70	the	the	DET
ap-3488	92	71	mobile	mobile	ADJ
ap-3488	92	72	robot	robot	NOUN
ap-3488	92	73	with	with	ADP
ap-3488	92	74	its	its	PRON
ap-3488	92	75	origin	origin	NOUN
ap-3488	92	76	located	locate	VERB
ap-3488	92	77	at	at	ADP
ap-3488	92	78	or	or	CCONJ
ap-3488	92	79	,	,	PUNCT
ap-3488	92	80	and	and	CCONJ
ap-3488	92	81	the	the	DET
ap-3488	92	82	basis	basis	NOUN
ap-3488	92	83	{	{	PUNCT
ap-3488	92	84	xr	xr	PROPN
ap-3488	92	85	,	,	PUNCT
ap-3488	92	86	yr	yr	NOUN
ap-3488	92	87	}	}	PUNCT
ap-3488	92	88	defines	define	VERB
ap-3488	92	89	two	two	NUM
ap-3488	92	90	axes	axis	NOUN
ap-3488	92	91	relative	relative	ADJ
ap-3488	92	92	to	to	ADP
ap-3488	92	93	or	or	CCONJ
ap-3488	92	94	on	on	ADP
ap-3488	92	95	the	the	DET
ap-3488	92	96	robot	robot	NOUN
ap-3488	92	97	chassis	chassis	NOUN
ap-3488	92	98	and	and	CCONJ
ap-3488	92	99	is	be	AUX
ap-3488	92	100	thus	thus	ADV
ap-3488	92	101	the	the	DET
ap-3488	92	102	robot	robot	NOUN
ap-3488	92	103	’s	’s	PART
ap-3488	92	104	local	local	ADJ
ap-3488	92	105	reference	reference	NOUN
ap-3488	92	106	frame	frame	NOUN
ap-3488	92	107	.	.	PUNCT
ap-3488	93	1	the	the	DET
ap-3488	93	2	position	position	NOUN
ap-3488	93	3	of	of	ADP
ap-3488	93	4	the	the	DET
ap-3488	93	5	robot	robot	NOUN
ap-3488	93	6	in	in	ADP
ap-3488	93	7	the	the	DET
ap-3488	93	8	global	global	ADJ
ap-3488	93	9	reference	reference	NOUN
ap-3488	93	10	is	be	AUX
ap-3488	93	11	specified	specify	VERB
ap-3488	93	12	by	by	ADP
ap-3488	93	13	coordinates	coordinate	NOUN
ap-3488	93	14	xi	xi	X
ap-3488	93	15	and	and	CCONJ
ap-3488	93	16	yi	yi	PROPN
ap-3488	93	17	,	,	PUNCT
ap-3488	93	18	and	and	CCONJ
ap-3488	93	19	the	the	DET
ap-3488	93	20	angular	angular	ADJ
ap-3488	93	21	difference	difference	NOUN
ap-3488	93	22	between	between	ADP
ap-3488	93	23	the	the	DET
ap-3488	93	24	global	global	ADJ
ap-3488	93	25	and	and	CCONJ
ap-3488	93	26	local	local	ADJ
ap-3488	93	27	reference	reference	NOUN
ap-3488	93	28	frames	frame	NOUN
ap-3488	93	29	is	be	AUX
ap-3488	93	30	given	give	VERB
ap-3488	93	31	by	by	ADP
ap-3488	93	32	θi	θi	PRON
ap-3488	93	33	.	.	PUNCT
ap-3488	94	1	then	then	ADV
ap-3488	94	2	the	the	DET
ap-3488	94	3	pose	pose	NOUN
ap-3488	94	4	of	of	ADP
ap-3488	94	5	the	the	DET
ap-3488	94	6	robot	robot	NOUN
ap-3488	94	7	could	could	AUX
ap-3488	94	8	be	be	AUX
ap-3488	94	9	described	describe	VERB
ap-3488	94	10	as	as	ADP
ap-3488	94	11	an	an	DET
ap-3488	94	12	element	element	NOUN
ap-3488	94	13	of	of	ADP
ap-3488	94	14	the	the	DET
ap-3488	94	15	lie	lie	NOUN
ap-3488	94	16	group	group	NOUN
ap-3488	94	17	se(2	se(2	PROPN
ap-3488	94	18	):	):	PUNCT
ap-3488	94	19	g	g	PROPN
ap-3488	94	20	=	=	PUNCT
ap-3488	94	21	[	[	PUNCT
ap-3488	94	22	r	r	NOUN
ap-3488	94	23	p	p	NOUN
ap-3488	94	24	0	0	NUM
ap-3488	94	25	1	1	NUM
ap-3488	94	26	]	]	PUNCT
ap-3488	94	27	=	=	SYM
ap-3488	94	28	cos	cos	PROPN
ap-3488	94	29	θi	θi	ADP
ap-3488	94	30	−	−	PROPN
ap-3488	94	31	sin	sin	PROPN
ap-3488	94	32	θi	θi	ADP
ap-3488	94	33	xi	xi	PROPN
ap-3488	94	34	sin	sin	PROPN
ap-3488	94	35	θi	θi	PROPN
ap-3488	94	36	cos	cos	PROPN
ap-3488	94	37	θi	θi	PROPN
ap-3488	94	38	yi	yi	PROPN
ap-3488	94	39	0	0	NUM
ap-3488	94	40	0	0	NUM
ap-3488	94	41	1	1	NUM
ap-3488	94	42			NOUN
ap-3488	94	43	,	,	PUNCT
ap-3488	94	44	where	where	SCONJ
ap-3488	94	45	p	p	NOUN
ap-3488	95	1	=	=	X
ap-3488	96	1	[	[	X
ap-3488	96	2	xi	xi	X
ap-3488	96	3	,	,	PUNCT
ap-3488	96	4	yi	yi	PROPN
ap-3488	96	5	]	]	PUNCT
ap-3488	96	6	t	t	PROPN
ap-3488	96	7	denotes	denote	VERB
ap-3488	96	8	the	the	DET
ap-3488	96	9	position	position	NOUN
ap-3488	96	10	of	of	ADP
ap-3488	96	11	the	the	DET
ap-3488	96	12	robot	robot	NOUN
ap-3488	96	13	in	in	ADP
ap-3488	96	14	the	the	DET
ap-3488	96	15	global	global	ADJ
ap-3488	96	16	reference	reference	NOUN
ap-3488	96	17	frame	frame	NOUN
ap-3488	96	18	,	,	PUNCT
ap-3488	96	19	and	and	CCONJ
ap-3488	96	20	r	r	NOUN
ap-3488	96	21	=	=	SYM
ap-3488	96	22	[	[	PUNCT
ap-3488	96	23	cos	cos	PROPN
ap-3488	96	24	θi	θi	PROPN
ap-3488	96	25	−	−	PROPN
ap-3488	96	26	sin	sin	NOUN
ap-3488	96	27	θi	θi	ADP
ap-3488	96	28	sin	sin	PROPN
ap-3488	96	29	θi	θi	PROPN
ap-3488	96	30	cos	cos	PROPN
ap-3488	96	31	θi	θi	PROPN
ap-3488	96	32	]	]	PUNCT
ap-3488	96	33	is	be	AUX
ap-3488	96	34	the	the	DET
ap-3488	96	35	rotation	rotation	NOUN
ap-3488	96	36	matrix	matrix	NOUN
ap-3488	96	37	of	of	ADP
ap-3488	96	38	the	the	DET
ap-3488	96	39	frame	frame	NOUN
ap-3488	96	40	fr	fr	PROPN
ap-3488	96	41	relative	relative	ADJ
ap-3488	96	42	to	to	ADP
ap-3488	96	43	frame	frame	NOUN
ap-3488	96	44	fi	fi	NOUN
ap-3488	96	45	.	.	PUNCT
ap-3488	97	1	then	then	ADV
ap-3488	97	2	the	the	DET
ap-3488	97	3	motion	motion	NOUN
ap-3488	97	4	of	of	ADP
ap-3488	97	5	a	a	DET
ap-3488	97	6	robot	robot	NOUN
ap-3488	97	7	could	could	AUX
ap-3488	97	8	be	be	AUX
ap-3488	97	9	described	describe	VERB
ap-3488	97	10	by	by	ADP
ap-3488	97	11	g(t	g(t	PROPN
ap-3488	97	12	)	)	PUNCT
ap-3488	97	13	,	,	PUNCT
ap-3488	97	14	which	which	PRON
ap-3488	97	15	is	be	AUX
ap-3488	97	16	a	a	DET
ap-3488	97	17	curve	curve	NOUN
ap-3488	97	18	parameterized	parameterize	VERB
ap-3488	97	19	by	by	ADP
ap-3488	97	20	time	time	NOUN
ap-3488	97	21	t	t	PROPN
ap-3488	97	22	in	in	ADP
ap-3488	97	23	se(2	se(2	PROPN
ap-3488	97	24	)	)	PUNCT
ap-3488	97	25	.	.	PUNCT
ap-3488	98	1	2	2	NUM
ap-3488	98	2	vol	vol	NOUN
ap-3488	98	3	.	.	PUNCT
ap-3488	99	1	56	56	NUM
ap-3488	99	2	no	no	NOUN
ap-3488	99	3	.	.	PUNCT
ap-3488	100	1	1/2016	1/2016	NUM
ap-3488	100	2	formation	formation	NOUN
ap-3488	100	3	control	control	NOUN
ap-3488	100	4	of	of	ADP
ap-3488	100	5	multiple	multiple	ADJ
ap-3488	100	6	unicycle	unicycle	NOUN
ap-3488	100	7	-	-	PUNCT
ap-3488	100	8	type	type	NOUN
ap-3488	100	9	robots	robot	NOUN
ap-3488	100	10	using	use	VERB
ap-3488	100	11	lie	lie	NOUN
ap-3488	100	12	group	group	NOUN
ap-3488	100	13	x	x	PROPN
ap-3488	101	1	y	y	PROPN
ap-3488	101	2	xryr	xryr	PROPN
ap-3488	101	3	θ	θ	PROPN
ap-3488	102	1	ω2	ω2	PROPN
ap-3488	102	2	ω	ω	NUM
ap-3488	102	3	u	u	NOUN
ap-3488	102	4	o	o	NOUN
ap-3488	102	5	or	or	CCONJ
ap-3488	102	6	ω1	ω1	ADJ
ap-3488	102	7	figure	figure	NOUN
ap-3488	102	8	1	1	NUM
ap-3488	102	9	.	.	PUNCT
ap-3488	103	1	representation	representation	NOUN
ap-3488	103	2	of	of	ADP
ap-3488	103	3	the	the	DET
ap-3488	103	4	frames	frame	NOUN
ap-3488	103	5	.	.	PUNCT
ap-3488	104	1	each	each	DET
ap-3488	104	2	pure	pure	ADJ
ap-3488	104	3	rotational	rotational	ADJ
ap-3488	104	4	motion	motion	NOUN
ap-3488	104	5	of	of	ADP
ap-3488	104	6	a	a	DET
ap-3488	104	7	robot	robot	NOUN
ap-3488	104	8	on	on	ADP
ap-3488	104	9	a	a	DET
ap-3488	104	10	plane	plane	NOUN
ap-3488	104	11	can	can	AUX
ap-3488	104	12	be	be	AUX
ap-3488	104	13	given	give	VERB
ap-3488	104	14	by	by	ADP
ap-3488	104	15	a	a	DET
ap-3488	104	16	2×	2×	NUM
ap-3488	104	17	2	2	NUM
ap-3488	104	18	orthogonal	orthogonal	ADJ
ap-3488	104	19	matrix	matrix	NOUN
ap-3488	104	20	r	r	NOUN
ap-3488	104	21	∈	∈	PROPN
ap-3488	104	22	so(2	so(2	NOUN
ap-3488	104	23	)	)	PUNCT
ap-3488	104	24	.	.	PUNCT
ap-3488	105	1	let	let	VERB
ap-3488	105	2	ω	ω	NUM
ap-3488	105	3	∈	∈	VERB
ap-3488	105	4	r	r	NOUN
ap-3488	105	5	be	be	VERB
ap-3488	105	6	the	the	DET
ap-3488	105	7	rotation	rotation	NOUN
ap-3488	105	8	velocity	velocity	NOUN
ap-3488	105	9	of	of	ADP
ap-3488	105	10	the	the	DET
ap-3488	105	11	robot	robot	NOUN
ap-3488	105	12	’s	’s	PART
ap-3488	105	13	chassis	chassis	NOUN
ap-3488	105	14	and	and	CCONJ
ap-3488	105	15	then	then	ADV
ap-3488	105	16	the	the	DET
ap-3488	105	17	exponential	exponential	ADJ
ap-3488	105	18	map	map	NOUN
ap-3488	105	19	exp	exp	NOUN
ap-3488	105	20	:	:	PUNCT
ap-3488	105	21	so(2)→	so(2)→	VERB
ap-3488	105	22	so(2	so(2	NOUN
ap-3488	105	23	)	)	PUNCT
ap-3488	105	24	,	,	PUNCT
ap-3488	105	25	ω̂	ω̂	PUNCT
ap-3488	105	26	→	→	SYM
ap-3488	105	27	exp(ω̂t	exp(ω̂t	PROPN
ap-3488	105	28	)	)	PUNCT
ap-3488	105	29	which	which	PRON
ap-3488	105	30	is	be	AUX
ap-3488	105	31	defined	define	VERB
ap-3488	105	32	by	by	ADP
ap-3488	105	33	equation	equation	NOUN
ap-3488	105	34	1	1	NUM
ap-3488	105	35	where	where	SCONJ
ap-3488	105	36	ω̂	ω̂	VERB
ap-3488	105	37	=	=	PUNCT
ap-3488	106	1	[	[	PUNCT
ap-3488	106	2	0	0	NUM
ap-3488	106	3	−ω	−ω	PROPN
ap-3488	106	4	ω	ω	PROPN
ap-3488	106	5	0	0	PUNCT
ap-3488	106	6	]	]	PUNCT
ap-3488	106	7	∈	∈	PROPN
ap-3488	106	8	so(2	so(2	NOUN
ap-3488	106	9	)	)	PUNCT
ap-3488	106	10	correspond	correspond	NOUN
ap-3488	106	11	to	to	ADP
ap-3488	106	12	the	the	DET
ap-3488	106	13	robot	robot	NOUN
ap-3488	106	14	chassis	chassis	NOUN
ap-3488	106	15	rotation	rotation	NOUN
ap-3488	106	16	.	.	PUNCT
ap-3488	107	1	this	this	DET
ap-3488	107	2	map	map	NOUN
ap-3488	107	3	represents	represent	VERB
ap-3488	107	4	the	the	DET
ap-3488	107	5	rotation	rotation	NOUN
ap-3488	107	6	from	from	ADP
ap-3488	107	7	the	the	DET
ap-3488	107	8	initial	initial	NOUN
ap-3488	107	9	(	(	PUNCT
ap-3488	107	10	t	t	NOUN
ap-3488	107	11	=	=	SYM
ap-3488	107	12	0	0	NUM
ap-3488	107	13	)	)	PUNCT
ap-3488	107	14	configuration	configuration	NOUN
ap-3488	107	15	of	of	ADP
ap-3488	107	16	the	the	DET
ap-3488	107	17	robot	robot	NOUN
ap-3488	107	18	to	to	ADP
ap-3488	107	19	its	its	PRON
ap-3488	107	20	final	final	ADJ
ap-3488	107	21	configuration	configuration	NOUN
ap-3488	107	22	with	with	ADP
ap-3488	107	23	the	the	DET
ap-3488	107	24	rotation	rotation	NOUN
ap-3488	107	25	velocity	velocity	NOUN
ap-3488	107	26	ω	ω	NOUN
ap-3488	107	27	.	.	PUNCT
ap-3488	108	1	the	the	DET
ap-3488	108	2	rigid	rigid	ADJ
ap-3488	108	3	motions	motion	NOUN
ap-3488	108	4	consist	consist	VERB
ap-3488	108	5	of	of	ADP
ap-3488	108	6	rotation	rotation	NOUN
ap-3488	108	7	and	and	CCONJ
ap-3488	108	8	translation	translation	NOUN
ap-3488	108	9	.	.	PUNCT
ap-3488	109	1	a	a	DET
ap-3488	109	2	general	general	ADJ
ap-3488	109	3	motion	motion	NOUN
ap-3488	109	4	could	could	AUX
ap-3488	109	5	also	also	ADV
ap-3488	109	6	be	be	AUX
ap-3488	109	7	described	describe	VERB
ap-3488	109	8	by	by	ADP
ap-3488	109	9	an	an	DET
ap-3488	109	10	exponential	exponential	ADJ
ap-3488	109	11	map	map	NOUN
ap-3488	109	12	exp	exp	NOUN
ap-3488	109	13	:	:	PUNCT
ap-3488	109	14	se(2	se(2	NOUN
ap-3488	109	15	)	)	PUNCT
ap-3488	109	16	→	→	SYM
ap-3488	109	17	se(2	se(2	NOUN
ap-3488	109	18	)	)	PUNCT
ap-3488	109	19	,	,	PUNCT
ap-3488	109	20	ξ̂	ξ̂	NUM
ap-3488	109	21	→	→	SYM
ap-3488	109	22	exp(ξ̂t	exp(ξ̂t	PROPN
ap-3488	109	23	)	)	PUNCT
ap-3488	109	24	defined	define	VERB
ap-3488	109	25	in	in	ADP
ap-3488	109	26	equation	equation	NOUN
ap-3488	109	27	2	2	NUM
ap-3488	109	28	,	,	PUNCT
ap-3488	110	1	where	where	SCONJ
ap-3488	110	2	ξ̂	ξ̂	NOUN
ap-3488	110	3	=	=	SYM
ap-3488	110	4	[	[	PUNCT
ap-3488	110	5	ω̂	ω̂	NUM
ap-3488	110	6	v	v	NOUN
ap-3488	110	7	0	0	NUM
ap-3488	110	8	0	0	NUM
ap-3488	110	9	]	]	PUNCT
ap-3488	110	10	∈	∈	PROPN
ap-3488	110	11	se(2	se(2	NOUN
ap-3488	110	12	)	)	PUNCT
ap-3488	110	13	represents	represent	VERB
ap-3488	110	14	the	the	DET
ap-3488	110	15	velocities	velocity	NOUN
ap-3488	110	16	of	of	ADP
ap-3488	110	17	movement	movement	NOUN
ap-3488	110	18	,	,	PUNCT
ap-3488	110	19	and	and	CCONJ
ap-3488	110	20	v	v	X
ap-3488	110	21	=	=	SYM
ap-3488	110	22	−ω̂p+	−ω̂p+	NUM
ap-3488	110	23	ṗ	ṗ	ADJ
ap-3488	110	24	=[	=[	NOUN
ap-3488	110	25	ωyi	ωyi	NOUN
ap-3488	110	26	+	+	CCONJ
ap-3488	110	27	ẋi	ẋi	PROPN
ap-3488	110	28	−ωxi	−ωxi	VERB
ap-3488	111	1	+	+	X
ap-3488	111	2	ẏi	ẏi	NOUN
ap-3488	111	3	]	]	PUNCT
ap-3488	111	4	where	where	SCONJ
ap-3488	111	5	(	(	PUNCT
ap-3488	111	6	xi	xi	PROPN
ap-3488	111	7	,	,	PUNCT
ap-3488	111	8	yi	yi	PROPN
ap-3488	111	9	)	)	PUNCT
ap-3488	111	10	is	be	AUX
ap-3488	111	11	the	the	DET
ap-3488	111	12	position	position	NOUN
ap-3488	111	13	of	of	ADP
ap-3488	111	14	the	the	DET
ap-3488	111	15	robot	robot	NOUN
ap-3488	111	16	and	and	CCONJ
ap-3488	111	17	v	v	NOUN
ap-3488	111	18	represents	represent	VERB
ap-3488	111	19	the	the	DET
ap-3488	111	20	velocity	velocity	NOUN
ap-3488	111	21	of	of	ADP
ap-3488	111	22	a	a	DET
ap-3488	111	23	(	(	PUNCT
ap-3488	111	24	possibly	possibly	ADV
ap-3488	111	25	imaginary	imaginary	ADJ
ap-3488	111	26	)	)	PUNCT
ap-3488	111	27	point	point	NOUN
ap-3488	111	28	on	on	ADP
ap-3488	111	29	the	the	DET
ap-3488	111	30	rigid	rigid	ADJ
ap-3488	111	31	body	body	NOUN
ap-3488	111	32	which	which	PRON
ap-3488	111	33	is	be	AUX
ap-3488	111	34	moving	move	VERB
ap-3488	111	35	through	through	ADP
ap-3488	111	36	the	the	DET
ap-3488	111	37	origin	origin	NOUN
ap-3488	111	38	of	of	ADP
ap-3488	111	39	the	the	DET
ap-3488	111	40	world	world	NOUN
ap-3488	111	41	frame	frame	NOUN
ap-3488	111	42	.	.	PUNCT
ap-3488	112	1	exp(ξ̂t	exp(ξ̂t	PROPN
ap-3488	112	2	)	)	PUNCT
ap-3488	112	3	is	be	AUX
ap-3488	112	4	a	a	DET
ap-3488	112	5	mapping	mapping	NOUN
ap-3488	112	6	from	from	ADP
ap-3488	112	7	the	the	DET
ap-3488	112	8	initial	initial	ADJ
ap-3488	112	9	configuration	configuration	NOUN
ap-3488	112	10	of	of	ADP
ap-3488	112	11	the	the	DET
ap-3488	112	12	robot	robot	NOUN
ap-3488	112	13	to	to	ADP
ap-3488	112	14	its	its	PRON
ap-3488	112	15	final	final	ADJ
ap-3488	112	16	configuration	configuration	NOUN
ap-3488	112	17	.	.	PUNCT
ap-3488	113	1	that	that	PRON
ap-3488	113	2	is	be	AUX
ap-3488	113	3	,	,	PUNCT
ap-3488	113	4	if	if	SCONJ
ap-3488	113	5	we	we	PRON
ap-3488	113	6	suppose	suppose	VERB
ap-3488	113	7	that	that	SCONJ
ap-3488	113	8	the	the	DET
ap-3488	113	9	initial	initial	ADJ
ap-3488	113	10	configuration	configuration	NOUN
ap-3488	113	11	of	of	ADP
ap-3488	113	12	the	the	DET
ap-3488	113	13	robot	robot	NOUN
ap-3488	113	14	is	be	AUX
ap-3488	113	15	g(0	g(0	NOUN
ap-3488	113	16	)	)	PUNCT
ap-3488	113	17	,	,	PUNCT
ap-3488	113	18	then	then	ADV
ap-3488	113	19	the	the	DET
ap-3488	113	20	final	final	ADJ
ap-3488	113	21	configuration	configuration	NOUN
ap-3488	113	22	is	be	AUX
ap-3488	113	23	given	give	VERB
ap-3488	113	24	by	by	ADP
ap-3488	113	25	g(t	g(t	PROPN
ap-3488	113	26	)	)	PUNCT
ap-3488	113	27	=	=	SYM
ap-3488	113	28	eξ̂tg(0	eξ̂tg(0	NOUN
ap-3488	113	29	)	)	PUNCT
ap-3488	113	30	.	.	PUNCT
ap-3488	114	1	(	(	PUNCT
ap-3488	114	2	3	3	X
ap-3488	114	3	)	)	PUNCT
ap-3488	114	4	the	the	DET
ap-3488	114	5	kinematic	kinematic	ADJ
ap-3488	114	6	model	model	NOUN
ap-3488	114	7	of	of	ADP
ap-3488	114	8	the	the	DET
ap-3488	114	9	unicycle	unicycle	NOUN
ap-3488	114	10	-	-	PUNCT
ap-3488	114	11	type	type	NOUN
ap-3488	114	12	robot	robot	NOUN
ap-3488	114	13	is	be	AUX
ap-3488	114	14	given	give	VERB
ap-3488	114	15	by	by	ADP
ap-3488	114	16			PRON
ap-3488	114	17	ẋi	ẋi	PUNCT
ap-3488	115	1	=	=	SYM
ap-3488	115	2	u	u	PROPN
ap-3488	115	3	cos	cos	PROPN
ap-3488	115	4	θi	θi	PROPN
ap-3488	115	5	,	,	PUNCT
ap-3488	115	6	ẏi	ẏi	NOUN
ap-3488	115	7	=	=	SYM
ap-3488	115	8	u	u	PROPN
ap-3488	115	9	sin	sin	NOUN
ap-3488	115	10	θi	θi	PROPN
ap-3488	115	11	,	,	PUNCT
ap-3488	115	12	θ̇i	θ̇i	PROPN
ap-3488	115	13	=	=	SYM
ap-3488	115	14	ω	ω	PROPN
ap-3488	115	15	,	,	PUNCT
ap-3488	115	16	where	where	SCONJ
ap-3488	115	17	u	u	NOUN
ap-3488	115	18	characterizes	characterize	VERB
ap-3488	115	19	the	the	DET
ap-3488	115	20	robot	robot	NOUN
ap-3488	115	21	’s	’s	PART
ap-3488	115	22	longitudinal	longitudinal	ADJ
ap-3488	115	23	velocity	velocity	NOUN
ap-3488	115	24	.	.	PUNCT
ap-3488	116	1	the	the	DET
ap-3488	116	2	variables	variables	PROPN
ap-3488	116	3	u	u	PROPN
ap-3488	116	4	and	and	CCONJ
ap-3488	116	5	ω	ω	NUM
ap-3488	116	6	are	be	AUX
ap-3488	116	7	related	relate	VERB
ap-3488	116	8	to	to	ADP
ap-3488	116	9	the	the	DET
ap-3488	116	10	angular	angular	ADJ
ap-3488	116	11	velocity	velocity	NOUN
ap-3488	116	12	of	of	ADP
ap-3488	116	13	the	the	DET
ap-3488	116	14	actuated	actuate	VERB
ap-3488	116	15	wheels	wheel	NOUN
ap-3488	116	16	via	via	ADP
ap-3488	116	17	the	the	DET
ap-3488	116	18	one	one	NUM
ap-3488	116	19	-	-	PUNCT
ap-3488	116	20	to	to	ADP
ap-3488	116	21	-	-	PUNCT
ap-3488	116	22	one	one	NUM
ap-3488	116	23	transformation	transformation	NOUN
ap-3488	116	24	:	:	PUNCT
ap-3488	116	25	[	[	PUNCT
ap-3488	116	26	u	u	X
ap-3488	116	27	ω	ω	X
ap-3488	116	28	]	]	PUNCT
ap-3488	116	29	=	=	PUNCT
ap-3488	117	1	[	[	PUNCT
ap-3488	117	2	rw/2	rw/2	NOUN
ap-3488	117	3	rw/2	rw/2	NOUN
ap-3488	117	4	rw	rw	NOUN
ap-3488	117	5	/	/	SYM
ap-3488	117	6	l	l	NOUN
ap-3488	117	7	−rw	−rw	PROPN
ap-3488	117	8	/	/	SYM
ap-3488	117	9	l	l	NOUN
ap-3488	117	10	]	]	PUNCT
ap-3488	117	11	[	[	PUNCT
ap-3488	117	12	ω1	ω1	PROPN
ap-3488	117	13	ω2	ω2	PROPN
ap-3488	117	14	]	]	X
ap-3488	117	15	(	(	PUNCT
ap-3488	117	16	4	4	X
ap-3488	117	17	)	)	PUNCT
ap-3488	117	18	where	where	SCONJ
ap-3488	117	19	rw	rw	PROPN
ap-3488	117	20	is	be	AUX
ap-3488	117	21	the	the	DET
ap-3488	117	22	wheels	wheel	NOUN
ap-3488	117	23	’	'	PUNCT
ap-3488	117	24	radius	radius	NOUN
ap-3488	117	25	,	,	PUNCT
ap-3488	117	26	l	l	PROPN
ap-3488	117	27	is	be	AUX
ap-3488	117	28	the	the	DET
ap-3488	117	29	distance	distance	NOUN
ap-3488	117	30	between	between	ADP
ap-3488	117	31	the	the	DET
ap-3488	117	32	two	two	NUM
ap-3488	117	33	actuated	actuate	VERB
ap-3488	117	34	wheels	wheel	NOUN
ap-3488	117	35	,	,	PUNCT
ap-3488	117	36	and	and	CCONJ
ap-3488	117	37	ω1	ω1	PROPN
ap-3488	117	38	and	and	CCONJ
ap-3488	117	39	ω2	ω2	NOUN
ap-3488	117	40	are	be	AUX
ap-3488	117	41	respectively	respectively	ADV
ap-3488	117	42	the	the	DET
ap-3488	117	43	angular	angular	ADJ
ap-3488	117	44	velocity	velocity	NOUN
ap-3488	117	45	of	of	ADP
ap-3488	117	46	the	the	DET
ap-3488	117	47	right	right	ADJ
ap-3488	117	48	wheel	wheel	NOUN
ap-3488	117	49	and	and	CCONJ
ap-3488	117	50	the	the	DET
ap-3488	117	51	left	left	ADJ
ap-3488	117	52	wheel	wheel	NOUN
ap-3488	117	53	.	.	PUNCT
ap-3488	118	1	we	we	PRON
ap-3488	118	2	differentiate	differentiate	VERB
ap-3488	118	3	the	the	DET
ap-3488	118	4	matrix	matrix	NOUN
ap-3488	118	5	given	give	VERB
ap-3488	118	6	in	in	ADP
ap-3488	118	7	equation	equation	NOUN
ap-3488	118	8	3	3	NUM
ap-3488	118	9	,	,	PUNCT
ap-3488	118	10	and	and	CCONJ
ap-3488	118	11	obtain	obtain	VERB
ap-3488	118	12	the	the	DET
ap-3488	118	13	kinematic	kinematic	ADJ
ap-3488	118	14	model	model	NOUN
ap-3488	118	15	of	of	ADP
ap-3488	118	16	a	a	DET
ap-3488	118	17	unicycle	unicycle	NOUN
ap-3488	118	18	-	-	PUNCT
ap-3488	118	19	type	type	NOUN
ap-3488	118	20	robot	robot	NOUN
ap-3488	118	21	on	on	ADP
ap-3488	118	22	the	the	DET
ap-3488	118	23	lie	lie	NOUN
ap-3488	118	24	group	group	NOUN
ap-3488	118	25	:	:	PUNCT
ap-3488	118	26	ġ(t	ġ(t	X
ap-3488	118	27	)	)	PUNCT
ap-3488	118	28	=	=	SYM
ap-3488	118	29	ξ̂g(t	ξ̂g(t	PROPN
ap-3488	118	30	)	)	PUNCT
ap-3488	118	31	(	(	PUNCT
ap-3488	118	32	5	5	X
ap-3488	118	33	)	)	PUNCT
ap-3488	118	34	where	where	SCONJ
ap-3488	118	35	ξ̂	ξ̂	NUM
ap-3488	118	36	is	be	AUX
ap-3488	118	37	the	the	DET
ap-3488	118	38	control	control	NOUN
ap-3488	118	39	input	input	NOUN
ap-3488	118	40	matrix	matrix	NOUN
ap-3488	118	41	given	give	VERB
ap-3488	118	42	by	by	ADP
ap-3488	118	43	ξ̂	ξ̂	NOUN
ap-3488	118	44	=	=	SYM
ap-3488	118	45	0	0	ADJ
ap-3488	118	46	−ω	−ω	NOUN
ap-3488	118	47	ωyi	ωyi	PROPN
ap-3488	118	48	+	+	CCONJ
ap-3488	118	49	u	u	PROPN
ap-3488	118	50	cos	cos	PROPN
ap-3488	118	51	θi	θi	PROPN
ap-3488	118	52	ω	ω	PROPN
ap-3488	118	53	0	0	NUM
ap-3488	118	54	−ωxi	−ωxi	NOUN
ap-3488	119	1	+	+	CCONJ
ap-3488	119	2	u	u	NOUN
ap-3488	119	3	sin	sin	NOUN
ap-3488	119	4	θi	θi	ADP
ap-3488	119	5	0	0	NUM
ap-3488	119	6	0	0	NUM
ap-3488	119	7	0	0	NUM
ap-3488	119	8			NOUN
ap-3488	119	9	.	.	PUNCT
ap-3488	120	1	(	(	PUNCT
ap-3488	120	2	6	6	X
ap-3488	120	3	)	)	PUNCT
ap-3488	120	4	this	this	PRON
ap-3488	120	5	is	be	AUX
ap-3488	120	6	the	the	DET
ap-3488	120	7	kinematic	kinematic	ADJ
ap-3488	120	8	model	model	NOUN
ap-3488	120	9	on	on	ADP
ap-3488	120	10	the	the	DET
ap-3488	120	11	lie	lie	NOUN
ap-3488	120	12	group	group	NOUN
ap-3488	120	13	for	for	ADP
ap-3488	120	14	a	a	DET
ap-3488	120	15	unicycle	unicycle	NOUN
ap-3488	120	16	-	-	PUNCT
ap-3488	120	17	type	type	NOUN
ap-3488	120	18	robot	robot	NOUN
ap-3488	120	19	.	.	PUNCT
ap-3488	121	1	for	for	ADP
ap-3488	121	2	one	one	NUM
ap-3488	121	3	robot	robot	NOUN
ap-3488	121	4	with	with	ADP
ap-3488	121	5	a	a	DET
ap-3488	121	6	certain	certain	ADJ
ap-3488	121	7	pose	pose	NOUN
ap-3488	121	8	(	(	PUNCT
ap-3488	121	9	xi	xi	X
ap-3488	121	10	,	,	PUNCT
ap-3488	121	11	yi	yi	PROPN
ap-3488	121	12	,	,	PUNCT
ap-3488	121	13	θi	θi	PROPN
ap-3488	121	14	)	)	PUNCT
ap-3488	121	15	,	,	PUNCT
ap-3488	121	16	a	a	DET
ap-3488	121	17	control	control	NOUN
ap-3488	121	18	vector	vector	NOUN
ap-3488	121	19	(	(	PUNCT
ap-3488	121	20	u	u	NOUN
ap-3488	121	21	,	,	PUNCT
ap-3488	121	22	ω	ω	NOUN
ap-3488	121	23	)	)	PUNCT
ap-3488	121	24	results	result	NOUN
ap-3488	121	25	in	in	ADP
ap-3488	121	26	a	a	DET
ap-3488	121	27	unique	unique	ADJ
ap-3488	121	28	control	control	NOUN
ap-3488	121	29	input	input	NOUN
ap-3488	121	30	matrix	matrix	NOUN
ap-3488	121	31	ξ̂	ξ̂	NUM
ap-3488	121	32	to	to	PART
ap-3488	121	33	update	update	VERB
ap-3488	121	34	the	the	DET
ap-3488	121	35	robot	robot	NOUN
ap-3488	121	36	’s	’s	PART
ap-3488	121	37	motion	motion	NOUN
ap-3488	121	38	.	.	PUNCT
ap-3488	122	1	3	3	X
ap-3488	122	2	.	.	X
ap-3488	122	3	formation	formation	NOUN
ap-3488	122	4	control	control	NOUN
ap-3488	122	5	law	law	NOUN
ap-3488	122	6	on	on	ADP
ap-3488	122	7	se(2	se(2	PROPN
ap-3488	122	8	)	)	PUNCT
ap-3488	122	9	3.1	3.1	NUM
ap-3488	122	10	.	.	PUNCT
ap-3488	123	1	controller	controller	NOUN
ap-3488	123	2	design	design	NOUN
ap-3488	123	3	we	we	PRON
ap-3488	123	4	consider	consider	VERB
ap-3488	123	5	n	n	PRON
ap-3488	123	6	unicycle	unicycle	NOUN
ap-3488	123	7	-	-	PUNCT
ap-3488	123	8	type	type	NOUN
ap-3488	123	9	mobile	mobile	ADJ
ap-3488	123	10	robots	robot	NOUN
ap-3488	123	11	,	,	PUNCT
ap-3488	123	12	and	and	CCONJ
ap-3488	123	13	use	use	VERB
ap-3488	123	14	gi	gi	X
ap-3488	123	15	∈	∈	PROPN
ap-3488	123	16	se(2	se(2	NOUN
ap-3488	123	17	)	)	PUNCT
ap-3488	123	18	and	and	CCONJ
ap-3488	123	19	ḡi	ḡi	PROPN
ap-3488	123	20	∈	∈	PROPN
ap-3488	123	21	se(2	se(2	PROPN
ap-3488	123	22	)	)	PUNCT
ap-3488	123	23	(	(	PUNCT
ap-3488	123	24	i	i	NOUN
ap-3488	123	25	=	=	NOUN
ap-3488	123	26	1	1	NUM
ap-3488	123	27	,	,	PUNCT
ap-3488	123	28	·	·	PUNCT
ap-3488	123	29	·	·	PUNCT
ap-3488	123	30	·	·	PUNCT
ap-3488	123	31	,	,	PUNCT
ap-3488	123	32	n	n	CCONJ
ap-3488	123	33	)	)	PUNCT
ap-3488	123	34	to	to	PART
ap-3488	123	35	denote	denote	VERB
ap-3488	123	36	respectively	respectively	ADV
ap-3488	123	37	the	the	DET
ap-3488	123	38	current	current	ADJ
ap-3488	123	39	configuration	configuration	NOUN
ap-3488	123	40	and	and	CCONJ
ap-3488	123	41	the	the	DET
ap-3488	123	42	desired	desire	VERB
ap-3488	123	43	configuration	configuration	NOUN
ap-3488	123	44	of	of	ADP
ap-3488	123	45	each	each	DET
ap-3488	123	46	robot	robot	NOUN
ap-3488	123	47	.	.	PUNCT
ap-3488	124	1	in	in	ADP
ap-3488	124	2	fact	fact	NOUN
ap-3488	124	3	,	,	PUNCT
ap-3488	124	4	gi	gi	X
ap-3488	124	5	is	be	AUX
ap-3488	124	6	the	the	DET
ap-3488	124	7	representation	representation	NOUN
ap-3488	124	8	of	of	ADP
ap-3488	124	9	the	the	DET
ap-3488	124	10	robot	robot	NOUN
ap-3488	124	11	frame	frame	NOUN
ap-3488	124	12	fr	fr	PROPN
ap-3488	124	13	shown	show	VERB
ap-3488	124	14	in	in	ADP
ap-3488	124	15	figure	figure	NOUN
ap-3488	124	16	1	1	NUM
ap-3488	124	17	relative	relative	ADJ
ap-3488	124	18	to	to	ADP
ap-3488	124	19	the	the	DET
ap-3488	124	20	spatial	spatial	ADJ
ap-3488	124	21	frame	frame	NOUN
ap-3488	124	22	fi	fi	NOUN
ap-3488	124	23	.	.	PUNCT
ap-3488	125	1	as	as	SCONJ
ap-3488	125	2	introduced	introduce	VERB
ap-3488	125	3	in	in	ADP
ap-3488	125	4	the	the	DET
ap-3488	125	5	previous	previous	ADJ
ap-3488	125	6	section	section	NOUN
ap-3488	125	7	,	,	PUNCT
ap-3488	125	8	the	the	DET
ap-3488	125	9	evolution	evolution	NOUN
ap-3488	125	10	of	of	ADP
ap-3488	125	11	system	system	NOUN
ap-3488	125	12	gi	gi	NOUN
ap-3488	125	13	can	can	AUX
ap-3488	125	14	be	be	AUX
ap-3488	125	15	expressed	express	VERB
ap-3488	125	16	by	by	ADP
ap-3488	125	17	ġi	ġi	PROPN
ap-3488	125	18	=	=	SYM
ap-3488	126	1	ξ̂igi	ξ̂igi	X
ap-3488	126	2	(	(	PUNCT
ap-3488	126	3	7	7	NUM
ap-3488	126	4	)	)	PUNCT
ap-3488	126	5	where	where	SCONJ
ap-3488	126	6	ξ̂i	ξ̂i	NUM
ap-3488	126	7	∈	∈	PROPN
ap-3488	126	8	se(2	se(2	NOUN
ap-3488	126	9	)	)	PUNCT
ap-3488	126	10	is	be	AUX
ap-3488	126	11	the	the	DET
ap-3488	126	12	control	control	NOUN
ap-3488	126	13	input	input	NOUN
ap-3488	126	14	matrix	matrix	NOUN
ap-3488	126	15	.	.	PUNCT
ap-3488	127	1	let	let	VERB
ap-3488	127	2	gij	gij	PROPN
ap-3488	127	3	be	be	AUX
ap-3488	127	4	the	the	DET
ap-3488	127	5	configuration	configuration	NOUN
ap-3488	127	6	of	of	ADP
ap-3488	127	7	the	the	DET
ap-3488	127	8	robot	robot	NOUN
ap-3488	127	9	-	-	PUNCT
ap-3488	127	10	j	j	PROPN
ap-3488	127	11	frame	frame	NOUN
ap-3488	127	12	relative	relative	ADJ
ap-3488	127	13	to	to	ADP
ap-3488	127	14	the	the	DET
ap-3488	127	15	robot	robot	NOUN
ap-3488	127	16	-	-	PUNCT
ap-3488	127	17	i	i	PRON
ap-3488	127	18	frame	frame	NOUN
ap-3488	127	19	,	,	PUNCT
ap-3488	127	20	then	then	ADV
ap-3488	127	21	we	we	PRON
ap-3488	127	22	have	have	VERB
ap-3488	127	23	gj	gj	NOUN
ap-3488	127	24	=	=	PUNCT
ap-3488	127	25	gigij	gigij	NOUN
ap-3488	127	26	.	.	PUNCT
ap-3488	128	1	(	(	PUNCT
ap-3488	128	2	8)	8)	NUM
ap-3488	128	3	thus	thus	ADV
ap-3488	128	4	gij	gij	NOUN
ap-3488	128	5	=	=	SYM
ap-3488	129	1	g−1	g−1	INTJ
ap-3488	129	2	i	i	PRON
ap-3488	129	3	gj	gj	VERB
ap-3488	129	4	.	.	PUNCT
ap-3488	130	1	we	we	PRON
ap-3488	130	2	can	can	AUX
ap-3488	130	3	use	use	VERB
ap-3488	130	4	ḡij	ḡij	NOUN
ap-3488	130	5	to	to	PART
ap-3488	130	6	represent	represent	VERB
ap-3488	130	7	the	the	DET
ap-3488	130	8	desired	desire	VERB
ap-3488	130	9	configuration	configuration	NOUN
ap-3488	130	10	of	of	ADP
ap-3488	130	11	the	the	DET
ap-3488	130	12	robot	robot	NOUN
ap-3488	130	13	-	-	PUNCT
ap-3488	130	14	j	j	PROPN
ap-3488	130	15	frame	frame	NOUN
ap-3488	130	16	in	in	ADP
ap-3488	130	17	the	the	DET
ap-3488	130	18	roboti	roboti	NOUN
ap-3488	130	19	frame	frame	NOUN
ap-3488	130	20	.	.	PUNCT
ap-3488	131	1	then	then	ADV
ap-3488	131	2	the	the	DET
ap-3488	131	3	robots	robot	NOUN
ap-3488	131	4	achieve	achieve	VERB
ap-3488	131	5	a	a	DET
ap-3488	131	6	desired	desire	VERB
ap-3488	131	7	formation	formation	NOUN
ap-3488	131	8	if	if	SCONJ
ap-3488	131	9	their	their	PRON
ap-3488	131	10	configurations	configuration	NOUN
ap-3488	131	11	satisfy	satisfy	VERB
ap-3488	131	12	the	the	DET
ap-3488	131	13	following	follow	VERB
ap-3488	131	14	equation	equation	NOUN
ap-3488	131	15	for	for	ADP
ap-3488	131	16	any	any	DET
ap-3488	131	17	k	k	NOUN
ap-3488	131	18	=	=	SYM
ap-3488	131	19	1	1	NUM
ap-3488	131	20	,	,	PUNCT
ap-3488	131	21	·	·	PUNCT
ap-3488	131	22	·	·	PUNCT
ap-3488	131	23	·	·	PUNCT
ap-3488	131	24	,	,	PUNCT
ap-3488	131	25	n	n	CCONJ
ap-3488	131	26	,	,	PUNCT
ap-3488	131	27	k	k	PROPN
ap-3488	131	28	6=	6=	PROPN
ap-3488	131	29	i	i	PRON
ap-3488	131	30	lim	lim	PROPN
ap-3488	131	31	t→∞	t→∞	X
ap-3488	132	1	g−1	g−1	PROPN
ap-3488	132	2	k	k	PROPN
ap-3488	132	3	gi	gi	NOUN
ap-3488	132	4	=	=	PUNCT
ap-3488	132	5	ḡki	ḡki	PROPN
ap-3488	132	6	,	,	PUNCT
ap-3488	132	7	i	i	PRON
ap-3488	132	8	=	=	NOUN
ap-3488	132	9	1	1	NUM
ap-3488	132	10	,	,	PUNCT
ap-3488	132	11	·	·	PUNCT
ap-3488	132	12	·	·	PUNCT
ap-3488	132	13	·	·	PUNCT
ap-3488	132	14	,	,	PUNCT
ap-3488	132	15	n.	n.	NOUN
ap-3488	132	16	(	(	PUNCT
ap-3488	132	17	9	9	NUM
ap-3488	132	18	)	)	PUNCT
ap-3488	132	19	ḡki	ḡki	PROPN
ap-3488	132	20	∈	∈	PROPN
ap-3488	132	21	se(2	se(2	PROPN
ap-3488	132	22	)	)	PUNCT
ap-3488	132	23	is	be	AUX
ap-3488	132	24	defined	define	VERB
ap-3488	132	25	according	accord	VERB
ap-3488	132	26	to	to	ADP
ap-3488	132	27	the	the	DET
ap-3488	132	28	task	task	NOUN
ap-3488	132	29	requirements	requirement	NOUN
ap-3488	132	30	and	and	CCONJ
ap-3488	132	31	is	be	AUX
ap-3488	132	32	often	often	ADV
ap-3488	132	33	used	use	VERB
ap-3488	132	34	to	to	PART
ap-3488	132	35	identify	identify	VERB
ap-3488	132	36	the	the	DET
ap-3488	132	37	geometric	geometric	ADJ
ap-3488	132	38	configuration	configuration	NOUN
ap-3488	132	39	of	of	ADP
ap-3488	132	40	the	the	DET
ap-3488	132	41	formation	formation	NOUN
ap-3488	132	42	.	.	PUNCT
ap-3488	133	1	we	we	PRON
ap-3488	133	2	study	study	VERB
ap-3488	133	3	the	the	DET
ap-3488	133	4	movement	movement	NOUN
ap-3488	133	5	of	of	ADP
ap-3488	133	6	gi	gi	NOUN
ap-3488	133	7	relative	relative	ADJ
ap-3488	133	8	to	to	ADP
ap-3488	133	9	gj	gj	PROPN
ap-3488	133	10	,	,	PUNCT
ap-3488	133	11	so	so	CCONJ
ap-3488	133	12	here	here	ADV
ap-3488	133	13	we	we	PRON
ap-3488	133	14	can	can	AUX
ap-3488	133	15	consider	consider	VERB
ap-3488	133	16	provisionally	provisionally	ADV
ap-3488	133	17	gj	gj	NOUN
ap-3488	133	18	=	=	PUNCT
ap-3488	133	19	ḡj	ḡj	PROPN
ap-3488	133	20	,	,	PUNCT
ap-3488	133	21	then	then	ADV
ap-3488	133	22	ḡij	ḡij	NOUN
ap-3488	133	23	could	could	AUX
ap-3488	133	24	be	be	AUX
ap-3488	133	25	written	write	VERB
ap-3488	133	26	as	as	ADP
ap-3488	133	27	ḡ−1	ḡ−1	PROPN
ap-3488	133	28	i	i	PRON
ap-3488	133	29	gj	gj	VERB
ap-3488	133	30	.	.	PUNCT
ap-3488	134	1	thus	thus	ADV
ap-3488	134	2	we	we	PRON
ap-3488	134	3	have	have	VERB
ap-3488	134	4	ḡ−1	ḡ−1	NOUN
ap-3488	135	1	i	i	PRON
ap-3488	135	2	gj	gj	NOUN
ap-3488	136	1	=	=	PUNCT
ap-3488	136	2	ḡ−1	ḡ−1	NOUN
ap-3488	137	1	i	i	PRON
ap-3488	137	2	ḡj	ḡj	PROPN
ap-3488	138	1	=	=	PUNCT
ap-3488	139	1	ḡ−1	ḡ−1	INTJ
ap-3488	140	1	i	i	PRON
ap-3488	140	2	(	(	PUNCT
ap-3488	140	3	ḡkḡ−1	ḡkḡ−1	PROPN
ap-3488	140	4	k	k	X
ap-3488	140	5	)	)	PUNCT
ap-3488	140	6	ḡj	ḡj	PROPN
ap-3488	140	7	=	=	SYM
ap-3488	141	1	(	(	PUNCT
ap-3488	141	2	ḡ−1	ḡ−1	NOUN
ap-3488	141	3	k	k	PROPN
ap-3488	142	1	ḡi)−1(ḡ−1	ḡi)−1(ḡ−1	PROPN
ap-3488	142	2	k	k	PROPN
ap-3488	142	3	ḡj	ḡj	PROPN
ap-3488	142	4	)	)	PUNCT
ap-3488	143	1	=	=	PRON
ap-3488	143	2	(	(	PUNCT
ap-3488	143	3	ḡki)−1ḡkj	ḡki)−1ḡkj	NOUN
ap-3488	143	4	which	which	PRON
ap-3488	143	5	gives	give	VERB
ap-3488	143	6	ḡi	ḡi	PROPN
ap-3488	143	7	=	=	SYM
ap-3488	143	8	gj(ḡkj)−1ḡki	gj(ḡkj)−1ḡki	PROPN
ap-3488	143	9	.	.	PUNCT
ap-3488	144	1	then	then	ADV
ap-3488	144	2	for	for	ADP
ap-3488	144	3	robot	robot	NOUN
ap-3488	144	4	-	-	PUNCT
ap-3488	144	5	i	i	PRON
ap-3488	144	6	(	(	PUNCT
ap-3488	144	7	in	in	ADP
ap-3488	144	8	the	the	DET
ap-3488	144	9	local	local	ADJ
ap-3488	144	10	frame	frame	NOUN
ap-3488	144	11	gi	gi	NOUN
ap-3488	144	12	)	)	PUNCT
ap-3488	144	13	,	,	PUNCT
ap-3488	144	14	the	the	DET
ap-3488	144	15	needed	need	VERB
ap-3488	144	16	transformation	transformation	NOUN
ap-3488	144	17	of	of	ADP
ap-3488	144	18	robot	robot	NOUN
ap-3488	144	19	-	-	PUNCT
ap-3488	144	20	i	i	PROPN
ap-3488	144	21	3	3	NUM
ap-3488	144	22	youwei	youwei	NOUN
ap-3488	144	23	dong	dong	PROPN
ap-3488	144	24	,	,	PUNCT
ap-3488	144	25	ahmed	ahmed	PROPN
ap-3488	144	26	rahmani	rahmani	PROPN
ap-3488	144	27	acta	acta	PROPN
ap-3488	144	28	polytechnica	polytechnica	PROPN
ap-3488	144	29	from	from	ADP
ap-3488	144	30	the	the	DET
ap-3488	144	31	current	current	ADJ
ap-3488	144	32	configuration	configuration	NOUN
ap-3488	144	33	to	to	ADP
ap-3488	144	34	the	the	DET
ap-3488	144	35	desired	desire	VERB
ap-3488	144	36	configuration	configuration	NOUN
ap-3488	144	37	while	while	SCONJ
ap-3488	144	38	considering	consider	VERB
ap-3488	144	39	the	the	DET
ap-3488	144	40	current	current	ADJ
ap-3488	144	41	configuration	configuration	NOUN
ap-3488	144	42	of	of	ADP
ap-3488	144	43	robot	robot	NOUN
ap-3488	144	44	-	-	PUNCT
ap-3488	144	45	j	j	PROPN
ap-3488	144	46	is	be	AUX
ap-3488	144	47	g̃i_j	g̃i_j	ADJ
ap-3488	144	48	=	=	SYM
ap-3488	144	49	g−1	g−1	INTJ
ap-3488	144	50	i	i	PRON
ap-3488	144	51	gj(ḡkj)−1ḡki	gj(ḡkj)−1ḡki	PROPN
ap-3488	144	52	.	.	PUNCT
ap-3488	145	1	(	(	PUNCT
ap-3488	145	2	10	10	NUM
ap-3488	145	3	)	)	PUNCT
ap-3488	145	4	to	to	PART
ap-3488	145	5	simplify	simplify	VERB
ap-3488	145	6	the	the	DET
ap-3488	145	7	notations	notation	NOUN
ap-3488	145	8	,	,	PUNCT
ap-3488	145	9	we	we	PRON
ap-3488	145	10	note	note	VERB
ap-3488	145	11	g̃ij	g̃ij	NOUN
ap-3488	145	12	instead	instead	ADV
ap-3488	145	13	of	of	ADV
ap-3488	145	14	g̃i_j	g̃i_j	VERB
ap-3488	145	15	.	.	PUNCT
ap-3488	146	1	in	in	ADP
ap-3488	146	2	[	[	X
ap-3488	146	3	1	1	NUM
ap-3488	146	4	]	]	PUNCT
ap-3488	146	5	,	,	PUNCT
ap-3488	146	6	noting	note	VERB
ap-3488	146	7	x̃ij	x̃ij	PROPN
ap-3488	146	8	=	=	PROPN
ap-3488	146	9	log	log	PROPN
ap-3488	146	10	g̃ij	g̃ij	PROPN
ap-3488	146	11	,	,	PUNCT
ap-3488	146	12	a	a	DET
ap-3488	146	13	control	control	NOUN
ap-3488	146	14	law	law	NOUN
ap-3488	146	15	for	for	ADP
ap-3488	146	16	agents	agent	NOUN
ap-3488	146	17	,	,	PUNCT
ap-3488	146	18	which	which	PRON
ap-3488	146	19	have	have	VERB
ap-3488	146	20	holonomic	holonomic	ADJ
ap-3488	146	21	constraints	constraint	NOUN
ap-3488	146	22	,	,	PUNCT
ap-3488	146	23	is	be	AUX
ap-3488	146	24	proposed	propose	VERB
ap-3488	146	25	as	as	ADP
ap-3488	146	26	ξ̂i	ξ̂i	NUM
ap-3488	146	27	=	=	SYM
ap-3488	146	28	c	c	AUX
ap-3488	146	29	ai	ai	VERB
ap-3488	146	30	n∑	n∑	ADV
ap-3488	146	31	j=1	j=1	PROPN
ap-3488	146	32	aij	aij	PROPN
ap-3488	146	33	x̃ij	x̃ij	PROPN
ap-3488	146	34	,	,	PUNCT
ap-3488	146	35	i	i	PRON
ap-3488	146	36	=	=	NOUN
ap-3488	146	37	1	1	NUM
ap-3488	146	38	,	,	PUNCT
ap-3488	146	39	·	·	PUNCT
ap-3488	146	40	·	·	PUNCT
ap-3488	146	41	·	·	PUNCT
ap-3488	146	42	,	,	PUNCT
ap-3488	146	43	n	n	CCONJ
ap-3488	146	44	where	where	SCONJ
ap-3488	146	45	aij	aij	PROPN
ap-3488	146	46	is	be	AUX
ap-3488	146	47	the	the	DET
ap-3488	146	48	element	element	NOUN
ap-3488	146	49	in	in	ADP
ap-3488	146	50	the	the	DET
ap-3488	146	51	adjacency	adjacency	NOUN
ap-3488	146	52	matrixa	matrixa	PROPN
ap-3488	146	53	and	and	CCONJ
ap-3488	146	54	ai	ai	VERB
ap-3488	146	55	=	=	ADJ
ap-3488	146	56	∑n	∑n	PROPN
ap-3488	146	57	j=1	j=1	PROPN
ap-3488	146	58	aij	aij	PROPN
ap-3488	146	59	.	.	PUNCT
ap-3488	147	1	however	however	ADV
ap-3488	147	2	,	,	PUNCT
ap-3488	147	3	in	in	ADP
ap-3488	147	4	our	our	PRON
ap-3488	147	5	mrs	mrs	PROPN
ap-3488	147	6	,	,	PUNCT
ap-3488	147	7	nonholonomic	nonholonomic	ADJ
ap-3488	147	8	constraints	constraint	NOUN
ap-3488	147	9	are	be	AUX
ap-3488	147	10	associated	associate	VERB
ap-3488	147	11	with	with	ADP
ap-3488	147	12	unicycle	unicycle	NOUN
ap-3488	147	13	-	-	PUNCT
ap-3488	147	14	type	type	NOUN
ap-3488	147	15	robots	robot	NOUN
ap-3488	147	16	,	,	PUNCT
ap-3488	147	17	so	so	SCONJ
ap-3488	147	18	we	we	PRON
ap-3488	147	19	develop	develop	VERB
ap-3488	147	20	a	a	DET
ap-3488	147	21	new	new	ADJ
ap-3488	147	22	nonlinear	nonlinear	ADJ
ap-3488	147	23	control	control	NOUN
ap-3488	147	24	approach	approach	NOUN
ap-3488	147	25	.	.	PUNCT
ap-3488	148	1	from	from	ADP
ap-3488	148	2	the	the	DET
ap-3488	148	3	matrix	matrix	NOUN
ap-3488	148	4	g̃ij	g̃ij	NOUN
ap-3488	148	5	,	,	PUNCT
ap-3488	148	6	we	we	PRON
ap-3488	148	7	could	could	AUX
ap-3488	148	8	know	know	VERB
ap-3488	148	9	the	the	DET
ap-3488	148	10	position	position	NOUN
ap-3488	148	11	error	error	NOUN
ap-3488	148	12	and	and	CCONJ
ap-3488	148	13	orientation	orientation	NOUN
ap-3488	148	14	error	error	NOUN
ap-3488	148	15	x̃ij	x̃ij	PROPN
ap-3488	148	16	,	,	PUNCT
ap-3488	148	17	ỹij	ỹij	PROPN
ap-3488	148	18	,	,	PUNCT
ap-3488	148	19	θ̃ij	θ̃ij	PROPN
ap-3488	148	20	.	.	PUNCT
ap-3488	149	1	we	we	PRON
ap-3488	149	2	suppose	suppose	VERB
ap-3488	149	3	that	that	SCONJ
ap-3488	149	4	the	the	DET
ap-3488	149	5	relative	relative	ADJ
ap-3488	149	6	configuration	configuration	NOUN
ap-3488	149	7	of	of	ADP
ap-3488	149	8	ḡi	ḡi	PROPN
ap-3488	149	9	with	with	ADP
ap-3488	149	10	respect	respect	NOUN
ap-3488	149	11	to	to	ADP
ap-3488	149	12	the	the	DET
ap-3488	149	13	robot	robot	NOUN
ap-3488	149	14	frame	frame	NOUN
ap-3488	149	15	gi	gi	NOUN
ap-3488	149	16	is	be	AUX
ap-3488	149	17	denoted	denote	VERB
ap-3488	149	18	by	by	ADP
ap-3488	149	19	ḡii	ḡii	PROPN
ap-3488	149	20	.	.	PUNCT
ap-3488	150	1	then	then	ADV
ap-3488	150	2	ḡii	ḡii	PROPN
ap-3488	150	3	could	could	AUX
ap-3488	150	4	be	be	AUX
ap-3488	150	5	obtained	obtain	VERB
ap-3488	150	6	by	by	ADP
ap-3488	150	7	the	the	DET
ap-3488	150	8	the	the	DET
ap-3488	150	9	mean	mean	ADJ
ap-3488	150	10	functionm	functionm	NOUN
ap-3488	150	11	:	:	PUNCT
ap-3488	150	12	se(2)×	se(2)×	X
ap-3488	150	13	·	·	PUNCT
ap-3488	150	14	·	·	PUNCT
ap-3488	150	15	·	·	PUNCT
ap-3488	151	1	×	×	NOUN
ap-3488	151	2	se(2)︸	se(2)︸	PROPN
ap-3488	151	3	︷︷	︷︷	PROPN
ap-3488	151	4	︸	︸	ADP
ap-3488	151	5	n−1	n−1	PROPN
ap-3488	151	6	→	→	SYM
ap-3488	151	7	se(2	se(2	PROPN
ap-3488	151	8	)	)	PUNCT
ap-3488	151	9	,	,	PUNCT
ap-3488	151	10	(	(	PUNCT
ap-3488	151	11	g̃i1	g̃i1	PROPN
ap-3488	151	12	,	,	PUNCT
ap-3488	151	13	·	·	PUNCT
ap-3488	151	14	·	·	PUNCT
ap-3488	151	15	·	·	PUNCT
ap-3488	151	16	,	,	PUNCT
ap-3488	151	17	g̃i	g̃i	NOUN
ap-3488	151	18	,	,	PUNCT
ap-3488	151	19	i−1	i−1	PROPN
ap-3488	151	20	,	,	PUNCT
ap-3488	151	21	g̃i	g̃i	NOUN
ap-3488	151	22	,	,	PUNCT
ap-3488	151	23	i+1	i+1	X
ap-3488	151	24	,	,	PUNCT
ap-3488	151	25	·	·	PUNCT
ap-3488	151	26	·	·	PUNCT
ap-3488	151	27	·	·	PUNCT
ap-3488	151	28	,	,	PUNCT
ap-3488	151	29	g̃in	g̃in	PROPN
ap-3488	151	30	)	)	PUNCT
ap-3488	151	31	7→	7→	NUM
ap-3488	151	32	g̃ii	g̃ii	PROPN
ap-3488	151	33	.	.	PUNCT
ap-3488	152	1	this	this	DET
ap-3488	152	2	function	function	NOUN
ap-3488	152	3	means	mean	VERB
ap-3488	152	4	to	to	PART
ap-3488	152	5	get	get	VERB
ap-3488	152	6	the	the	DET
ap-3488	152	7	weighted	weight	VERB
ap-3488	152	8	arithmetic	arithmetic	ADJ
ap-3488	152	9	mean	mean	NOUN
ap-3488	152	10	of	of	ADP
ap-3488	152	11	all	all	DET
ap-3488	152	12	the	the	DET
ap-3488	152	13	arguments	argument	NOUN
ap-3488	152	14	,	,	PUNCT
ap-3488	152	15	that	that	ADV
ap-3488	152	16	is	is	ADV
ap-3488	152	17	,	,	PUNCT
ap-3488	152	18	if	if	SCONJ
ap-3488	152	19	we	we	PRON
ap-3488	152	20	note	note	VERB
ap-3488	152	21	g̃ij	g̃ij	PROPN
ap-3488	152	22	=	=	SYM
ap-3488	152	23	cos	cos	PROPN
ap-3488	152	24	θ̃ij	θ̃ij	NOUN
ap-3488	152	25	−	−	PROPN
ap-3488	152	26	sin	sin	NOUN
ap-3488	152	27	θ̃ij	θ̃ij	PROPN
ap-3488	152	28	x̃ij	x̃ij	PROPN
ap-3488	152	29	sin	sin	VERB
ap-3488	152	30	θ̃ij	θ̃ij	PROPN
ap-3488	152	31	cos	cos	PROPN
ap-3488	152	32	θ̃ij	θ̃ij	PROPN
ap-3488	152	33	ỹij	ỹij	PROPN
ap-3488	152	34	0	0	NUM
ap-3488	152	35	0	0	NUM
ap-3488	152	36	1	1	NUM
ap-3488	152	37			NOUN
ap-3488	152	38	j=1	j=1	NOUN
ap-3488	152	39	,	,	PUNCT
ap-3488	152	40	·	·	PUNCT
ap-3488	152	41	·	·	PUNCT
ap-3488	152	42	·	·	PUNCT
ap-3488	152	43	,	,	PUNCT
ap-3488	152	44	n	n	CCONJ
ap-3488	152	45	,	,	PUNCT
ap-3488	152	46	j	j	PROPN
ap-3488	152	47	6	6	NUM
ap-3488	153	1	=	=	NOUN
ap-3488	153	2	i	i	PROPN
ap-3488	153	3	,	,	PUNCT
ap-3488	153	4	then	then	ADV
ap-3488	153	5	x̃ii	x̃ii	PROPN
ap-3488	153	6	,	,	PUNCT
ap-3488	153	7	ỹii	ỹii	PROPN
ap-3488	153	8	,	,	PUNCT
ap-3488	153	9	θ̃ii	θ̃ii	PROPN
ap-3488	153	10	are	be	AUX
ap-3488	153	11	given	give	VERB
ap-3488	153	12	by	by	ADP
ap-3488	153	13	:	:	PUNCT
ap-3488	153	14	∆ii	∆ii	PROPN
ap-3488	153	15	=	=	SYM
ap-3488	154	1	1	1	NUM
ap-3488	154	2	ai	ai	NOUN
ap-3488	154	3	n∑	n∑	PROPN
ap-3488	154	4	j=1	j=1	PROPN
ap-3488	154	5	aij∆ij	aij∆ij	PROPN
ap-3488	154	6	,	,	PUNCT
ap-3488	154	7	j	j	PROPN
ap-3488	154	8	6=	6=	PROPN
ap-3488	154	9	i	i	PROPN
ap-3488	154	10	,	,	PUNCT
ap-3488	154	11	∆	∆	PROPN
ap-3488	154	12	=	=	SYM
ap-3488	154	13	x̃	x̃	PROPN
ap-3488	154	14	,	,	PUNCT
ap-3488	154	15	ỹ	ỹ	PROPN
ap-3488	154	16	,	,	PUNCT
ap-3488	154	17	θ̃	θ̃	NOUN
ap-3488	154	18	(	(	PUNCT
ap-3488	154	19	11	11	NUM
ap-3488	154	20	)	)	PUNCT
ap-3488	154	21	where	where	SCONJ
ap-3488	154	22	aij	aij	PROPN
ap-3488	154	23	is	be	AUX
ap-3488	154	24	the	the	DET
ap-3488	154	25	element	element	NOUN
ap-3488	154	26	of	of	ADP
ap-3488	154	27	adjacency	adjacency	PROPN
ap-3488	154	28	matrix	matrix	NOUN
ap-3488	154	29	a	a	PRON
ap-3488	154	30	and	and	CCONJ
ap-3488	154	31	ai	ai	VERB
ap-3488	154	32	=	=	ADJ
ap-3488	154	33	∑n	∑n	PROPN
ap-3488	154	34	j=1	j=1	PROPN
ap-3488	154	35	aij	aij	PROPN
ap-3488	154	36	.	.	PUNCT
ap-3488	155	1	when	when	SCONJ
ap-3488	155	2	x̃ii	x̃ii	PROPN
ap-3488	155	3	,	,	PUNCT
ap-3488	155	4	ỹii	ỹii	PROPN
ap-3488	155	5	and	and	CCONJ
ap-3488	155	6	θ̃ii	θ̃ii	PROPN
ap-3488	155	7	are	be	AUX
ap-3488	155	8	obtained	obtain	VERB
ap-3488	155	9	,	,	PUNCT
ap-3488	155	10	g̃ii	g̃ii	PROPN
ap-3488	155	11	can	can	AUX
ap-3488	155	12	be	be	AUX
ap-3488	155	13	rewritten	rewrite	VERB
ap-3488	155	14	as	as	ADP
ap-3488	155	15	g̃ii	g̃ii	PROPN
ap-3488	155	16	=	=	SYM
ap-3488	155	17	cos	cos	PROPN
ap-3488	155	18	θ̃ii	θ̃ii	PROPN
ap-3488	155	19	−	−	PROPN
ap-3488	156	1	sin	sin	NOUN
ap-3488	156	2	θ̃ii	θ̃ii	PROPN
ap-3488	156	3	x̃ii	x̃ii	PROPN
ap-3488	156	4	sin	sin	VERB
ap-3488	156	5	θ̃ii	θ̃ii	PROPN
ap-3488	156	6	cos	cos	PROPN
ap-3488	156	7	θ̃ii	θ̃ii	PROPN
ap-3488	156	8	ỹii	ỹii	PROPN
ap-3488	156	9	0	0	NUM
ap-3488	156	10	0	0	NUM
ap-3488	156	11	1	1	NUM
ap-3488	156	12			NOUN
ap-3488	156	13	.	.	PUNCT
ap-3488	157	1	we	we	PRON
ap-3488	157	2	take	take	VERB
ap-3488	157	3	the	the	DET
ap-3488	157	4	inverse	inverse	NOUN
ap-3488	157	5	of	of	ADP
ap-3488	157	6	the	the	DET
ap-3488	157	7	matrix	matrix	NOUN
ap-3488	157	8	g̃−1	g̃−1	PROPN
ap-3488	157	9	ii	ii	NUM
ap-3488	157	10	which	which	PRON
ap-3488	157	11	represents	represent	VERB
ap-3488	157	12	the	the	DET
ap-3488	157	13	relative	relative	ADJ
ap-3488	157	14	configuration	configuration	NOUN
ap-3488	157	15	of	of	ADP
ap-3488	157	16	gi	gi	NOUN
ap-3488	157	17	with	with	ADP
ap-3488	157	18	respect	respect	NOUN
ap-3488	157	19	to	to	ADP
ap-3488	157	20	the	the	DET
ap-3488	157	21	desired	desire	VERB
ap-3488	157	22	configuration	configuration	NOUN
ap-3488	157	23	ḡi	ḡi	PROPN
ap-3488	157	24	when	when	SCONJ
ap-3488	157	25	the	the	DET
ap-3488	157	26	predefined	predefine	VERB
ap-3488	157	27	communication	communication	NOUN
ap-3488	157	28	topology	topology	NOUN
ap-3488	157	29	is	be	AUX
ap-3488	157	30	considered	consider	VERB
ap-3488	157	31	.	.	PUNCT
ap-3488	158	1	let	let	VERB
ap-3488	158	2	us	we	PRON
ap-3488	158	3	consider	consider	VERB
ap-3488	158	4	figure	figure	NOUN
ap-3488	158	5	2	2	NUM
ap-3488	158	6	,	,	PUNCT
ap-3488	158	7	where	where	SCONJ
ap-3488	158	8	the	the	DET
ap-3488	158	9	unknowns	unknown	NOUN
ap-3488	158	10	are	be	AUX
ap-3488	158	11	annotated	annotate	VERB
ap-3488	158	12	in	in	ADP
ap-3488	158	13	the	the	DET
ap-3488	158	14	list	list	NOUN
ap-3488	158	15	of	of	ADP
ap-3488	158	16	symbols	symbol	NOUN
ap-3488	158	17	after	after	ADP
ap-3488	158	18	the	the	DET
ap-3488	158	19	article	article	NOUN
ap-3488	158	20	.	.	PUNCT
ap-3488	159	1	o′x	o′x	NUM
ap-3488	159	2	′y	′y	NOUN
ap-3488	159	3	′	′	NUM
ap-3488	159	4	is	be	AUX
ap-3488	159	5	the	the	DET
ap-3488	159	6	frame	frame	NOUN
ap-3488	159	7	of	of	ADP
ap-3488	159	8	the	the	DET
ap-3488	159	9	desired	desire	VERB
ap-3488	159	10	configuration	configuration	NOUN
ap-3488	159	11	of	of	ADP
ap-3488	159	12	robot	robot	NOUN
ap-3488	159	13	i	i	PROPN
ap-3488	159	14	,	,	PUNCT
ap-3488	159	15	and	and	CCONJ
ap-3488	159	16	(	(	PUNCT
ap-3488	159	17	a	a	DET
ap-3488	159	18	,	,	PUNCT
ap-3488	159	19	θ	θ	NOUN
ap-3488	159	20	)	)	PUNCT
ap-3488	159	21	,	,	PUNCT
ap-3488	159	22	related	relate	VERB
ap-3488	159	23	to	to	ADP
ap-3488	159	24	g̃−1	g̃−1	PROPN
ap-3488	159	25	ii	ii	PROPN
ap-3488	159	26	,	,	PUNCT
ap-3488	159	27	is	be	AUX
ap-3488	159	28	the	the	DET
ap-3488	159	29	current	current	ADJ
ap-3488	159	30	pose	pose	NOUN
ap-3488	159	31	of	of	ADP
ap-3488	159	32	robot	robot	NOUN
ap-3488	159	33	i	i	PRON
ap-3488	159	34	in	in	ADP
ap-3488	159	35	the	the	DET
ap-3488	159	36	frame	frame	NOUN
ap-3488	159	37	o′x	o′x	NUM
ap-3488	159	38	′y	′y	PROPN
ap-3488	159	39	′.	′.	NOUN
ap-3488	159	40	in	in	ADP
ap-3488	159	41	this	this	DET
ap-3488	159	42	frame	frame	NOUN
ap-3488	159	43	,	,	PUNCT
ap-3488	159	44	we	we	PRON
ap-3488	159	45	assume	assume	VERB
ap-3488	159	46	a	a	DET
ap-3488	159	47	circle	circle	NOUN
ap-3488	159	48	of	of	ADP
ap-3488	159	49	radius	radius	PROPN
ap-3488	159	50	|r|	|r|	PROPN
ap-3488	159	51	,	,	PUNCT
ap-3488	159	52	denoted	denote	VERB
ap-3488	159	53	by	by	ADP
ap-3488	159	54	cb	cb	PROPN
ap-3488	159	55	,	,	PUNCT
ap-3488	159	56	and	and	CCONJ
ap-3488	159	57	then	then	ADV
ap-3488	159	58	we	we	PRON
ap-3488	159	59	propose	propose	VERB
ap-3488	159	60	a	a	DET
ap-3488	159	61	control	control	NOUN
ap-3488	159	62	law	law	NOUN
ap-3488	159	63	to	to	PART
ap-3488	159	64	drive	drive	VERB
ap-3488	159	65	the	the	DET
ap-3488	159	66	robot	robot	NOUN
ap-3488	159	67	to	to	ADP
ap-3488	159	68	the	the	DET
ap-3488	159	69	origin	origin	NOUN
ap-3488	159	70	with	with	ADP
ap-3488	159	71	the	the	DET
ap-3488	159	72	help	help	NOUN
ap-3488	159	73	of	of	ADP
ap-3488	159	74	this	this	DET
ap-3488	159	75	circle	circle	NOUN
ap-3488	159	76	.	.	PUNCT
ap-3488	160	1	the	the	DET
ap-3488	160	2	absolute	absolute	ADJ
ap-3488	160	3	value	value	NOUN
ap-3488	160	4	|r|	|r|	NOUN
ap-3488	160	5	is	be	AUX
ap-3488	160	6	always	always	ADV
ap-3488	160	7	positive	positive	ADJ
ap-3488	160	8	,	,	PUNCT
ap-3488	160	9	and	and	CCONJ
ap-3488	160	10	it	it	PRON
ap-3488	160	11	is	be	AUX
ap-3488	160	12	supposed	suppose	VERB
ap-3488	160	13	appropriately	appropriately	ADV
ap-3488	160	14	according	accord	VERB
ap-3488	160	15	to	to	ADP
ap-3488	160	16	the	the	DET
ap-3488	160	17	initial	initial	ADJ
ap-3488	160	18	conditions	condition	NOUN
ap-3488	160	19	.	.	PUNCT
ap-3488	161	1	r	r	NOUN
ap-3488	161	2	is	be	AUX
ap-3488	161	3	signed	sign	VERB
ap-3488	161	4	:	:	PUNCT
ap-3488	161	5	when	when	SCONJ
ap-3488	161	6	the	the	DET
ap-3488	161	7	robot	robot	NOUN
ap-3488	161	8	is	be	AUX
ap-3488	161	9	located	locate	VERB
ap-3488	161	10	in	in	ADP
ap-3488	161	11	the	the	DET
ap-3488	161	12	lower	low	ADJ
ap-3488	161	13	half	half	ADJ
ap-3488	161	14	-	-	PUNCT
ap-3488	161	15	plane	plane	NOUN
ap-3488	161	16	,	,	PUNCT
ap-3488	161	17	r	r	NOUN
ap-3488	161	18	=	=	SYM
ap-3488	161	19	−|r|	−|r|	NOUN
ap-3488	161	20	and	and	CCONJ
ap-3488	161	21	thus	thus	ADV
ap-3488	161	22	the	the	DET
ap-3488	161	23	angle	angle	NOUN
ap-3488	161	24	α	α	PROPN
ap-3488	161	25	is	be	AUX
ap-3488	161	26	also	also	ADV
ap-3488	161	27	a	a	DET
ap-3488	161	28	θ	θ	PROPN
ap-3488	161	29	b	b	NOUN
ap-3488	161	30	o′	o′	PROPN
ap-3488	161	31	x′	x′	PROPN
ap-3488	161	32	y′	y′	NOUN
ap-3488	161	33	pr	pr	X
ap-3488	161	34	φ	φ	PROPN
ap-3488	161	35	l	l	PROPN
ap-3488	161	36	p′	p′	PROPN
ap-3488	161	37	b′	b′	NUM
ap-3488	161	38	o″	o″	ADV
ap-3488	161	39	β	β	X
ap-3488	161	40	α	α	X
ap-3488	161	41	ψ	ψ	X
ap-3488	161	42	d	d	X
ap-3488	161	43	_	_	PRON
ap-3488	161	44	figure	figure	NOUN
ap-3488	162	1	2	2	NUM
ap-3488	162	2	.	.	PUNCT
ap-3488	162	3	geometrical	geometrical	ADJ
ap-3488	162	4	relations	relation	NOUN
ap-3488	162	5	between	between	ADP
ap-3488	162	6	the	the	DET
ap-3488	162	7	robot	robot	NOUN
ap-3488	162	8	actual	actual	ADJ
ap-3488	162	9	configuration	configuration	NOUN
ap-3488	162	10	and	and	CCONJ
ap-3488	162	11	the	the	DET
ap-3488	162	12	desired	desire	VERB
ap-3488	162	13	configuration	configuration	NOUN
ap-3488	162	14	.	.	PUNCT
ap-3488	163	1	negative	negative	ADJ
ap-3488	163	2	.	.	PUNCT
ap-3488	164	1	the	the	DET
ap-3488	164	2	coordinate	coordinate	NOUN
ap-3488	164	3	r	r	NOUN
ap-3488	164	4	is	be	AUX
ap-3488	164	5	determined	determine	VERB
ap-3488	164	6	according	accord	VERB
ap-3488	164	7	to	to	ADP
ap-3488	164	8	the	the	DET
ap-3488	164	9	following	follow	VERB
ap-3488	164	10	rules:	rules:	PROPN
ap-3488	164	11	r	r	NOUN
ap-3488	164	12	is	be	AUX
ap-3488	164	13	chosen	choose	VERB
ap-3488	164	14	arbitrarily	arbitrarily	ADV
ap-3488	164	15	without	without	ADP
ap-3488	164	16	changing	change	VERB
ap-3488	164	17	sign	sign	NOUN
ap-3488	164	18	if	if	SCONJ
ap-3488	164	19	|r|	|r|	DET
ap-3488	164	20	≤	≤	X
ap-3488	164	21	l/2	l/2	NUM
ap-3488	164	22	,	,	PUNCT
ap-3488	165	1	r	r	NOUN
ap-3488	165	2	=	=	PUNCT
ap-3488	165	3	−y+sgn	−y+sgn	NOUN
ap-3488	165	4	y	y	NOUN
ap-3488	165	5	√	√	PROPN
ap-3488	165	6	4y2	4y2	VERB
ap-3488	165	7	+	+	PROPN
ap-3488	165	8	3x2	3x2	NUM
ap-3488	165	9	3	3	NUM
ap-3488	165	10	if	if	SCONJ
ap-3488	165	11	|r|	|r|	PROPN
ap-3488	165	12	>	>	X
ap-3488	165	13	l/2	l/2	PROPN
ap-3488	165	14	,	,	PUNCT
ap-3488	165	15	(	(	PUNCT
ap-3488	165	16	12	12	NUM
ap-3488	165	17	)	)	PUNCT
ap-3488	165	18	where	where	SCONJ
ap-3488	165	19	the	the	DET
ap-3488	165	20	function	function	NOUN
ap-3488	165	21	“	"	PUNCT
ap-3488	165	22	sgn	sgn	NOUN
ap-3488	165	23	”	"	PUNCT
ap-3488	165	24	is	be	AUX
ap-3488	165	25	defined	define	VERB
ap-3488	165	26	as	as	ADP
ap-3488	165	27	:	:	PUNCT
ap-3488	165	28	sgn	sgn	NOUN
ap-3488	165	29	x	x	SYM
ap-3488	165	30	=	=	NOUN
ap-3488	165	31	{	{	PUNCT
ap-3488	165	32	1	1	NUM
ap-3488	165	33	,	,	PUNCT
ap-3488	165	34	x	x	X
ap-3488	165	35	≥	≥	NOUN
ap-3488	165	36	0	0	NUM
ap-3488	165	37	,	,	PUNCT
ap-3488	165	38	−1	−1	NOUN
ap-3488	165	39	,	,	PUNCT
ap-3488	165	40	x	x	X
ap-3488	165	41	<	<	X
ap-3488	165	42	0	0	X
ap-3488	165	43	.	.	PUNCT
ap-3488	166	1	we	we	PRON
ap-3488	166	2	denote	denote	VERB
ap-3488	166	3	β	β	X
ap-3488	166	4	=	=	X
ap-3488	166	5	arcsin	arcsin	PROPN
ap-3488	166	6	sin	sin	PROPN
ap-3488	166	7	β̄	β̄	PROPN
ap-3488	166	8	,	,	PUNCT
ap-3488	166	9	then	then	ADV
ap-3488	166	10	the	the	DET
ap-3488	166	11	local	local	ADJ
ap-3488	166	12	control	control	NOUN
ap-3488	166	13	law	law	NOUN
ap-3488	166	14	is	be	AUX
ap-3488	166	15	proposed	propose	VERB
ap-3488	166	16	as	as	SCONJ
ap-3488	166	17	follows	follow	VERB
ap-3488	166	18	:	:	PUNCT
ap-3488	166	19	{	{	PUNCT
ap-3488	166	20	u	u	NOUN
ap-3488	166	21	=	=	NOUN
ap-3488	166	22	−	−	PROPN
ap-3488	166	23	sgn	sgn	NOUN
ap-3488	166	24	cos	cos	PROPN
ap-3488	166	25	β̄λl	β̄λl	PROPN
ap-3488	166	26	ω	ω	PROPN
ap-3488	167	1	=	=	SYM
ap-3488	167	2	u	u	SYM
ap-3488	167	3	|r|	|r|	NOUN
ap-3488	167	4	(	(	PUNCT
ap-3488	167	5	β	β	NOUN
ap-3488	167	6	−	−	NOUN
ap-3488	167	7	α	α	NOUN
ap-3488	167	8	)	)	PUNCT
ap-3488	167	9	(	(	PUNCT
ap-3488	167	10	13	13	NUM
ap-3488	167	11	)	)	PUNCT
ap-3488	167	12	where	where	SCONJ
ap-3488	167	13	λ	λ	PROPN
ap-3488	167	14	is	be	AUX
ap-3488	167	15	a	a	DET
ap-3488	167	16	positive	positive	ADJ
ap-3488	167	17	constant	constant	NOUN
ap-3488	167	18	.	.	PUNCT
ap-3488	168	1	from	from	ADP
ap-3488	168	2	the	the	DET
ap-3488	168	3	proposed	propose	VERB
ap-3488	168	4	law	law	NOUN
ap-3488	168	5	,	,	PUNCT
ap-3488	168	6	we	we	PRON
ap-3488	168	7	have	have	VERB
ap-3488	168	8	ui	ui	NOUN
ap-3488	168	9	and	and	CCONJ
ap-3488	168	10	ωi	ωi	NOUN
ap-3488	168	11	,	,	PUNCT
ap-3488	168	12	then	then	ADV
ap-3488	168	13	the	the	DET
ap-3488	168	14	control	control	NOUN
ap-3488	168	15	input	input	NOUN
ap-3488	168	16	matrix	matrix	NOUN
ap-3488	168	17	of	of	ADP
ap-3488	168	18	robot	robot	NOUN
ap-3488	168	19	i	i	PRON
ap-3488	168	20	is	be	AUX
ap-3488	168	21	obtained	obtain	VERB
ap-3488	168	22	from	from	ADP
ap-3488	168	23	equation	equation	NOUN
ap-3488	168	24	6	6	NUM
ap-3488	168	25	.	.	NOUN
ap-3488	168	26	3.2	3.2	NUM
ap-3488	168	27	.	.	PUNCT
ap-3488	169	1	stability	stability	NOUN
ap-3488	169	2	analysis	analysis	NOUN
ap-3488	169	3	from	from	ADP
ap-3488	169	4	the	the	DET
ap-3488	169	5	previous	previous	ADJ
ap-3488	169	6	section	section	NOUN
ap-3488	169	7	,	,	PUNCT
ap-3488	169	8	we	we	PRON
ap-3488	169	9	know	know	VERB
ap-3488	169	10	that	that	SCONJ
ap-3488	169	11	g̃ii	g̃ii	PROPN
ap-3488	169	12	is	be	AUX
ap-3488	169	13	the	the	DET
ap-3488	169	14	representation	representation	NOUN
ap-3488	169	15	of	of	ADP
ap-3488	169	16	ḡi	ḡi	PROPN
ap-3488	169	17	in	in	ADP
ap-3488	169	18	frame	frame	NOUN
ap-3488	169	19	gi	gi	NOUN
ap-3488	169	20	,	,	PUNCT
ap-3488	169	21	while	while	SCONJ
ap-3488	169	22	its	its	PRON
ap-3488	169	23	inverse	inverse	NOUN
ap-3488	169	24	g̃−1	g̃−1	PROPN
ap-3488	169	25	ii	ii	PROPN
ap-3488	169	26	is	be	AUX
ap-3488	169	27	the	the	DET
ap-3488	169	28	representation	representation	NOUN
ap-3488	169	29	of	of	ADP
ap-3488	169	30	gi	gi	NOUN
ap-3488	169	31	in	in	ADP
ap-3488	169	32	frame	frame	PROPN
ap-3488	169	33	ḡi	ḡi	PROPN
ap-3488	169	34	.	.	PUNCT
ap-3488	170	1	to	to	PART
ap-3488	170	2	explain	explain	VERB
ap-3488	170	3	the	the	DET
ap-3488	170	4	convergence	convergence	NOUN
ap-3488	170	5	of	of	ADP
ap-3488	170	6	gi	gi	NOUN
ap-3488	170	7	to	to	PART
ap-3488	170	8	ḡi	ḡi	VERB
ap-3488	170	9	,	,	PUNCT
ap-3488	170	10	we	we	PRON
ap-3488	170	11	just	just	ADV
ap-3488	170	12	need	need	VERB
ap-3488	170	13	to	to	PART
ap-3488	170	14	prove	prove	VERB
ap-3488	170	15	that	that	SCONJ
ap-3488	170	16	ḡ−1	ḡ−1	PROPN
ap-3488	170	17	ii	ii	PROPN
ap-3488	170	18	converges	converge	VERB
ap-3488	170	19	to	to	ADP
ap-3488	170	20	the	the	DET
ap-3488	170	21	origin	origin	NOUN
ap-3488	170	22	,	,	PUNCT
ap-3488	170	23	which	which	PRON
ap-3488	170	24	is	be	AUX
ap-3488	170	25	also	also	ADV
ap-3488	170	26	the	the	DET
ap-3488	170	27	identity	identity	NOUN
ap-3488	170	28	matrix	matrix	NOUN
ap-3488	170	29	i.	i.	NOUN
ap-3488	170	30	to	to	PART
ap-3488	170	31	prove	prove	VERB
ap-3488	170	32	this	this	PRON
ap-3488	170	33	,	,	PUNCT
ap-3488	170	34	with	with	ADP
ap-3488	170	35	the	the	DET
ap-3488	170	36	help	help	NOUN
ap-3488	170	37	of	of	ADP
ap-3488	170	38	the	the	DET
ap-3488	170	39	notations	notation	NOUN
ap-3488	170	40	depicted	depict	VERB
ap-3488	170	41	in	in	ADP
ap-3488	170	42	figure	figure	NOUN
ap-3488	170	43	2	2	NUM
ap-3488	170	44	,	,	PUNCT
ap-3488	170	45	we	we	PRON
ap-3488	170	46	will	will	AUX
ap-3488	170	47	divide	divide	VERB
ap-3488	170	48	the	the	DET
ap-3488	170	49	movement	movement	NOUN
ap-3488	170	50	of	of	ADP
ap-3488	170	51	each	each	DET
ap-3488	170	52	robot	robot	NOUN
ap-3488	170	53	into	into	ADP
ap-3488	170	54	three	three	NUM
ap-3488	170	55	phases	phase	NOUN
ap-3488	170	56	.	.	PUNCT
ap-3488	171	1	phase	phase	NOUN
ap-3488	171	2	1	1	NUM
ap-3488	171	3	.	.	PUNCT
ap-3488	172	1	l	l	NOUN
ap-3488	172	2	≥	≥	NUM
ap-3488	172	3	2|r|	2|r|	NUM
ap-3488	172	4	,	,	PUNCT
ap-3488	172	5	β	β	X
ap-3488	172	6	−	−	PROPN
ap-3488	172	7	α	α	PROPN
ap-3488	172	8	6=	6=	PROPN
ap-3488	172	9	0	0	NUM
ap-3488	172	10	.	.	PUNCT
ap-3488	173	1	lemma	lemma	PROPN
ap-3488	173	2	1	1	NUM
ap-3488	173	3	.	.	PUNCT
ap-3488	174	1	if	if	SCONJ
ap-3488	174	2	we	we	PRON
ap-3488	174	3	choose	choose	VERB
ap-3488	174	4	a	a	DET
ap-3488	174	5	convenient	convenient	ADJ
ap-3488	174	6	r	r	NOUN
ap-3488	174	7	which	which	PRON
ap-3488	174	8	satisfies	satisfy	VERB
ap-3488	174	9	l	l	PROPN
ap-3488	174	10	≥	≥	X
ap-3488	174	11	2|r|	2|r|	NUM
ap-3488	174	12	,	,	PUNCT
ap-3488	174	13	then	then	ADV
ap-3488	174	14	the	the	DET
ap-3488	174	15	angle	angle	NOUN
ap-3488	174	16	between	between	ADP
ap-3488	174	17	the	the	DET
ap-3488	174	18	direction	direction	NOUN
ap-3488	174	19	of	of	ADP
ap-3488	174	20	movement	movement	NOUN
ap-3488	174	21	and	and	CCONJ
ap-3488	174	22	one	one	NUM
ap-3488	174	23	tangent	tangent	NOUN
ap-3488	174	24	of	of	ADP
ap-3488	174	25	the	the	DET
ap-3488	174	26	circle	circle	NOUN
ap-3488	174	27	cb	cb	PROPN
ap-3488	174	28	converges	converge	VERB
ap-3488	174	29	to	to	ADP
ap-3488	174	30	0	0	NUM
ap-3488	174	31	,	,	PUNCT
ap-3488	174	32	that	that	PRON
ap-3488	174	33	is	be	AUX
ap-3488	174	34	δ	δ	PROPN
ap-3488	174	35	=	=	PRON
ap-3488	174	36	|β	|β	VERB
ap-3488	174	37	−	−	PROPN
ap-3488	174	38	α|	α|	PROPN
ap-3488	174	39	→	→	X
ap-3488	174	40	0	0	NUM
ap-3488	174	41	.	.	NOUN
ap-3488	174	42	4	4	NUM
ap-3488	174	43	vol	vol	NOUN
ap-3488	174	44	.	.	PUNCT
ap-3488	175	1	56	56	NUM
ap-3488	175	2	no	no	NOUN
ap-3488	175	3	.	.	PUNCT
ap-3488	176	1	1/2016	1/2016	NUM
ap-3488	176	2	formation	formation	NOUN
ap-3488	176	3	control	control	NOUN
ap-3488	176	4	of	of	ADP
ap-3488	176	5	multiple	multiple	ADJ
ap-3488	176	6	unicycle	unicycle	NOUN
ap-3488	176	7	-	-	PUNCT
ap-3488	176	8	type	type	NOUN
ap-3488	176	9	robots	robot	NOUN
ap-3488	176	10	using	use	VERB
ap-3488	176	11	lie	lie	NOUN
ap-3488	176	12	group	group	NOUN
ap-3488	176	13	proof	proof	NOUN
ap-3488	176	14	.	.	PUNCT
ap-3488	177	1	if	if	SCONJ
ap-3488	177	2	r	r	NOUN
ap-3488	177	3	>	>	X
ap-3488	177	4	0	0	NUM
ap-3488	177	5	,	,	PUNCT
ap-3488	177	6	we	we	PRON
ap-3488	177	7	have	have	VERB
ap-3488	177	8	δ	δ	PROPN
ap-3488	177	9	=	=	PRON
ap-3488	177	10	|β	|β	VERB
ap-3488	177	11	−	−	PROPN
ap-3488	177	12	α|	α|	NOUN
ap-3488	177	13	=	=	NOUN
ap-3488	178	1	√	√	PROPN
ap-3488	178	2	(	(	PUNCT
ap-3488	178	3	β	β	X
ap-3488	178	4	−	−	NOUN
ap-3488	178	5	α)2	α)2	NOUN
ap-3488	178	6	,	,	PUNCT
ap-3488	178	7	then	then	ADV
ap-3488	178	8	δ̇	δ̇	X
ap-3488	178	9	=	=	PUNCT
ap-3488	178	10	β	β	NOUN
ap-3488	178	11	−	−	NUM
ap-3488	179	1	α√	α√	PROPN
ap-3488	179	2	(	(	PUNCT
ap-3488	179	3	β	β	X
ap-3488	179	4	−	−	NOUN
ap-3488	179	5	α)2	α)2	NOUN
ap-3488	179	6	(	(	PUNCT
ap-3488	179	7	β̇	β̇	NOUN
ap-3488	179	8	−	−	PROPN
ap-3488	179	9	α̇	α̇	NOUN
ap-3488	179	10	)	)	PUNCT
ap-3488	179	11	=	=	SYM
ap-3488	180	1	sgn(β	sgn(β	PROPN
ap-3488	180	2	−	−	PROPN
ap-3488	180	3	α)(β̇	α)(β̇	NOUN
ap-3488	180	4	−	−	PROPN
ap-3488	180	5	α̇	α̇	NOUN
ap-3488	180	6	)	)	PUNCT
ap-3488	180	7	.	.	PUNCT
ap-3488	181	1	because	because	SCONJ
ap-3488	181	2	β	β	X
ap-3488	181	3	=	=	PUNCT
ap-3488	181	4	arcsin	arcsin	PROPN
ap-3488	181	5	sin	sin	PROPN
ap-3488	181	6	β̄	β̄	PROPN
ap-3488	182	1	=	=	SYM
ap-3488	182	2	arcsin	arcsin	PROPN
ap-3488	182	3	sin	sin	NOUN
ap-3488	182	4	θ	θ	PROPN
ap-3488	182	5	−	−	PROPN
ap-3488	183	1	ϕ	ϕ	NOUN
ap-3488	183	2	,	,	PUNCT
ap-3488	183	3	so	so	ADV
ap-3488	183	4	β̇	β̇	NOUN
ap-3488	183	5	=	=	SYM
ap-3488	183	6	1	1	NUM
ap-3488	183	7	1−	1−	NUM
ap-3488	183	8	sin2(θ	sin2(θ	VERB
ap-3488	183	9	−	−	PROPN
ap-3488	183	10	ϕ	ϕ	NOUN
ap-3488	183	11	)	)	PUNCT
ap-3488	183	12	cos(θ	cos(θ	VERB
ap-3488	183	13	−	−	PROPN
ap-3488	183	14	ϕ	ϕ	NOUN
ap-3488	183	15	)	)	PUNCT
ap-3488	183	16	(	(	PUNCT
ap-3488	183	17	θ̇	θ̇	ADV
ap-3488	183	18	−	−	NOUN
ap-3488	183	19	ϕ̇	ϕ̇	NOUN
ap-3488	183	20	)	)	PUNCT
ap-3488	183	21	=	=	SYM
ap-3488	183	22	sgn	sgn	NOUN
ap-3488	183	23	cos	cos	PROPN
ap-3488	183	24	β̄	β̄	PROPN
ap-3488	184	1	(	(	PUNCT
ap-3488	184	2	θ̇	θ̇	DET
ap-3488	184	3	−	−	NOUN
ap-3488	184	4	ϕ̇	ϕ̇	NOUN
ap-3488	184	5	)	)	PUNCT
ap-3488	184	6	.	.	PUNCT
ap-3488	185	1	consider	consider	VERB
ap-3488	185	2	the	the	DET
ap-3488	185	3	coordinate	coordinate	ADJ
ap-3488	185	4	transformation	transformation	NOUN
ap-3488	185	5	into	into	ADP
ap-3488	185	6	polar	polar	ADJ
ap-3488	185	7	coordinates	coordinate	NOUN
ap-3488	185	8	,	,	PUNCT
ap-3488	185	9	we	we	PRON
ap-3488	185	10	have	have	VERB
ap-3488	185	11	ϕ̇	ϕ̇	PRON
ap-3488	185	12	=	=	SYM
ap-3488	185	13	u	u	NOUN
ap-3488	185	14	sin	sin	VERB
ap-3488	185	15	β	β	NOUN
ap-3488	185	16	/	/	SYM
ap-3488	185	17	l	l	NOUN
ap-3488	185	18	and	and	CCONJ
ap-3488	185	19	l̇	l̇	PROPN
ap-3488	185	20	=	=	SYM
ap-3488	185	21	u	u	PROPN
ap-3488	185	22	cosβ	cosβ	NOUN
ap-3488	185	23	.	.	PUNCT
ap-3488	186	1	we	we	PRON
ap-3488	186	2	distinguish	distinguish	VERB
ap-3488	186	3	three	three	NUM
ap-3488	186	4	cases	case	NOUN
ap-3488	186	5	:	:	PUNCT
ap-3488	186	6	(	(	PUNCT
ap-3488	186	7	1	1	NUM
ap-3488	186	8	.	.	PUNCT
ap-3488	186	9	)	)	PUNCT
ap-3488	186	10	case	case	NOUN
ap-3488	186	11	β̄	β̄	NOUN
ap-3488	187	1	∈	∈	PROPN
ap-3488	188	1	[	[	X
ap-3488	188	2	−π2	−π2	NOUN
ap-3488	188	3	,	,	PUNCT
ap-3488	188	4	π	π	PROPN
ap-3488	188	5	2	2	NUM
ap-3488	188	6	]	]	PUNCT
ap-3488	188	7	.	.	PUNCT
ap-3488	189	1	in	in	ADP
ap-3488	189	2	this	this	DET
ap-3488	189	3	case	case	NOUN
ap-3488	189	4	,	,	PUNCT
ap-3488	189	5	the	the	DET
ap-3488	189	6	control	control	NOUN
ap-3488	189	7	law	law	NOUN
ap-3488	189	8	is	be	AUX
ap-3488	189	9	u	u	NOUN
ap-3488	189	10	=	=	PROPN
ap-3488	189	11	−λl	−λl	PROPN
ap-3488	189	12	,	,	PUNCT
ap-3488	189	13	ω	ω	X
ap-3488	189	14	=	=	NOUN
ap-3488	189	15	−λl(β	−λl(β	PROPN
ap-3488	189	16	−	−	PROPN
ap-3488	189	17	α)/r	α)/r	PROPN
ap-3488	189	18	.	.	PUNCT
ap-3488	190	1	and	and	CCONJ
ap-3488	190	2	sinα	sinα	NOUN
ap-3488	190	3	=	=	SYM
ap-3488	190	4	r	r	NOUN
ap-3488	190	5	l	l	NOUN
ap-3488	190	6	⇒	⇒	NOUN
ap-3488	190	7	α̇	α̇	NOUN
ap-3488	191	1	=	=	SYM
ap-3488	192	1	−	−	PROPN
ap-3488	192	2	rl̇	rl̇	NOUN
ap-3488	192	3	l2	l2	NOUN
ap-3488	192	4	cosα	cosα	NOUN
ap-3488	192	5	=	=	NOUN
ap-3488	192	6	λr	λr	NOUN
ap-3488	192	7	cosβ	cosβ	NOUN
ap-3488	192	8	l	l	NOUN
ap-3488	192	9	cosα	cosα	NOUN
ap-3488	193	1	=	=	SYM
ap-3488	193	2	λ	λ	PROPN
ap-3488	193	3	cosβ	cosβ	NOUN
ap-3488	193	4	tanα	tanα	VERB
ap-3488	193	5	.	.	PUNCT
ap-3488	194	1	then	then	ADV
ap-3488	194	2	we	we	PRON
ap-3488	194	3	have	have	VERB
ap-3488	194	4	δ̇	δ̇	X
ap-3488	194	5	=	=	SYM
ap-3488	194	6	sgn(β	sgn(β	PROPN
ap-3488	194	7	−	−	PROPN
ap-3488	194	8	α	α	NOUN
ap-3488	194	9	)	)	PUNCT
ap-3488	194	10	(	(	PUNCT
ap-3488	194	11	ω	ω	NUM
ap-3488	194	12	−	−	NOUN
ap-3488	194	13	u	u	NOUN
ap-3488	194	14	sin	sin	NOUN
ap-3488	194	15	β	β	X
ap-3488	194	16	l	l	NOUN
ap-3488	194	17	−	−	PROPN
ap-3488	195	1	λ	λ	INTJ
ap-3488	195	2	cosβ	cosβ	NOUN
ap-3488	195	3	tanα	tanα	VERB
ap-3488	195	4	)	)	PUNCT
ap-3488	196	1	=	=	SYM
ap-3488	196	2	sgn(β	sgn(β	PROPN
ap-3488	196	3	−	−	NOUN
ap-3488	196	4	α)λ	α)λ	NOUN
ap-3488	197	1	[	[	PUNCT
ap-3488	197	2	−	−	PUNCT
ap-3488	197	3	l	l	NOUN
ap-3488	197	4	r	r	NOUN
ap-3488	197	5	(	(	PUNCT
ap-3488	197	6	β	β	NOUN
ap-3488	197	7	−	−	NOUN
ap-3488	197	8	α	α	NOUN
ap-3488	197	9	)	)	PUNCT
ap-3488	197	10	+	+	CCONJ
ap-3488	197	11	sin	sin	NOUN
ap-3488	197	12	β	β	X
ap-3488	197	13	−	−	PROPN
ap-3488	197	14	cosβ	cosβ	NOUN
ap-3488	197	15	tanα	tanα	VERB
ap-3488	197	16	]	]	PUNCT
ap-3488	197	17	.	.	PUNCT
ap-3488	198	1	suppose	suppose	VERB
ap-3488	198	2	eβ	eβ	NOUN
ap-3488	198	3	=	=	PUNCT
ap-3488	198	4	−	−	PROPN
ap-3488	198	5	l	l	NOUN
ap-3488	198	6	r	r	NOUN
ap-3488	198	7	(	(	PUNCT
ap-3488	198	8	β	β	NOUN
ap-3488	198	9	−	−	NOUN
ap-3488	198	10	α	α	NOUN
ap-3488	198	11	)	)	PUNCT
ap-3488	199	1	+	+	CCONJ
ap-3488	199	2	sin	sin	NOUN
ap-3488	199	3	β	β	X
ap-3488	199	4	−	−	PROPN
ap-3488	199	5	cosβ	cosβ	NOUN
ap-3488	199	6	tanα	tanα	VERB
ap-3488	199	7	.	.	PUNCT
ap-3488	200	1	because	because	SCONJ
ap-3488	200	2	sinα	sinα	NOUN
ap-3488	200	3	=	=	SYM
ap-3488	200	4	r	r	NOUN
ap-3488	200	5	/	/	SYM
ap-3488	200	6	l	l	NOUN
ap-3488	200	7	and	and	CCONJ
ap-3488	200	8	l	l	NOUN
ap-3488	200	9	≥	≥	NUM
ap-3488	200	10	2r	2r	NUM
ap-3488	200	11	,	,	PUNCT
ap-3488	200	12	so	so	ADV
ap-3488	200	13	deβ	deβ	VERB
ap-3488	200	14	dβ	dβ	ADP
ap-3488	200	15	<	<	X
ap-3488	200	16	0	0	NUM
ap-3488	200	17	.	.	PUNCT
ap-3488	201	1	then	then	ADV
ap-3488	201	2	we	we	PRON
ap-3488	201	3	can	can	AUX
ap-3488	201	4	say	say	VERB
ap-3488	201	5	that	that	SCONJ
ap-3488	201	6	eβ	eβ	NOUN
ap-3488	201	7	is	be	AUX
ap-3488	201	8	a	a	DET
ap-3488	201	9	monotonically	monotonically	ADV
ap-3488	201	10	decreasing	decrease	VERB
ap-3488	201	11	function	function	NOUN
ap-3488	201	12	about	about	ADP
ap-3488	201	13	β	β	NOUN
ap-3488	201	14	,	,	PUNCT
ap-3488	201	15	and	and	CCONJ
ap-3488	201	16	β	β	X
ap-3488	201	17	=	=	PUNCT
ap-3488	201	18	α	α	PROPN
ap-3488	201	19	is	be	AUX
ap-3488	201	20	the	the	DET
ap-3488	201	21	unique	unique	ADJ
ap-3488	201	22	zero	zero	NUM
ap-3488	201	23	value	value	NOUN
ap-3488	201	24	point	point	NOUN
ap-3488	201	25	of	of	ADP
ap-3488	201	26	eβ	eβ	NOUN
ap-3488	201	27	.	.	PUNCT
ap-3488	202	1	hence	hence	ADV
ap-3488	202	2	:	:	PUNCT
ap-3488	202	3	•	•	INTJ
ap-3488	202	4	if	if	SCONJ
ap-3488	202	5	−π2	−π2	VERB
ap-3488	202	6	≤	≤	NOUN
ap-3488	202	7	β	β	X
ap-3488	202	8	<	<	X
ap-3488	202	9	α	α	PROPN
ap-3488	202	10	,	,	PUNCT
ap-3488	202	11	then	then	ADV
ap-3488	202	12	eβ	eβ	VERB
ap-3488	202	13	>	>	X
ap-3488	202	14	0	0	PROPN
ap-3488	202	15	,	,	PUNCT
ap-3488	202	16	β	β	X
ap-3488	202	17	−	−	PROPN
ap-3488	202	18	α	α	PROPN
ap-3488	202	19	<	<	X
ap-3488	202	20	0	0	NUM
ap-3488	202	21	and	and	CCONJ
ap-3488	202	22	δ̇	δ̇	X
ap-3488	202	23	≤	≤	ADJ
ap-3488	202	24	0	0	NUM
ap-3488	202	25	;	;	PUNCT
ap-3488	202	26	•	•	NUM
ap-3488	202	27	if	if	SCONJ
ap-3488	202	28	α	α	NOUN
ap-3488	202	29	≤	≤	X
ap-3488	202	30	β	β	X
ap-3488	202	31	≤	≤	NUM
ap-3488	202	32	π	π	PROPN
ap-3488	202	33	2	2	NUM
ap-3488	202	34	,	,	PUNCT
ap-3488	202	35	then	then	ADV
ap-3488	202	36	eβ	eβ	VERB
ap-3488	202	37	≤	≤	NUM
ap-3488	202	38	0	0	NUM
ap-3488	202	39	,	,	PUNCT
ap-3488	202	40	β	β	X
ap-3488	202	41	−	−	PROPN
ap-3488	202	42	α	α	X
ap-3488	202	43	>	>	X
ap-3488	202	44	0	0	PUNCT
ap-3488	202	45	and	and	CCONJ
ap-3488	202	46	δ̇	δ̇	X
ap-3488	202	47	≤	≤	ADJ
ap-3488	202	48	0	0	NUM
ap-3488	202	49	.	.	PUNCT
ap-3488	203	1	so	so	ADV
ap-3488	203	2	δ	δ	PROPN
ap-3488	203	3	converges	converge	VERB
ap-3488	203	4	monotonically	monotonically	ADV
ap-3488	203	5	to	to	ADP
ap-3488	203	6	0	0	NUM
ap-3488	203	7	.	.	PUNCT
ap-3488	204	1	(	(	PUNCT
ap-3488	204	2	2	2	NUM
ap-3488	204	3	.	.	PUNCT
ap-3488	204	4	)	)	PUNCT
ap-3488	205	1	case	case	NOUN
ap-3488	205	2	β̄	β̄	NOUN
ap-3488	205	3	∈	∈	PROPN
ap-3488	205	4	(	(	PUNCT
ap-3488	205	5	π2	π2	X
ap-3488	205	6	,	,	PUNCT
ap-3488	205	7	π	π	PROPN
ap-3488	205	8	]	]	X
ap-3488	205	9	.	.	PUNCT
ap-3488	206	1	we	we	PRON
ap-3488	206	2	have	have	VERB
ap-3488	206	3	β	β	NOUN
ap-3488	206	4	=	=	PUNCT
ap-3488	207	1	π−	π−	NOUN
ap-3488	207	2	β̄	β̄	PROPN
ap-3488	207	3	∈	∈	PROPN
ap-3488	207	4	(	(	PUNCT
ap-3488	207	5	0	0	NUM
ap-3488	207	6	,	,	PUNCT
ap-3488	207	7	π2	π2	NOUN
ap-3488	207	8	]	]	PUNCT
ap-3488	207	9	,	,	PUNCT
ap-3488	207	10	and	and	CCONJ
ap-3488	207	11	the	the	DET
ap-3488	207	12	control	control	NOUN
ap-3488	207	13	law	law	NOUN
ap-3488	207	14	is	be	AUX
ap-3488	207	15	u	u	NOUN
ap-3488	207	16	=	=	SYM
ap-3488	207	17	λl	λl	PROPN
ap-3488	207	18	,	,	PUNCT
ap-3488	207	19	ω	ω	NOUN
ap-3488	207	20	=	=	SYM
ap-3488	207	21	λl	λl	VERB
ap-3488	207	22	r	r	NOUN
ap-3488	207	23	(	(	PUNCT
ap-3488	207	24	π	π	PROPN
ap-3488	207	25	−	−	PROPN
ap-3488	207	26	β̄	β̄	NOUN
ap-3488	207	27	−	−	PROPN
ap-3488	207	28	α	α	NOUN
ap-3488	207	29	)	)	PUNCT
ap-3488	207	30	.	.	PUNCT
ap-3488	208	1	in	in	ADP
ap-3488	208	2	this	this	DET
ap-3488	208	3	case	case	NOUN
ap-3488	208	4	,	,	PUNCT
ap-3488	208	5	we	we	PRON
ap-3488	208	6	get	get	VERB
ap-3488	208	7	δ̇	δ̇	NOUN
ap-3488	208	8	=	=	SYM
ap-3488	208	9	sgn(β	sgn(β	PROPN
ap-3488	208	10	−	−	NOUN
ap-3488	208	11	α)λ	α)λ	NOUN
ap-3488	208	12	[	[	PUNCT
ap-3488	208	13	sgn	sgn	NOUN
ap-3488	208	14	cos	cos	PROPN
ap-3488	208	15	β̄	β̄	PROPN
ap-3488	209	1	(	(	PUNCT
ap-3488	209	2	l	l	NOUN
ap-3488	209	3	r	r	NOUN
ap-3488	209	4	(	(	PUNCT
ap-3488	209	5	π	π	PROPN
ap-3488	209	6	−	−	PROPN
ap-3488	209	7	β̄	β̄	NOUN
ap-3488	209	8	−	−	PROPN
ap-3488	209	9	α	α	X
ap-3488	209	10	)	)	PUNCT
ap-3488	209	11	−	−	PROPN
ap-3488	209	12	sin	sin	NOUN
ap-3488	209	13	β̄	β̄	NOUN
ap-3488	209	14	)	)	PUNCT
ap-3488	210	1	+	+	CCONJ
ap-3488	210	2	cos	cos	PROPN
ap-3488	210	3	β̄	β̄	ADJ
ap-3488	210	4	tanα	tanα	PROPN
ap-3488	210	5	]	]	PUNCT
ap-3488	210	6	.	.	PUNCT
ap-3488	211	1	suppose	suppose	VERB
ap-3488	211	2	eβ	eβ	NOUN
ap-3488	211	3	=	=	SYM
ap-3488	211	4	sgn	sgn	NOUN
ap-3488	211	5	cos	cos	PROPN
ap-3488	211	6	β̄	β̄	PROPN
ap-3488	211	7	[	[	PUNCT
ap-3488	211	8	lr	lr	X
ap-3488	211	9	(	(	PUNCT
ap-3488	211	10	π	π	PROPN
ap-3488	211	11	−	−	PROPN
ap-3488	211	12	β̄	β̄	NOUN
ap-3488	211	13	−	−	PROPN
ap-3488	211	14	α	α	X
ap-3488	211	15	)	)	PUNCT
ap-3488	211	16	−	−	PROPN
ap-3488	211	17	sin	sin	NOUN
ap-3488	211	18	β̄	β̄	X
ap-3488	211	19	]	]	PUNCT
ap-3488	212	1	+	+	CCONJ
ap-3488	212	2	cos	cos	PROPN
ap-3488	212	3	β̄	β̄	PROPN
ap-3488	212	4	tanα	tanα	NOUN
ap-3488	212	5	,	,	PUNCT
ap-3488	212	6	then	then	ADV
ap-3488	212	7	deβ	deβ	VERB
ap-3488	212	8	dβ	dβ	ADJ
ap-3488	212	9	=	=	NOUN
ap-3488	212	10	−	−	PROPN
ap-3488	212	11	l	l	NOUN
ap-3488	212	12	r	r	NOUN
ap-3488	212	13	+	+	NUM
ap-3488	212	14	cosβ	cosβ	NOUN
ap-3488	212	15	+	+	CCONJ
ap-3488	212	16	sin	sin	NOUN
ap-3488	212	17	β	β	AUX
ap-3488	212	18	tanα	tanα	NOUN
ap-3488	212	19	<	<	X
ap-3488	212	20	0	0	NUM
ap-3488	212	21	.	.	PUNCT
ap-3488	213	1	α	α	X
ap-3488	213	2	=	=	X
ap-3488	214	1	β	β	X
ap-3488	214	2	=	=	PUNCT
ap-3488	215	1	π	π	NOUN
ap-3488	215	2	−	−	NOUN
ap-3488	215	3	β̄	β̄	NOUN
ap-3488	215	4	is	be	AUX
ap-3488	215	5	the	the	DET
ap-3488	215	6	equilibrium	equilibrium	NOUN
ap-3488	215	7	point	point	NOUN
ap-3488	215	8	of	of	ADP
ap-3488	215	9	eβ	eβ	NOUN
ap-3488	215	10	,	,	PUNCT
ap-3488	215	11	so	so	ADV
ap-3488	215	12	δ	δ	PROPN
ap-3488	215	13	converge	converge	VERB
ap-3488	215	14	monotonically	monotonically	ADV
ap-3488	215	15	to	to	ADP
ap-3488	215	16	0	0	NUM
ap-3488	215	17	.	.	PUNCT
ap-3488	216	1	(	(	PUNCT
ap-3488	216	2	3	3	NUM
ap-3488	216	3	.	.	PUNCT
ap-3488	216	4	)	)	PUNCT
ap-3488	217	1	case	case	NOUN
ap-3488	217	2	β̄	β̄	X
ap-3488	217	3	∈	∈	PROPN
ap-3488	218	1	[	[	X
ap-3488	218	2	−π,−π2	−π,−π2	PROPN
ap-3488	218	3	)	)	PUNCT
ap-3488	218	4	.	.	PUNCT
ap-3488	219	1	we	we	PRON
ap-3488	219	2	have	have	VERB
ap-3488	219	3	β	β	NOUN
ap-3488	219	4	=	=	PUNCT
ap-3488	220	1	−π	−π	ADJ
ap-3488	220	2	−	−	PROPN
ap-3488	220	3	β̄	β̄	INTJ
ap-3488	220	4	,	,	PUNCT
ap-3488	220	5	we	we	PRON
ap-3488	220	6	can	can	AUX
ap-3488	220	7	get	get	VERB
ap-3488	220	8	a	a	DET
ap-3488	220	9	similar	similar	ADJ
ap-3488	220	10	result	result	NOUN
ap-3488	220	11	to	to	PART
ap-3488	220	12	case	case	NOUN
ap-3488	220	13	2	2	NUM
ap-3488	220	14	.	.	PUNCT
ap-3488	221	1	if	if	SCONJ
ap-3488	221	2	r	r	NOUN
ap-3488	221	3	<	<	X
ap-3488	221	4	0	0	NUM
ap-3488	221	5	,	,	PUNCT
ap-3488	221	6	the	the	DET
ap-3488	221	7	same	same	ADJ
ap-3488	221	8	calculus	calculus	NOUN
ap-3488	221	9	leads	lead	VERB
ap-3488	221	10	to	to	ADP
ap-3488	221	11	the	the	DET
ap-3488	221	12	same	same	ADJ
ap-3488	221	13	results	result	NOUN
ap-3488	221	14	.	.	PUNCT
ap-3488	222	1	hence	hence	ADV
ap-3488	222	2	we	we	PRON
ap-3488	222	3	have	have	VERB
ap-3488	222	4	the	the	DET
ap-3488	222	5	conclusion	conclusion	NOUN
ap-3488	222	6	δ	δ	PROPN
ap-3488	222	7	=	=	PUNCT
ap-3488	222	8	|β	|β	VERB
ap-3488	222	9	−	−	PROPN
ap-3488	222	10	α|	α|	PROPN
ap-3488	222	11	→	→	X
ap-3488	222	12	0	0	NUM
ap-3488	222	13	.	.	PUNCT
ap-3488	223	1	a	a	DET
ap-3488	223	2	θ	θ	PROPN
ap-3488	223	3	p′	p′	NOUN
ap-3488	223	4	o′	o′	X
ap-3488	224	1	x′	x′	PUNCT
ap-3488	225	1	y′	y′	NOUN
ap-3488	225	2	b	b	PROPN
ap-3488	225	3	r	r	NOUN
ap-3488	225	4	φ	φ	X
ap-3488	225	5	l	l	NOUN
ap-3488	225	6	p	p	NOUN
ap-3488	225	7	figure	figure	NOUN
ap-3488	225	8	3	3	NUM
ap-3488	225	9	.	.	PUNCT
ap-3488	225	10	movement	movement	NOUN
ap-3488	225	11	in	in	ADP
ap-3488	225	12	phase	phase	NOUN
ap-3488	225	13	3	3	NUM
ap-3488	225	14	.	.	NOUN
ap-3488	225	15	phase	phase	NOUN
ap-3488	225	16	2	2	NUM
ap-3488	225	17	.	.	PUNCT
ap-3488	226	1	l	l	NOUN
ap-3488	226	2	≥	≥	NOUN
ap-3488	226	3	2|r|	2|r|	NUM
ap-3488	226	4	,	,	PUNCT
ap-3488	226	5	δ	δ	X
ap-3488	226	6	=	=	PUNCT
ap-3488	226	7	β	β	PROPN
ap-3488	226	8	−	−	NOUN
ap-3488	226	9	α	α	NOUN
ap-3488	226	10	=	=	NOUN
ap-3488	226	11	0	0	PROPN
ap-3488	226	12	.	.	PUNCT
ap-3488	227	1	because	because	SCONJ
ap-3488	227	2	of	of	ADP
ap-3488	227	3	the	the	DET
ap-3488	227	4	regulation	regulation	NOUN
ap-3488	227	5	of	of	ADP
ap-3488	227	6	phase	phase	NOUN
ap-3488	227	7	1	1	NUM
ap-3488	227	8	,	,	PUNCT
ap-3488	227	9	in	in	ADP
ap-3488	227	10	this	this	DET
ap-3488	227	11	phase	phase	NOUN
ap-3488	227	12	,	,	PUNCT
ap-3488	227	13	the	the	DET
ap-3488	227	14	robot	robot	NOUN
ap-3488	227	15	will	will	AUX
ap-3488	227	16	moves	move	VERB
ap-3488	227	17	towards	towards	ADP
ap-3488	227	18	the	the	DET
ap-3488	227	19	origin	origin	NOUN
ap-3488	227	20	along	along	ADP
ap-3488	227	21	the	the	DET
ap-3488	227	22	tangent	tangent	NOUN
ap-3488	227	23	of	of	ADP
ap-3488	227	24	circle	circle	PROPN
ap-3488	227	25	cb	cb	PROPN
ap-3488	227	26	,	,	PUNCT
ap-3488	227	27	thus	thus	ADV
ap-3488	227	28	δ	δ	X
ap-3488	227	29	=	=	SYM
ap-3488	227	30	0	0	NUM
ap-3488	227	31	and	and	CCONJ
ap-3488	227	32	ω	ω	NUM
ap-3488	227	33	=	=	PUNCT
ap-3488	228	1	u(β	u(β	PROPN
ap-3488	228	2	−	−	PROPN
ap-3488	228	3	α)/|r|	α)/|r|	NUM
ap-3488	228	4	=	=	SYM
ap-3488	228	5	0	0	X
ap-3488	228	6	.	.	PUNCT
ap-3488	229	1	lemma	lemma	PROPN
ap-3488	229	2	2	2	X
ap-3488	229	3	.	.	PUNCT
ap-3488	229	4	suppose	suppose	VERB
ap-3488	229	5	d	d	X
ap-3488	229	6	=	=	SYM
ap-3488	229	7	|o′a|	|o′a|	NOUN
ap-3488	229	8	and	and	CCONJ
ap-3488	229	9	the	the	DET
ap-3488	229	10	lyapunov	lyapunov	ADJ
ap-3488	229	11	function	function	NOUN
ap-3488	229	12	is	be	AUX
ap-3488	229	13	chosen	choose	VERB
ap-3488	229	14	as	as	ADP
ap-3488	229	15	v	v	NOUN
ap-3488	229	16	=	=	SYM
ap-3488	229	17	1	1	NUM
ap-3488	229	18	2d	2d	NUM
ap-3488	229	19	2	2	NUM
ap-3488	229	20	+	+	CCONJ
ap-3488	229	21	1	1	NUM
ap-3488	229	22	2θ	2θ	NUM
ap-3488	229	23	2	2	NUM
ap-3488	229	24	.	.	PUNCT
ap-3488	230	1	if	if	SCONJ
ap-3488	230	2	the	the	DET
ap-3488	230	3	robot	robot	NOUN
ap-3488	230	4	moves	move	VERB
ap-3488	230	5	towards	towards	ADP
ap-3488	230	6	the	the	DET
ap-3488	230	7	origin	origin	NOUN
ap-3488	230	8	along	along	ADP
ap-3488	230	9	the	the	DET
ap-3488	230	10	tangent	tangent	NOUN
ap-3488	230	11	of	of	ADP
ap-3488	230	12	circle	circle	PROPN
ap-3488	230	13	cb	cb	PROPN
ap-3488	230	14	,	,	PUNCT
ap-3488	230	15	then	then	ADV
ap-3488	230	16	v̇	v̇	VERB
ap-3488	230	17	<	<	X
ap-3488	230	18	0	0	X
ap-3488	230	19	.	.	PUNCT
ap-3488	231	1	proof	proof	NOUN
ap-3488	231	2	.	.	PUNCT
ap-3488	232	1	consider	consider	VERB
ap-3488	232	2	the	the	DET
ap-3488	232	3	polar	polar	ADJ
ap-3488	232	4	coordinates	coordinate	NOUN
ap-3488	232	5	,	,	PUNCT
ap-3488	232	6	we	we	PRON
ap-3488	232	7	have	have	VERB
ap-3488	232	8	ḋ	ḋ	NOUN
ap-3488	232	9	=	=	SYM
ap-3488	232	10	u	u	PROPN
ap-3488	232	11	cos(β̄	cos(β̄	NOUN
ap-3488	232	12	−	−	PROPN
ap-3488	232	13	ψ	ψ	NOUN
ap-3488	232	14	)	)	PUNCT
ap-3488	233	1	sgn	sgn	NOUN
ap-3488	233	2	x	x	SYM
ap-3488	233	3	sgn	sgn	NOUN
ap-3488	233	4	y	y	PROPN
ap-3488	233	5	=	=	SYM
ap-3488	233	6	cos(β̄	cos(β̄	PROPN
ap-3488	233	7	−	−	NOUN
ap-3488	233	8	ψ)sxsy	ψ)sxsy	NOUN
ap-3488	233	9	,	,	PUNCT
ap-3488	233	10	where	where	SCONJ
ap-3488	233	11	sx	sx	PROPN
ap-3488	233	12	is	be	AUX
ap-3488	233	13	sgn	sgn	NOUN
ap-3488	233	14	x	x	PUNCT
ap-3488	233	15	for	for	ADP
ap-3488	233	16	short	short	ADJ
ap-3488	233	17	.	.	PUNCT
ap-3488	234	1	we	we	PRON
ap-3488	234	2	find	find	VERB
ap-3488	234	3	that	that	SCONJ
ap-3488	234	4	if	if	SCONJ
ap-3488	234	5	u	u	PROPN
ap-3488	234	6	<	<	X
ap-3488	234	7	0	0	NUM
ap-3488	234	8	,	,	PUNCT
ap-3488	234	9	then	then	ADV
ap-3488	234	10	0	0	NUM
ap-3488	234	11	<	<	X
ap-3488	234	12	|β̄|	|β̄|	PROPN
ap-3488	234	13	≤	≤	PROPN
ap-3488	234	14	π	π	PROPN
ap-3488	234	15	6	6	NUM
ap-3488	234	16	;	;	PUNCT
ap-3488	234	17	if	if	SCONJ
ap-3488	234	18	u	u	PROPN
ap-3488	234	19	>	>	X
ap-3488	234	20	0	0	NUM
ap-3488	234	21	,	,	PUNCT
ap-3488	234	22	then	then	ADV
ap-3488	234	23	5π	5π	PROPN
ap-3488	234	24	6	6	NUM
ap-3488	234	25	≤	≤	NOUN
ap-3488	234	26	|β̄|	|β̄|	PROPN
ap-3488	234	27	<	<	X
ap-3488	234	28	π	π	PROPN
ap-3488	234	29	.	.	PUNCT
ap-3488	235	1	angle	angle	PROPN
ap-3488	235	2	ψ	ψ	NOUN
ap-3488	235	3	is	be	AUX
ap-3488	235	4	always	always	ADV
ap-3488	235	5	positive	positive	ADJ
ap-3488	235	6	.	.	PUNCT
ap-3488	236	1	if	if	SCONJ
ap-3488	236	2	l	l	NOUN
ap-3488	236	3	=	=	SYM
ap-3488	236	4	2|r|	2|r|	NUM
ap-3488	236	5	,	,	PUNCT
ap-3488	236	6	ψ	ψ	X
ap-3488	236	7	is	be	AUX
ap-3488	236	8	maximal	maximal	ADJ
ap-3488	236	9	:	:	PUNCT
ap-3488	236	10	ψmax	ψmax	NOUN
ap-3488	236	11	=	=	PUNCT
ap-3488	236	12	arccos(7/8	arccos(7/8	X
ap-3488	236	13	)	)	PUNCT
ap-3488	237	1	≈	≈	PROPN
ap-3488	237	2	0.5054	0.5054	NUM
ap-3488	237	3	,	,	PUNCT
ap-3488	237	4	then	then	ADV
ap-3488	237	5	no	no	ADV
ap-3488	237	6	matter	matter	ADV
ap-3488	237	7	what	what	PRON
ap-3488	237	8	sign	sign	NOUN
ap-3488	237	9	x	x	PUNCT
ap-3488	237	10	and	and	CCONJ
ap-3488	237	11	y	y	PROPN
ap-3488	237	12	have	have	VERB
ap-3488	237	13	,	,	PUNCT
ap-3488	237	14	we	we	PRON
ap-3488	237	15	have	have	VERB
ap-3488	237	16	ḋ	ḋ	PROPN
ap-3488	237	17	=	=	NOUN
ap-3488	238	1	−	−	PROPN
ap-3488	238	2	sgn	sgn	NOUN
ap-3488	238	3	cos	cos	PROPN
ap-3488	238	4	β̄	β̄	PROPN
ap-3488	238	5	λl	λl	PROPN
ap-3488	238	6	cos(β̄	cos(β̄	NOUN
ap-3488	238	7	−	−	PROPN
ap-3488	238	8	ψsxsy	ψsxsy	NOUN
ap-3488	238	9	)	)	PUNCT
ap-3488	238	10	<	<	X
ap-3488	238	11	0	0	X
ap-3488	238	12	.	.	PUNCT
ap-3488	239	1	in	in	ADP
ap-3488	239	2	this	this	DET
ap-3488	239	3	phase	phase	NOUN
ap-3488	239	4	,	,	PUNCT
ap-3488	239	5	δ	δ	PROPN
ap-3488	239	6	=	=	SYM
ap-3488	239	7	0	0	NUM
ap-3488	239	8	,	,	PUNCT
ap-3488	239	9	so	so	ADV
ap-3488	239	10	θ̇	θ̇	X
ap-3488	239	11	=	=	SYM
ap-3488	239	12	ω	ω	NOUN
ap-3488	239	13	=	=	SYM
ap-3488	239	14	0	0	PROPN
ap-3488	239	15	.	.	PUNCT
ap-3488	240	1	hence	hence	ADV
ap-3488	240	2	v̇	v̇	NOUN
ap-3488	240	3	=	=	PUNCT
ap-3488	240	4	dḋ+	dḋ+	NOUN
ap-3488	240	5	θθ̇	θθ̇	X
ap-3488	240	6	<	<	X
ap-3488	240	7	0	0	X
ap-3488	240	8	.	.	PUNCT
ap-3488	241	1	the	the	DET
ap-3488	241	2	lemma	lemma	PROPN
ap-3488	241	3	is	be	AUX
ap-3488	241	4	proved	prove	VERB
ap-3488	241	5	.	.	PUNCT
ap-3488	242	1	phase	phase	NOUN
ap-3488	242	2	3	3	NUM
ap-3488	242	3	.	.	PUNCT
ap-3488	243	1	l	l	NOUN
ap-3488	243	2	=	=	SYM
ap-3488	243	3	2|r|	2|r|	NUM
ap-3488	243	4	.	.	PUNCT
ap-3488	244	1	in	in	ADP
ap-3488	244	2	this	this	DET
ap-3488	244	3	phase	phase	NOUN
ap-3488	244	4	,	,	PUNCT
ap-3488	244	5	we	we	PRON
ap-3488	244	6	have	have	VERB
ap-3488	244	7	always	always	ADV
ap-3488	244	8	l	l	NOUN
ap-3488	244	9	=	=	PUNCT
ap-3488	244	10	2r	2r	NUM
ap-3488	244	11	and	and	CCONJ
ap-3488	244	12	β	β	X
ap-3488	244	13	=	=	SYM
ap-3488	244	14	α	α	PROPN
ap-3488	245	1	=	=	PUNCT
ap-3488	245	2	π	π	NOUN
ap-3488	245	3	6	6	NUM
ap-3488	245	4	(	(	PUNCT
ap-3488	245	5	shown	show	VERB
ap-3488	245	6	in	in	ADP
ap-3488	245	7	figure	figure	NOUN
ap-3488	245	8	3	3	NUM
ap-3488	245	9	)	)	PUNCT
ap-3488	245	10	.	.	PUNCT
ap-3488	246	1	we	we	PRON
ap-3488	246	2	use	use	VERB
ap-3488	246	3	y(x	y(x	NOUN
ap-3488	246	4	)	)	PUNCT
ap-3488	246	5	to	to	PART
ap-3488	246	6	represent	represent	VERB
ap-3488	246	7	the	the	DET
ap-3488	246	8	movement	movement	NOUN
ap-3488	246	9	of	of	ADP
ap-3488	246	10	the	the	DET
ap-3488	246	11	robot	robot	NOUN
ap-3488	246	12	and	and	CCONJ
ap-3488	246	13	suppose	suppose	VERB
ap-3488	246	14	r	r	NOUN
ap-3488	246	15	≥	≥	NOUN
ap-3488	246	16	0	0	NUM
ap-3488	246	17	.	.	PUNCT
ap-3488	247	1	the	the	DET
ap-3488	247	2	case	case	NOUN
ap-3488	247	3	r	r	NOUN
ap-3488	247	4	<	<	X
ap-3488	247	5	0	0	NUM
ap-3488	247	6	could	could	AUX
ap-3488	247	7	be	be	AUX
ap-3488	247	8	studied	study	VERB
ap-3488	247	9	in	in	ADP
ap-3488	247	10	the	the	DET
ap-3488	247	11	same	same	ADJ
ap-3488	247	12	way	way	NOUN
ap-3488	247	13	and	and	CCONJ
ap-3488	247	14	the	the	DET
ap-3488	247	15	same	same	ADJ
ap-3488	247	16	conclusion	conclusion	NOUN
ap-3488	247	17	will	will	AUX
ap-3488	247	18	be	be	AUX
ap-3488	247	19	obtained	obtain	VERB
ap-3488	247	20	.	.	PUNCT
ap-3488	248	1	(	(	PUNCT
ap-3488	248	2	x	x	X
ap-3488	248	3	,	,	PUNCT
ap-3488	248	4	y	y	NOUN
ap-3488	248	5	)	)	PUNCT
ap-3488	248	6	is	be	AUX
ap-3488	248	7	the	the	DET
ap-3488	248	8	position	position	NOUN
ap-3488	248	9	of	of	ADP
ap-3488	248	10	point	point	NOUN
ap-3488	248	11	a.	a.	NOUN
ap-3488	248	12	theorem	theorem	NOUN
ap-3488	248	13	1	1	X
ap-3488	248	14	.	.	PUNCT
ap-3488	248	15	suppose	suppose	VERB
ap-3488	248	16	that	that	SCONJ
ap-3488	248	17	one	one	NUM
ap-3488	248	18	robot	robot	NOUN
ap-3488	248	19	,	,	PUNCT
ap-3488	248	20	with	with	ADP
ap-3488	248	21	the	the	DET
ap-3488	248	22	velocity	velocity	NOUN
ap-3488	248	23	defined	define	VERB
ap-3488	248	24	by	by	ADP
ap-3488	248	25	the	the	DET
ap-3488	248	26	proposed	propose	VERB
ap-3488	248	27	control	control	NOUN
ap-3488	248	28	law	law	NOUN
ap-3488	248	29	(	(	PUNCT
ap-3488	248	30	equation	equation	NOUN
ap-3488	248	31	13	13	NUM
ap-3488	248	32	)	)	PUNCT
ap-3488	248	33	,	,	PUNCT
ap-3488	248	34	moves	move	NOUN
ap-3488	248	35	towards	towards	ADP
ap-3488	248	36	the	the	DET
ap-3488	248	37	origin	origin	NOUN
ap-3488	248	38	along	along	ADP
ap-3488	248	39	the	the	DET
ap-3488	248	40	tangent	tangent	NOUN
ap-3488	248	41	of	of	ADP
ap-3488	248	42	the	the	DET
ap-3488	248	43	circle	circle	NOUN
ap-3488	248	44	cb	cb	PROPN
ap-3488	248	45	(	(	PUNCT
ap-3488	248	46	figure	figure	NOUN
ap-3488	248	47	3	3	NUM
ap-3488	248	48	)	)	PUNCT
ap-3488	248	49	of	of	ADP
ap-3488	248	50	which	which	PRON
ap-3488	248	51	the	the	DET
ap-3488	248	52	radius	radius	NOUN
ap-3488	248	53	|r|	|r|	NOUN
ap-3488	248	54	satisfies	satisfy	VERB
ap-3488	248	55	l	l	NOUN
ap-3488	248	56	=	=	SYM
ap-3488	248	57	2|r|	2|r|	NUM
ap-3488	248	58	and	and	CCONJ
ap-3488	248	59	r	r	NOUN
ap-3488	248	60	is	be	AUX
ap-3488	248	61	determined	determine	VERB
ap-3488	248	62	by	by	ADP
ap-3488	248	63	rule	rule	NOUN
ap-3488	248	64	(	(	PUNCT
ap-3488	248	65	equation	equation	NOUN
ap-3488	248	66	12	12	NUM
ap-3488	248	67	)	)	PUNCT
ap-3488	248	68	,	,	PUNCT
ap-3488	248	69	then	then	ADV
ap-3488	248	70	both	both	DET
ap-3488	248	71	d	d	NOUN
ap-3488	248	72	and	and	CCONJ
ap-3488	248	73	θ	θ	PROPN
ap-3488	248	74	asymptotically	asymptotically	ADV
ap-3488	248	75	converge	converge	VERB
ap-3488	248	76	to	to	ADP
ap-3488	248	77	0	0	NUM
ap-3488	248	78	.	.	NOUN
ap-3488	248	79	5	5	NUM
ap-3488	248	80	youwei	youwei	PROPN
ap-3488	248	81	dong	dong	PROPN
ap-3488	248	82	,	,	PUNCT
ap-3488	248	83	ahmed	ahmed	PROPN
ap-3488	248	84	rahmani	rahmani	PROPN
ap-3488	248	85	acta	acta	PROPN
ap-3488	248	86	polytechnica	polytechnica	PROPN
ap-3488	248	87	proof	proof	NOUN
ap-3488	248	88	.	.	PUNCT
ap-3488	249	1	we	we	PRON
ap-3488	249	2	consider	consider	VERB
ap-3488	249	3	first	first	ADV
ap-3488	249	4	the	the	DET
ap-3488	249	5	case	case	NOUN
ap-3488	249	6	where	where	SCONJ
ap-3488	249	7	r	r	NOUN
ap-3488	249	8	>	>	X
ap-3488	249	9	0	0	NUM
ap-3488	249	10	.	.	PUNCT
ap-3488	250	1	in	in	ADP
ap-3488	250	2	this	this	DET
ap-3488	250	3	case	case	NOUN
ap-3488	250	4	,	,	PUNCT
ap-3488	250	5	l	l	NOUN
ap-3488	250	6	=	=	SYM
ap-3488	250	7	2r	2r	NUM
ap-3488	250	8	,	,	PUNCT
ap-3488	250	9	(	(	PUNCT
ap-3488	250	10	x	x	NOUN
ap-3488	250	11	,	,	PUNCT
ap-3488	250	12	y	y	NOUN
ap-3488	250	13	)	)	PUNCT
ap-3488	250	14	satisfies	satisfy	VERB
ap-3488	250	15	the	the	DET
ap-3488	250	16	equation	equation	NOUN
ap-3488	250	17	x2+(y−r)2	x2+(y−r)2	PROPN
ap-3488	251	1	=	=	SYM
ap-3488	251	2	4r2	4r2	X
ap-3488	251	3	.	.	PUNCT
ap-3488	252	1	then	then	ADV
ap-3488	252	2	we	we	PRON
ap-3488	252	3	get	get	VERB
ap-3488	252	4	r	r	NOUN
ap-3488	252	5	=	=	SYM
ap-3488	252	6	−y+	−y+	NOUN
ap-3488	252	7	√	√	NUM
ap-3488	252	8	3x2	3x2	NUM
ap-3488	252	9	+	+	NOUN
ap-3488	252	10	4y2	4y2	NUM
ap-3488	252	11	3	3	NUM
ap-3488	252	12	(	(	PUNCT
ap-3488	252	13	the	the	DET
ap-3488	252	14	negative	negative	ADJ
ap-3488	252	15	solution	solution	NOUN
ap-3488	252	16	is	be	AUX
ap-3488	252	17	omitted	omit	VERB
ap-3488	252	18	)	)	PUNCT
ap-3488	252	19	.	.	PUNCT
ap-3488	253	1	using	use	VERB
ap-3488	253	2	bp⊥pa	bp⊥pa	PROPN
ap-3488	253	3	,	,	PUNCT
ap-3488	253	4	we	we	PRON
ap-3488	253	5	could	could	AUX
ap-3488	253	6	have	have	VERB
ap-3488	253	7	y′	y′	NOUN
ap-3488	254	1	=	=	SYM
ap-3488	254	2	dy	dy	VERB
ap-3488	254	3	dx	dx	PROPN
ap-3488	255	1	=	=	PUNCT
ap-3488	256	1	−3x+	−3x+	PROPN
ap-3488	257	1	√	√	INTJ
ap-3488	257	2	3(4y	3(4y	NUM
ap-3488	257	3	−	−	NOUN
ap-3488	257	4	√	√	NUM
ap-3488	257	5	3x2	3x2	NUM
ap-3488	257	6	+	+	CCONJ
ap-3488	257	7	4y2	4y2	NUM
ap-3488	257	8	)	)	PUNCT
ap-3488	257	9	−3	−3	NOUN
ap-3488	258	1	√	√	NOUN
ap-3488	258	2	3x+	3x+	NUM
ap-3488	258	3	4y	4y	NUM
ap-3488	258	4	−	−	ADP
ap-3488	258	5	√	√	NUM
ap-3488	258	6	3x2	3x2	NUM
ap-3488	259	1	+	+	CCONJ
ap-3488	259	2	4y2	4y2	NUM
ap-3488	259	3	.	.	PUNCT
ap-3488	260	1	this	this	PRON
ap-3488	260	2	is	be	AUX
ap-3488	260	3	an	an	DET
ap-3488	260	4	homogeneous	homogeneous	ADJ
ap-3488	260	5	differential	differential	NOUN
ap-3488	260	6	equation	equation	NOUN
ap-3488	260	7	.	.	PUNCT
ap-3488	261	1	we	we	PRON
ap-3488	261	2	suppose	suppose	VERB
ap-3488	261	3	y	y	PROPN
ap-3488	261	4	=	=	SYM
ap-3488	261	5	zx	zx	PROPN
ap-3488	261	6	and	and	CCONJ
ap-3488	261	7	differentiate	differentiate	VERB
ap-3488	261	8	it	it	PRON
ap-3488	261	9	about	about	ADP
ap-3488	261	10	x	x	NOUN
ap-3488	261	11	:	:	PUNCT
ap-3488	261	12	dy	dy	X
ap-3488	261	13	dx	dx	PROPN
ap-3488	261	14	=	=	PROPN
ap-3488	261	15	z	z	PROPN
ap-3488	262	1	+	+	NUM
ap-3488	262	2	x	x	SYM
ap-3488	262	3	dz	dz	X
ap-3488	262	4	dx	dx	PROPN
ap-3488	262	5	=	=	PUNCT
ap-3488	262	6	3x+	3x+	NUM
ap-3488	262	7	√	√	NUM
ap-3488	262	8	3(4y	3(4y	NUM
ap-3488	262	9	−	−	NOUN
ap-3488	262	10	√	√	NUM
ap-3488	262	11	3x2	3x2	NUM
ap-3488	262	12	+	+	CCONJ
ap-3488	262	13	4y2	4y2	NUM
ap-3488	262	14	)	)	PUNCT
ap-3488	262	15	3	3	NUM
ap-3488	262	16	√	√	NOUN
ap-3488	262	17	3x−	3x−	PROPN
ap-3488	262	18	4y	4y	PROPN
ap-3488	262	19	+	+	CCONJ
ap-3488	262	20	√	√	NUM
ap-3488	262	21	3x2	3x2	NUM
ap-3488	262	22	+	+	CCONJ
ap-3488	262	23	4y2	4y2	NUM
ap-3488	262	24	=	=	SYM
ap-3488	262	25	3	3	NUM
ap-3488	262	26	+	+	CCONJ
ap-3488	262	27	√	√	PROPN
ap-3488	262	28	3(4z	3(4z	NUM
ap-3488	262	29	−	−	NOUN
ap-3488	262	30	√	√	NOUN
ap-3488	262	31	3	3	NUM
ap-3488	262	32	+	+	SYM
ap-3488	262	33	4z2	4z2	NOUN
ap-3488	262	34	)	)	PUNCT
ap-3488	262	35	3	3	NUM
ap-3488	262	36	√	√	ADP
ap-3488	262	37	3−	3−	NUM
ap-3488	262	38	4z	4z	NOUN
ap-3488	262	39	+	+	CCONJ
ap-3488	262	40	√	√	NUM
ap-3488	262	41	3	3	NUM
ap-3488	262	42	+	+	SYM
ap-3488	262	43	4z2	4z2	NOUN
ap-3488	262	44	.	.	PUNCT
ap-3488	263	1	simplify	simplify	VERB
ap-3488	263	2	this	this	DET
ap-3488	263	3	result	result	NOUN
ap-3488	263	4	and	and	CCONJ
ap-3488	263	5	get	get	VERB
ap-3488	263	6	dx	dx	PROPN
ap-3488	263	7	x	x	PUNCT
ap-3488	263	8	=	=	SYM
ap-3488	263	9	3	3	NUM
ap-3488	263	10	√	√	NUM
ap-3488	263	11	3−	3−	NUM
ap-3488	263	12	4z	4z	NOUN
ap-3488	263	13	+	+	CCONJ
ap-3488	263	14	√	√	NUM
ap-3488	263	15	3	3	NUM
ap-3488	263	16	+	+	NUM
ap-3488	263	17	4z2	4z2	NUM
ap-3488	263	18	3	3	NUM
ap-3488	263	19	+	+	CCONJ
ap-3488	263	20	√	√	PROPN
ap-3488	263	21	z	z	NOUN
ap-3488	264	1	+	+	CCONJ
ap-3488	264	2	4z2	4z2	NUM
ap-3488	265	1	−	−	PROPN
ap-3488	265	2	(	(	PUNCT
ap-3488	265	3	√	√	NUM
ap-3488	265	4	3	3	NUM
ap-3488	265	5	+	+	CCONJ
ap-3488	265	6	z	z	X
ap-3488	265	7	)	)	PUNCT
ap-3488	265	8	√	√	ADV
ap-3488	265	9	3	3	NUM
ap-3488	266	1	+	+	CCONJ
ap-3488	266	2	4z2	4z2	NUM
ap-3488	266	3	dz	dz	PROPN
ap-3488	266	4	.	.	PROPN
ap-3488	266	5	integrate	integrate	VERB
ap-3488	266	6	it	it	PRON
ap-3488	266	7	and	and	CCONJ
ap-3488	266	8	get	get	VERB
ap-3488	266	9	ln	ln	ADJ
ap-3488	266	10	|x|	|x|	PROPN
ap-3488	266	11	=	=	SYM
ap-3488	266	12	∫	∫	PROPN
ap-3488	266	13	3	3	NUM
ap-3488	266	14	√	√	PROPN
ap-3488	266	15	3−	3−	NUM
ap-3488	266	16	4z	4z	NOUN
ap-3488	266	17	+	+	CCONJ
ap-3488	266	18	√	√	NUM
ap-3488	266	19	3	3	NUM
ap-3488	266	20	+	+	NUM
ap-3488	266	21	4z2	4z2	NUM
ap-3488	266	22	3	3	NUM
ap-3488	266	23	+	+	CCONJ
ap-3488	266	24	√	√	PROPN
ap-3488	266	25	z	z	NOUN
ap-3488	267	1	+	+	CCONJ
ap-3488	267	2	4z2	4z2	NUM
ap-3488	268	1	−	−	PROPN
ap-3488	268	2	(	(	PUNCT
ap-3488	268	3	√	√	NUM
ap-3488	268	4	3	3	NUM
ap-3488	268	5	+	+	CCONJ
ap-3488	268	6	z	z	X
ap-3488	268	7	)	)	PUNCT
ap-3488	268	8	√	√	ADV
ap-3488	268	9	3	3	NUM
ap-3488	269	1	+	+	SYM
ap-3488	269	2	4z2	4z2	NUM
ap-3488	269	3	dz	dz	X
ap-3488	269	4	=	=	PUNCT
ap-3488	269	5	√	√	PROPN
ap-3488	269	6	3	3	NUM
ap-3488	269	7	z	z	NOUN
ap-3488	269	8	(	(	PUNCT
ap-3488	269	9	−	−	PROPN
ap-3488	269	10	√	√	NOUN
ap-3488	269	11	1	1	NUM
ap-3488	269	12	+	+	CCONJ
ap-3488	269	13	4	4	NUM
ap-3488	269	14	3z	3z	NUM
ap-3488	269	15	2	2	NUM
ap-3488	269	16	−	−	NOUN
ap-3488	269	17	1	1	NUM
ap-3488	269	18	)	)	PUNCT
ap-3488	269	19	−	−	PROPN
ap-3488	269	20	1	1	NUM
ap-3488	269	21	2	2	NUM
ap-3488	269	22	ln(z2	ln(z2	NOUN
ap-3488	269	23	+	+	NOUN
ap-3488	269	24	1	1	NUM
ap-3488	269	25	)	)	PUNCT
ap-3488	269	26	+	+	CCONJ
ap-3488	269	27	arctanh	arctanh	PROPN
ap-3488	269	28	z√	z√	PROPN
ap-3488	269	29	3	3	NUM
ap-3488	269	30	+	+	NUM
ap-3488	269	31	4z2	4z2	NUM
ap-3488	269	32	+	+	CCONJ
ap-3488	269	33	const	const	ADJ
ap-3488	269	34	,	,	PUNCT
ap-3488	269	35	where	where	SCONJ
ap-3488	269	36	“	"	PUNCT
ap-3488	269	37	const	const	NOUN
ap-3488	269	38	”	"	PUNCT
ap-3488	269	39	is	be	AUX
ap-3488	269	40	a	a	DET
ap-3488	269	41	constant	constant	ADJ
ap-3488	269	42	and	and	CCONJ
ap-3488	269	43	its	its	PRON
ap-3488	269	44	value	value	NOUN
ap-3488	269	45	is	be	AUX
ap-3488	269	46	determined	determine	VERB
ap-3488	269	47	by	by	ADP
ap-3488	269	48	the	the	DET
ap-3488	269	49	initial	initial	ADJ
ap-3488	269	50	conditions	condition	NOUN
ap-3488	269	51	.	.	PUNCT
ap-3488	270	1	when	when	SCONJ
ap-3488	270	2	x	x	X
ap-3488	270	3	>	>	X
ap-3488	270	4	0	0	NUM
ap-3488	270	5	,	,	PUNCT
ap-3488	270	6	x	x	X
ap-3488	270	7	=	=	PUNCT
ap-3488	270	8	l	l	NOUN
ap-3488	270	9	cosϕ	cosϕ	NOUN
ap-3488	270	10	,	,	PUNCT
ap-3488	270	11	so	so	ADV
ap-3488	270	12	ẋ	ẋ	PROPN
ap-3488	270	13	=	=	SYM
ap-3488	270	14	l̇	l̇	PROPN
ap-3488	270	15	cosϕ−	cosϕ−	PROPN
ap-3488	270	16	lϕ̇	lϕ̇	PROPN
ap-3488	270	17	sinϕ	sinϕ	PROPN
ap-3488	270	18	=	=	PUNCT
ap-3488	270	19	−λl	−λl	PROPN
ap-3488	270	20	cosβ	cosβ	NOUN
ap-3488	270	21	−	−	PROPN
ap-3488	270	22	lλ	lλ	INTJ
ap-3488	270	23	sin	sin	VERB
ap-3488	270	24	β	β	X
ap-3488	270	25	sinϕ	sinϕ	NOUN
ap-3488	270	26	=	=	PUNCT
ap-3488	270	27	−λl2	−λl2	PROPN
ap-3488	270	28	(	(	PUNCT
ap-3488	270	29	√	√	NUM
ap-3488	270	30	3	3	NUM
ap-3488	270	31	+	+	CCONJ
ap-3488	270	32	sinϕ	sinϕ	NOUN
ap-3488	270	33	)	)	PUNCT
ap-3488	270	34	<	<	X
ap-3488	270	35	0	0	X
ap-3488	270	36	.	.	PUNCT
ap-3488	271	1	l	l	NOUN
ap-3488	271	2	=	=	PUNCT
ap-3488	271	3	0	0	NUM
ap-3488	271	4	is	be	AUX
ap-3488	271	5	the	the	DET
ap-3488	271	6	equilibrium	equilibrium	NOUN
ap-3488	271	7	point	point	NOUN
ap-3488	271	8	,	,	PUNCT
ap-3488	271	9	so	so	ADV
ap-3488	271	10	x→	x→	PROPN
ap-3488	271	11	0	0	NUM
ap-3488	271	12	.	.	PUNCT
ap-3488	272	1	this	this	PRON
ap-3488	272	2	is	be	AUX
ap-3488	272	3	also	also	ADV
ap-3488	272	4	the	the	DET
ap-3488	272	5	conclusion	conclusion	NOUN
ap-3488	272	6	for	for	ADP
ap-3488	272	7	x	x	PUNCT
ap-3488	272	8	<	<	X
ap-3488	272	9	0	0	NUM
ap-3488	272	10	.	.	PUNCT
ap-3488	273	1	so	so	ADV
ap-3488	273	2	we	we	PRON
ap-3488	273	3	just	just	ADV
ap-3488	273	4	need	need	VERB
ap-3488	273	5	to	to	PART
ap-3488	273	6	consider	consider	VERB
ap-3488	273	7	the	the	DET
ap-3488	273	8	right	right	ADJ
ap-3488	273	9	neighborhood	neighborhood	NOUN
ap-3488	273	10	of	of	ADP
ap-3488	273	11	the	the	DET
ap-3488	273	12	origin	origin	NOUN
ap-3488	273	13	,	,	PUNCT
ap-3488	273	14	hence	hence	ADV
ap-3488	273	15	x	x	X
ap-3488	273	16	=	=	SYM
ap-3488	273	17	exp	exp	NOUN
ap-3488	273	18	(	(	PUNCT
ap-3488	273	19	√	√	PROPN
ap-3488	273	20	3	3	NUM
ap-3488	273	21	z	z	NOUN
ap-3488	273	22	(	(	PUNCT
ap-3488	273	23	−	−	PROPN
ap-3488	273	24	√	√	NOUN
ap-3488	273	25	1	1	NUM
ap-3488	273	26	+	+	CCONJ
ap-3488	273	27	4	4	NUM
ap-3488	273	28	3z	3z	NUM
ap-3488	273	29	2	2	NUM
ap-3488	273	30	−	−	NOUN
ap-3488	273	31	1	1	NUM
ap-3488	273	32	)	)	PUNCT
ap-3488	273	33	−	−	PROPN
ap-3488	273	34	1	1	NUM
ap-3488	273	35	2	2	NUM
ap-3488	273	36	ln(z2	ln(z2	NOUN
ap-3488	273	37	+	+	NOUN
ap-3488	273	38	1	1	NUM
ap-3488	273	39	)	)	PUNCT
ap-3488	273	40	+	+	CCONJ
ap-3488	274	1	arctanh	arctanh	PROPN
ap-3488	274	2	z√	z√	PROPN
ap-3488	274	3	3	3	NUM
ap-3488	274	4	+	+	NUM
ap-3488	274	5	4z2	4z2	NUM
ap-3488	274	6	+	+	CCONJ
ap-3488	274	7	const	const	NOUN
ap-3488	274	8	)	)	PUNCT
ap-3488	274	9	.	.	PUNCT
ap-3488	275	1	thus	thus	ADV
ap-3488	275	2	dx	dx	X
ap-3488	275	3	dz	dz	PROPN
ap-3488	275	4	=	=	PUNCT
ap-3488	275	5	x	x	X
ap-3488	275	6	(	(	PUNCT
ap-3488	275	7	−z3	−z3	PROPN
ap-3488	275	8	+	+	CCONJ
ap-3488	275	9	√	√	NUM
ap-3488	275	10	3z2	3z2	NUM
ap-3488	275	11	+	+	CCONJ
ap-3488	275	12	√	√	NUM
ap-3488	275	13	3	3	NUM
ap-3488	275	14	)	)	PUNCT
ap-3488	275	15	√	√	NOUN
ap-3488	275	16	3	3	NUM
ap-3488	276	1	+	+	CCONJ
ap-3488	276	2	4z2	4z2	NUM
ap-3488	276	3	+	+	CCONJ
ap-3488	276	4	4z2	4z2	NUM
ap-3488	277	1	+	+	CCONJ
ap-3488	277	2	3	3	NUM
ap-3488	277	3	z2(z2	z2(z2	NUM
ap-3488	277	4	+	+	CCONJ
ap-3488	277	5	1	1	NUM
ap-3488	277	6	)	)	PUNCT
ap-3488	277	7	√	√	NOUN
ap-3488	277	8	3	3	NUM
ap-3488	278	1	+	+	SYM
ap-3488	278	2	4z2	4z2	NOUN
ap-3488	278	3	.	.	PUNCT
ap-3488	279	1	solve	solve	VERB
ap-3488	279	2	the	the	DET
ap-3488	279	3	equation	equation	NOUN
ap-3488	279	4	dx	dx	PROPN
ap-3488	279	5	dz	dz	PROPN
ap-3488	279	6	=	=	SYM
ap-3488	279	7	0	0	NUM
ap-3488	279	8	,	,	PUNCT
ap-3488	279	9	get	get	VERB
ap-3488	279	10	z0	z0	NOUN
ap-3488	279	11	=	=	ADJ
ap-3488	279	12	1	1	NUM
ap-3488	279	13	+	+	CCONJ
ap-3488	279	14	√	√	NUM
ap-3488	279	15	3	3	NUM
ap-3488	279	16	.	.	PUNCT
ap-3488	280	1	and	and	CCONJ
ap-3488	280	2	when	when	SCONJ
ap-3488	280	3	z	z	NOUN
ap-3488	280	4	<	<	X
ap-3488	280	5	z0	z0	PROPN
ap-3488	280	6	,	,	PUNCT
ap-3488	280	7	dx	dx	PROPN
ap-3488	280	8	dz	dz	PROPN
ap-3488	280	9	>	>	X
ap-3488	280	10	0	0	NUM
ap-3488	280	11	;	;	PUNCT
ap-3488	280	12	when	when	SCONJ
ap-3488	280	13	z	z	X
ap-3488	280	14	>	>	X
ap-3488	280	15	z0	z0	PROPN
ap-3488	280	16	,	,	PUNCT
ap-3488	280	17	dx	dx	PROPN
ap-3488	280	18	dz	dz	X
ap-3488	280	19	<	<	X
ap-3488	280	20	0	0	X
ap-3488	280	21	.	.	PUNCT
ap-3488	281	1	so	so	ADV
ap-3488	281	2	in	in	ADP
ap-3488	281	3	the	the	DET
ap-3488	281	4	right	right	ADJ
ap-3488	281	5	neighborhood	neighborhood	NOUN
ap-3488	281	6	of	of	ADP
ap-3488	281	7	the	the	DET
ap-3488	281	8	origin	origin	NOUN
ap-3488	281	9	,	,	PUNCT
ap-3488	281	10	dxdz	dxdz	VERB
ap-3488	281	11	<	<	X
ap-3488	281	12	0	0	X
ap-3488	281	13	.	.	PUNCT
ap-3488	282	1	hence	hence	ADV
ap-3488	282	2	if	if	SCONJ
ap-3488	282	3	z	z	NOUN
ap-3488	282	4	→	→	SYM
ap-3488	282	5	0	0	NUM
ap-3488	282	6	,	,	PUNCT
ap-3488	282	7	then	then	ADV
ap-3488	282	8	x→	x→	PROPN
ap-3488	282	9	0	0	NUM
ap-3488	282	10	,	,	PUNCT
ap-3488	282	11	and	and	CCONJ
ap-3488	282	12	we	we	PRON
ap-3488	282	13	have	have	VERB
ap-3488	282	14	the	the	DET
ap-3488	282	15	approximate	approximate	ADJ
ap-3488	282	16	relation	relation	NOUN
ap-3488	282	17	between	between	ADP
ap-3488	282	18	x	x	PROPN
ap-3488	282	19	and	and	CCONJ
ap-3488	282	20	z	z	NOUN
ap-3488	282	21	:	:	PUNCT
ap-3488	282	22	ln	ln	ADJ
ap-3488	282	23	x	x	SYM
ap-3488	282	24	=	=	PUNCT
ap-3488	282	25	−2	−2	NOUN
ap-3488	283	1	√	√	NOUN
ap-3488	283	2	3	3	NUM
ap-3488	283	3	z	z	NOUN
ap-3488	283	4	−	−	PROPN
ap-3488	283	5	z√	z√	PROPN
ap-3488	283	6	3	3	NUM
ap-3488	283	7	−	−	PROPN
ap-3488	283	8	z2	z2	PROPN
ap-3488	283	9	2	2	NUM
ap-3488	283	10	+	+	NOUN
ap-3488	283	11	o(z3	o(z3	ADJ
ap-3488	283	12	)	)	PUNCT
ap-3488	283	13	.	.	PUNCT
ap-3488	284	1	now	now	ADV
ap-3488	284	2	z	z	NOUN
ap-3488	284	3	is	be	AUX
ap-3488	284	4	very	very	ADV
ap-3488	284	5	close	close	ADJ
ap-3488	284	6	to	to	ADP
ap-3488	284	7	0	0	NUM
ap-3488	284	8	,	,	PUNCT
ap-3488	284	9	so	so	SCONJ
ap-3488	284	10	the	the	DET
ap-3488	284	11	terms	term	NOUN
ap-3488	284	12	of	of	ADP
ap-3488	284	13	higher	high	ADJ
ap-3488	284	14	orders	order	NOUN
ap-3488	284	15	could	could	AUX
ap-3488	284	16	be	be	AUX
ap-3488	284	17	omitted	omit	VERB
ap-3488	284	18	and	and	CCONJ
ap-3488	284	19	we	we	PRON
ap-3488	284	20	get	get	VERB
ap-3488	284	21	ln	ln	ADJ
ap-3488	284	22	x	x	PUNCT
ap-3488	284	23	=	=	PUNCT
ap-3488	284	24	−2	−2	NOUN
ap-3488	285	1	√	√	NOUN
ap-3488	285	2	3	3	NUM
ap-3488	285	3	z	z	NOUN
ap-3488	285	4	=	=	SYM
ap-3488	285	5	−2	−2	NOUN
ap-3488	286	1	√	√	ADV
ap-3488	286	2	3x	3x	NUM
ap-3488	286	3	y	y	PROPN
ap-3488	286	4	.	.	PUNCT
ap-3488	287	1	thus	thus	ADV
ap-3488	287	2	y	y	PROPN
ap-3488	287	3	=	=	PUNCT
ap-3488	288	1	−	−	PROPN
ap-3488	288	2	2	2	NUM
ap-3488	288	3	√	√	NUM
ap-3488	288	4	3x	3x	NUM
ap-3488	288	5	ln	ln	NOUN
ap-3488	288	6	x	x	PUNCT
ap-3488	288	7	→	→	SYM
ap-3488	288	8	0	0	NUM
ap-3488	288	9	when	when	SCONJ
ap-3488	288	10	x→	x→	PROPN
ap-3488	288	11	0	0	X
ap-3488	288	12	.	.	PUNCT
ap-3488	289	1	the	the	DET
ap-3488	289	2	inclination	inclination	NOUN
ap-3488	289	3	also	also	ADV
ap-3488	289	4	converges	converge	VERB
ap-3488	289	5	to	to	ADP
ap-3488	289	6	0	0	NUM
ap-3488	289	7	,	,	PUNCT
ap-3488	289	8	because	because	SCONJ
ap-3488	289	9	tan	tan	PROPN
ap-3488	289	10	θ	θ	NOUN
ap-3488	289	11	=	=	PUNCT
ap-3488	289	12	dy	dy	VERB
ap-3488	289	13	dx	dx	PROPN
ap-3488	289	14	∼	∼	NOUN
ap-3488	289	15	d	d	X
ap-3488	289	16	dx	dx	PROPN
ap-3488	289	17	(	(	PUNCT
ap-3488	289	18	−2	−2	NOUN
ap-3488	289	19	√	√	ADV
ap-3488	289	20	3	3	NUM
ap-3488	289	21	x	x	SYM
ap-3488	289	22	ln	ln	NOUN
ap-3488	289	23	x	x	NOUN
ap-3488	289	24	)	)	PUNCT
ap-3488	290	1	=	=	SYM
ap-3488	290	2	−2	−2	NOUN
ap-3488	290	3	√	√	NOUN
ap-3488	290	4	3	3	NUM
ap-3488	290	5	(	(	PUNCT
ap-3488	290	6	1	1	NUM
ap-3488	290	7	ln	ln	NOUN
ap-3488	290	8	x	x	NOUN
ap-3488	290	9	−	−	PROPN
ap-3488	290	10	1	1	NUM
ap-3488	290	11	ln2	ln2	NOUN
ap-3488	290	12	x	x	SYM
ap-3488	290	13	)	)	PUNCT
ap-3488	290	14	,	,	PUNCT
ap-3488	290	15	when	when	SCONJ
ap-3488	290	16	x	x	X
ap-3488	290	17	→	→	SYM
ap-3488	290	18	0	0	NUM
ap-3488	290	19	,	,	PUNCT
ap-3488	290	20	tan	tan	NOUN
ap-3488	290	21	θ	θ	PROPN
ap-3488	290	22	→	→	SYM
ap-3488	290	23	0	0	NUM
ap-3488	290	24	,	,	PUNCT
ap-3488	290	25	then	then	ADV
ap-3488	290	26	θ	θ	PROPN
ap-3488	290	27	→	→	SYM
ap-3488	290	28	0	0	NUM
ap-3488	290	29	.	.	PUNCT
ap-3488	291	1	from	from	ADP
ap-3488	291	2	the	the	DET
ap-3488	291	3	proposed	propose	VERB
ap-3488	291	4	control	control	NOUN
ap-3488	291	5	law	law	NOUN
ap-3488	291	6	,	,	PUNCT
ap-3488	291	7	we	we	PRON
ap-3488	291	8	know	know	VERB
ap-3488	291	9	that	that	DET
ap-3488	291	10	l	l	NOUN
ap-3488	292	1	=	=	SYM
ap-3488	292	2	0	0	NUM
ap-3488	292	3	is	be	AUX
ap-3488	292	4	the	the	DET
ap-3488	292	5	equilibrium	equilibrium	NOUN
ap-3488	292	6	point	point	NOUN
ap-3488	292	7	,	,	PUNCT
ap-3488	292	8	and	and	CCONJ
ap-3488	292	9	here	here	ADV
ap-3488	292	10	it	it	PRON
ap-3488	292	11	is	be	AUX
ap-3488	292	12	demonstrated	demonstrate	VERB
ap-3488	292	13	that	that	SCONJ
ap-3488	292	14	when	when	SCONJ
ap-3488	292	15	l→	l→	NOUN
ap-3488	292	16	0	0	NUM
ap-3488	292	17	,	,	PUNCT
ap-3488	292	18	the	the	DET
ap-3488	292	19	limit	limit	NOUN
ap-3488	292	20	of	of	ADP
ap-3488	292	21	d	d	PROPN
ap-3488	292	22	and	and	CCONJ
ap-3488	292	23	θ	θ	PROPN
ap-3488	292	24	are	be	AUX
ap-3488	292	25	both	both	PRON
ap-3488	292	26	0	0	NUM
ap-3488	292	27	.	.	PUNCT
ap-3488	293	1	in	in	ADP
ap-3488	293	2	the	the	DET
ap-3488	293	3	polar	polar	ADJ
ap-3488	293	4	coordinate	coordinate	NOUN
ap-3488	293	5	frame	frame	NOUN
ap-3488	293	6	,	,	PUNCT
ap-3488	293	7	we	we	PRON
ap-3488	293	8	have	have	VERB
ap-3488	293	9	l̇	l̇	NOUN
ap-3488	293	10	=	=	SYM
ap-3488	293	11	u	u	PROPN
ap-3488	293	12	cos	cos	PROPN
ap-3488	293	13	β̄	β̄	ADJ
ap-3488	293	14	=	=	SYM
ap-3488	293	15	−	−	PROPN
ap-3488	293	16	sgn	sgn	NOUN
ap-3488	294	1	cos	cos	PROPN
ap-3488	294	2	β̄	β̄	PROPN
ap-3488	294	3	λl	λl	PROPN
ap-3488	294	4	cos	cos	INTJ
ap-3488	294	5	β̄	β̄	PROPN
ap-3488	294	6	=	=	PUNCT
ap-3488	294	7	−λl|	−λl|	NOUN
ap-3488	294	8	cos	co	NOUN
ap-3488	294	9	β̄|	β̄|	NOUN
ap-3488	294	10	,	,	PUNCT
ap-3488	294	11	hence	hence	ADV
ap-3488	294	12	l→	l→	X
ap-3488	294	13	0	0	NUM
ap-3488	294	14	.	.	PUNCT
ap-3488	295	1	with	with	ADP
ap-3488	295	2	the	the	DET
ap-3488	295	3	trigonometric	trigonometric	ADJ
ap-3488	295	4	relations	relation	NOUN
ap-3488	295	5	,	,	PUNCT
ap-3488	295	6	we	we	PRON
ap-3488	295	7	could	could	AUX
ap-3488	295	8	prove	prove	VERB
ap-3488	295	9	that	that	SCONJ
ap-3488	295	10	v̇	v̇	NOUN
ap-3488	295	11	=	=	PUNCT
ap-3488	295	12	dḋ	dḋ	PROPN
ap-3488	296	1	+	+	CCONJ
ap-3488	296	2	θθ̇	θθ̇	X
ap-3488	296	3	<	<	X
ap-3488	296	4	0	0	NUM
ap-3488	296	5	,	,	PUNCT
ap-3488	296	6	and	and	CCONJ
ap-3488	296	7	the	the	DET
ap-3488	296	8	gain	gain	NOUN
ap-3488	296	9	λ	λ	PROPN
ap-3488	296	10	does	do	AUX
ap-3488	296	11	not	not	PART
ap-3488	296	12	affect	affect	VERB
ap-3488	296	13	the	the	DET
ap-3488	296	14	stability	stability	NOUN
ap-3488	296	15	.	.	PUNCT
ap-3488	297	1	when	when	SCONJ
ap-3488	297	2	r	r	NOUN
ap-3488	297	3	<	<	X
ap-3488	297	4	0	0	NUM
ap-3488	297	5	,	,	PUNCT
ap-3488	297	6	the	the	DET
ap-3488	297	7	same	same	ADJ
ap-3488	297	8	reasoning	reasoning	NOUN
ap-3488	297	9	can	can	AUX
ap-3488	297	10	be	be	AUX
ap-3488	297	11	made	make	VERB
ap-3488	297	12	.	.	PUNCT
ap-3488	298	1	this	this	PRON
ap-3488	298	2	completes	complete	VERB
ap-3488	298	3	the	the	DET
ap-3488	298	4	proof	proof	NOUN
ap-3488	298	5	.	.	PUNCT
ap-3488	299	1	suppose	suppose	VERB
ap-3488	299	2	d	d	AUX
ap-3488	299	3	to	to	PART
ap-3488	299	4	be	be	AUX
ap-3488	299	5	a	a	DET
ap-3488	299	6	length	length	NOUN
ap-3488	299	7	that	that	PRON
ap-3488	299	8	has	have	VERB
ap-3488	299	9	the	the	DET
ap-3488	299	10	same	same	ADJ
ap-3488	299	11	order	order	NOUN
ap-3488	299	12	of	of	ADP
ap-3488	299	13	the	the	DET
ap-3488	299	14	workspace	workspace	NOUN
ap-3488	299	15	of	of	ADP
ap-3488	299	16	the	the	DET
ap-3488	299	17	system	system	NOUN
ap-3488	299	18	and	and	CCONJ
ap-3488	299	19	satisfies	satisfie	NOUN
ap-3488	299	20	l	l	NOUN
ap-3488	299	21	≤	≤	NUM
ap-3488	299	22	d	d	NOUN
ap-3488	299	23	for	for	ADP
ap-3488	299	24	any	any	DET
ap-3488	299	25	t	t	NOUN
ap-3488	299	26	∈	∈	NOUN
ap-3488	299	27	r	r	NOUN
ap-3488	299	28	and	and	CCONJ
ap-3488	299	29	any	any	DET
ap-3488	299	30	robot	robot	NOUN
ap-3488	299	31	.	.	PUNCT
ap-3488	300	1	the	the	DET
ap-3488	300	2	two	two	NUM
ap-3488	300	3	wheel	wheel	NOUN
ap-3488	300	4	velocities	velocity	NOUN
ap-3488	300	5	are	be	AUX
ap-3488	300	6	ω1	ω1	ADJ
ap-3488	300	7	=	=	PUNCT
ap-3488	300	8	2u+	2u+	NUM
ap-3488	300	9	ωl	ωl	ADP
ap-3488	300	10	2rw	2rw	ADJ
ap-3488	300	11	,	,	PUNCT
ap-3488	301	1	ω2	ω2	NOUN
ap-3488	301	2	=	=	SYM
ap-3488	301	3	2u−	2u−	NUM
ap-3488	301	4	ωl	ωl	ADP
ap-3488	301	5	2rw	2rw	ADJ
ap-3488	301	6	,	,	PUNCT
ap-3488	301	7	and	and	CCONJ
ap-3488	301	8	satisfy	satisfy	PROPN
ap-3488	301	9	|ω1|	|ω1|	PROPN
ap-3488	301	10	≤	≤	NOUN
ap-3488	301	11	ωmax	ωmax	ADV
ap-3488	301	12	,	,	PUNCT
ap-3488	301	13	|ω2|	|ω2|	VERB
ap-3488	301	14	≤	≤	PROPN
ap-3488	301	15	ωmax	ωmax	ADV
ap-3488	301	16	,	,	PUNCT
ap-3488	301	17	then	then	ADV
ap-3488	301	18	we	we	PRON
ap-3488	301	19	get	get	VERB
ap-3488	301	20	the	the	DET
ap-3488	301	21	range	range	NOUN
ap-3488	301	22	of	of	ADP
ap-3488	301	23	λ	λ	PROPN
ap-3488	301	24	:	:	PUNCT
ap-3488	301	25	0	0	NUM
ap-3488	301	26	<	<	X
ap-3488	301	27	λ	λ	X
ap-3488	301	28	≤	≤	NOUN
ap-3488	301	29	λmax	λmax	NOUN
ap-3488	302	1	=	=	SYM
ap-3488	302	2	rwωmax	rwωmax	PROPN
ap-3488	303	1	d	d	PROPN
ap-3488	303	2	+	+	NUM
ap-3488	303	3	2π	2π	PROPN
ap-3488	303	4	3	3	NUM
ap-3488	303	5	µrchassis	µrchassis	NOUN
ap-3488	303	6	where	where	SCONJ
ap-3488	303	7	rchassis	rchassis	NOUN
ap-3488	303	8	=	=	PUNCT
ap-3488	303	9	l/2	l/2	PROPN
ap-3488	303	10	is	be	AUX
ap-3488	303	11	the	the	DET
ap-3488	303	12	radius	radius	NOUN
ap-3488	303	13	of	of	ADP
ap-3488	303	14	the	the	DET
ap-3488	303	15	robot	robot	NOUN
ap-3488	303	16	chassis	chassis	NOUN
ap-3488	303	17	,	,	PUNCT
ap-3488	303	18	and	and	CCONJ
ap-3488	303	19	µ	µ	NOUN
ap-3488	303	20	is	be	AUX
ap-3488	303	21	a	a	DET
ap-3488	303	22	convenient	convenient	ADJ
ap-3488	303	23	number	number	NOUN
ap-3488	303	24	that	that	PRON
ap-3488	303	25	satisfies	satisfy	VERB
ap-3488	303	26	l/|r|	l/|r|	PART
ap-3488	303	27	≤	≤	NOUN
ap-3488	303	28	µ	µ	NOUN
ap-3488	303	29	for	for	ADP
ap-3488	303	30	all	all	DET
ap-3488	303	31	t.	t.	NOUN
ap-3488	303	32	3.3	3.3	NUM
ap-3488	303	33	.	.	PUNCT
ap-3488	304	1	stability	stability	NOUN
ap-3488	304	2	of	of	ADP
ap-3488	304	3	formation	formation	NOUN
ap-3488	304	4	control	control	NOUN
ap-3488	304	5	because	because	SCONJ
ap-3488	304	6	of	of	ADP
ap-3488	304	7	the	the	DET
ap-3488	304	8	nonholonomic	nonholonomic	ADJ
ap-3488	304	9	constraints	constraint	NOUN
ap-3488	304	10	,	,	PUNCT
ap-3488	304	11	if	if	SCONJ
ap-3488	304	12	there	there	PRON
ap-3488	304	13	is	be	VERB
ap-3488	304	14	a	a	DET
ap-3488	304	15	bidirectional	bidirectional	ADJ
ap-3488	304	16	path	path	NOUN
ap-3488	304	17	between	between	ADP
ap-3488	304	18	any	any	DET
ap-3488	304	19	two	two	NUM
ap-3488	304	20	unicycle	unicycle	NOUN
ap-3488	304	21	-	-	PUNCT
ap-3488	304	22	type	type	NOUN
ap-3488	304	23	robots	robot	NOUN
ap-3488	304	24	which	which	PRON
ap-3488	304	25	are	be	AUX
ap-3488	304	26	equipped	equip	VERB
ap-3488	304	27	with	with	ADP
ap-3488	304	28	this	this	DET
ap-3488	304	29	local	local	ADJ
ap-3488	304	30	control	control	NOUN
ap-3488	304	31	law	law	NOUN
ap-3488	304	32	,	,	PUNCT
ap-3488	304	33	the	the	DET
ap-3488	304	34	system	system	NOUN
ap-3488	304	35	will	will	AUX
ap-3488	304	36	not	not	PART
ap-3488	304	37	converge	converge	VERB
ap-3488	304	38	,	,	PUNCT
ap-3488	304	39	so	so	SCONJ
ap-3488	304	40	we	we	PRON
ap-3488	304	41	propose	propose	VERB
ap-3488	304	42	a	a	DET
ap-3488	304	43	rooted	rooted	ADJ
ap-3488	304	44	directed	direct	VERB
ap-3488	304	45	acyclic	acyclic	ADJ
ap-3488	304	46	graph	graph	NOUN
ap-3488	304	47	as	as	ADP
ap-3488	304	48	the	the	DET
ap-3488	304	49	communication	communication	NOUN
ap-3488	304	50	topology	topology	NOUN
ap-3488	304	51	of	of	ADP
ap-3488	304	52	the	the	DET
ap-3488	304	53	multi	multi	ADJ
ap-3488	304	54	-	-	ADJ
ap-3488	304	55	robot	robot	ADJ
ap-3488	304	56	system	system	NOUN
ap-3488	304	57	and	and	CCONJ
ap-3488	304	58	the	the	DET
ap-3488	304	59	theorem	theorem	NOUN
ap-3488	304	60	below	below	ADV
ap-3488	304	61	.	.	PUNCT
ap-3488	305	1	theorem	theorem	NOUN
ap-3488	305	2	2	2	NUM
ap-3488	305	3	.	.	PUNCT
ap-3488	306	1	if	if	SCONJ
ap-3488	306	2	the	the	DET
ap-3488	306	3	communication	communication	NOUN
ap-3488	306	4	topology	topology	NOUN
ap-3488	306	5	between	between	ADP
ap-3488	306	6	n	n	PRON
ap-3488	306	7	unicycle	unicycle	NOUN
ap-3488	306	8	-	-	PUNCT
ap-3488	306	9	type	type	NOUN
ap-3488	306	10	robots	robot	NOUN
ap-3488	306	11	is	be	AUX
ap-3488	306	12	a	a	DET
ap-3488	306	13	rooted	rooted	ADJ
ap-3488	306	14	directed	direct	VERB
ap-3488	306	15	acyclic	acyclic	ADJ
ap-3488	306	16	graph	graph	NOUN
ap-3488	306	17	,	,	PUNCT
ap-3488	306	18	then	then	ADV
ap-3488	306	19	the	the	DET
ap-3488	306	20	system	system	NOUN
ap-3488	306	21	(	(	PUNCT
ap-3488	306	22	equation	equation	NOUN
ap-3488	306	23	7	7	NUM
ap-3488	306	24	)	)	PUNCT
ap-3488	306	25	will	will	AUX
ap-3488	306	26	achieve	achieve	VERB
ap-3488	306	27	the	the	DET
ap-3488	306	28	desired	desire	VERB
ap-3488	306	29	formation	formation	NOUN
ap-3488	306	30	(	(	PUNCT
ap-3488	306	31	equation	equation	NOUN
ap-3488	306	32	9	9	NUM
ap-3488	306	33	)	)	PUNCT
ap-3488	306	34	under	under	ADP
ap-3488	306	35	the	the	DET
ap-3488	306	36	local	local	ADJ
ap-3488	306	37	control	control	NOUN
ap-3488	306	38	law	law	NOUN
ap-3488	306	39	(	(	PUNCT
ap-3488	306	40	equation	equation	NOUN
ap-3488	306	41	11	11	NUM
ap-3488	306	42	,	,	PUNCT
ap-3488	306	43	13	13	NUM
ap-3488	306	44	)	)	PUNCT
ap-3488	306	45	.	.	PUNCT
ap-3488	307	1	especially	especially	ADV
ap-3488	307	2	,	,	PUNCT
ap-3488	307	3	each	each	DET
ap-3488	307	4	robot	robot	NOUN
ap-3488	307	5	,	,	PUNCT
ap-3488	307	6	in	in	ADP
ap-3488	307	7	phase	phase	NOUN
ap-3488	307	8	3	3	NUM
ap-3488	307	9	,	,	PUNCT
ap-3488	307	10	converges	converge	VERB
ap-3488	307	11	to	to	ADP
ap-3488	307	12	the	the	DET
ap-3488	307	13	desired	desire	VERB
ap-3488	307	14	formation	formation	NOUN
ap-3488	307	15	asymptotically	asymptotically	ADV
ap-3488	307	16	.	.	PUNCT
ap-3488	308	1	proof	proof	NOUN
ap-3488	308	2	.	.	PUNCT
ap-3488	309	1	there	there	PRON
ap-3488	309	2	is	be	VERB
ap-3488	309	3	no	no	DET
ap-3488	309	4	directed	direct	VERB
ap-3488	309	5	circle	circle	NOUN
ap-3488	309	6	,	,	PUNCT
ap-3488	309	7	so	so	SCONJ
ap-3488	309	8	the	the	DET
ap-3488	309	9	root	root	NOUN
ap-3488	309	10	node	node	NOUN
ap-3488	309	11	(	(	PUNCT
ap-3488	309	12	robot	robot	NOUN
ap-3488	309	13	)	)	PUNCT
ap-3488	309	14	will	will	AUX
ap-3488	309	15	not	not	PART
ap-3488	309	16	receive	receive	VERB
ap-3488	309	17	any	any	DET
ap-3488	309	18	information	information	NOUN
ap-3488	309	19	and	and	CCONJ
ap-3488	309	20	will	will	AUX
ap-3488	309	21	be	be	AUX
ap-3488	309	22	static	static	ADJ
ap-3488	309	23	.	.	PUNCT
ap-3488	310	1	let	let	VERB
ap-3488	310	2	km	km	NOUN
ap-3488	310	3	denote	denote	VERB
ap-3488	310	4	the	the	DET
ap-3488	310	5	set	set	NOUN
ap-3488	310	6	of	of	ADP
ap-3488	310	7	the	the	DET
ap-3488	310	8	nodes	node	NOUN
ap-3488	310	9	(	(	PUNCT
ap-3488	310	10	robots	robot	NOUN
ap-3488	310	11	)	)	PUNCT
ap-3488	310	12	6	6	NUM
ap-3488	310	13	vol	vol	NOUN
ap-3488	310	14	.	.	PUNCT
ap-3488	311	1	56	56	NUM
ap-3488	311	2	no	no	NOUN
ap-3488	311	3	.	.	PUNCT
ap-3488	312	1	1/2016	1/2016	NUM
ap-3488	312	2	formation	formation	NOUN
ap-3488	312	3	control	control	NOUN
ap-3488	312	4	of	of	ADP
ap-3488	312	5	multiple	multiple	ADJ
ap-3488	312	6	unicycle	unicycle	NOUN
ap-3488	312	7	-	-	PUNCT
ap-3488	312	8	type	type	NOUN
ap-3488	312	9	robots	robot	NOUN
ap-3488	312	10	using	use	VERB
ap-3488	312	11	lie	lie	NOUN
ap-3488	312	12	group	group	NOUN
ap-3488	312	13	1	1	NUM
ap-3488	312	14	2	2	NUM
ap-3488	312	15	3	3	NUM
ap-3488	312	16	4	4	NUM
ap-3488	312	17	5	5	NUM
ap-3488	312	18	6	6	NUM
ap-3488	312	19	figure	figure	NOUN
ap-3488	312	20	4	4	NUM
ap-3488	312	21	.	.	PUNCT
ap-3488	312	22	communication	communication	NOUN
ap-3488	312	23	topology	topology	NOUN
ap-3488	312	24	of	of	ADP
ap-3488	312	25	simulation	simulation	NOUN
ap-3488	312	26	.	.	PUNCT
ap-3488	313	1	to	to	PART
ap-3488	313	2	which	which	PRON
ap-3488	313	3	there	there	PRON
ap-3488	313	4	is	be	VERB
ap-3488	313	5	a	a	DET
ap-3488	313	6	directed	direct	VERB
ap-3488	313	7	path	path	NOUN
ap-3488	313	8	from	from	ADP
ap-3488	313	9	the	the	DET
ap-3488	313	10	root	root	NOUN
ap-3488	313	11	and	and	CCONJ
ap-3488	313	12	this	this	DET
ap-3488	313	13	path	path	NOUN
ap-3488	313	14	consists	consist	VERB
ap-3488	313	15	of	of	ADP
ap-3488	313	16	at	at	ADP
ap-3488	313	17	most	most	ADJ
ap-3488	313	18	m	m	NOUN
ap-3488	313	19	edges	edge	NOUN
ap-3488	313	20	.	.	PUNCT
ap-3488	314	1	then	then	ADV
ap-3488	314	2	k0	k0	PROPN
ap-3488	314	3	has	have	VERB
ap-3488	314	4	only	only	ADV
ap-3488	314	5	one	one	NUM
ap-3488	314	6	element	element	NOUN
ap-3488	314	7	–	–	PUNCT
ap-3488	314	8	the	the	DET
ap-3488	314	9	root	root	NOUN
ap-3488	314	10	robot	robot	NOUN
ap-3488	314	11	,	,	PUNCT
ap-3488	314	12	denoted	denote	VERB
ap-3488	314	13	by	by	ADP
ap-3488	314	14	v0	v0	NOUN
ap-3488	314	15	.	.	PUNCT
ap-3488	315	1	the	the	DET
ap-3488	315	2	configuration	configuration	NOUN
ap-3488	315	3	of	of	ADP
ap-3488	315	4	this	this	DET
ap-3488	315	5	robot	robot	NOUN
ap-3488	315	6	in	in	ADP
ap-3488	315	7	the	the	DET
ap-3488	315	8	fixed	fix	VERB
ap-3488	315	9	frame	frame	NOUN
ap-3488	315	10	is	be	AUX
ap-3488	315	11	denoted	denote	VERB
ap-3488	315	12	by	by	ADP
ap-3488	315	13	g0	g0	PROPN
ap-3488	315	14	=	=	SYM
ap-3488	315	15	ḡ0	ḡ0	PROPN
ap-3488	315	16	.	.	PUNCT
ap-3488	316	1	then	then	ADV
ap-3488	316	2	we	we	PRON
ap-3488	316	3	use	use	VERB
ap-3488	316	4	the	the	DET
ap-3488	316	5	mathematical	mathematical	ADJ
ap-3488	316	6	induction	induction	NOUN
ap-3488	316	7	method	method	NOUN
ap-3488	316	8	.	.	PUNCT
ap-3488	317	1	(	(	PUNCT
ap-3488	317	2	1	1	NUM
ap-3488	317	3	.	.	PUNCT
ap-3488	317	4	)	)	PUNCT
ap-3488	318	1	for	for	ADP
ap-3488	318	2	k1	k1	NOUN
ap-3488	318	3	,	,	PUNCT
ap-3488	318	4	suppose	suppose	VERB
ap-3488	318	5	that	that	SCONJ
ap-3488	318	6	there	there	PRON
ap-3488	318	7	are	be	VERB
ap-3488	318	8	n1	n1	ADJ
ap-3488	318	9	elements	element	NOUN
ap-3488	318	10	in	in	ADP
ap-3488	318	11	k1	k1	PROPN
ap-3488	318	12	.	.	PUNCT
ap-3488	319	1	one	one	NUM
ap-3488	319	2	element	element	NOUN
ap-3488	319	3	is	be	AUX
ap-3488	319	4	denoted	denote	VERB
ap-3488	319	5	by	by	ADP
ap-3488	319	6	v1i	v1i	NOUN
ap-3488	319	7	where	where	SCONJ
ap-3488	319	8	1	1	NUM
ap-3488	319	9	≤	≤	NUM
ap-3488	319	10	i	i	NOUN
ap-3488	319	11	≤	≤	ADJ
ap-3488	319	12	n1	n1	NOUN
ap-3488	319	13	,	,	PUNCT
ap-3488	319	14	and	and	CCONJ
ap-3488	319	15	the	the	DET
ap-3488	319	16	configuration	configuration	NOUN
ap-3488	319	17	of	of	ADP
ap-3488	319	18	v1i	v1i	NOUN
ap-3488	319	19	is	be	AUX
ap-3488	319	20	denoted	denote	VERB
ap-3488	319	21	by	by	ADP
ap-3488	319	22	g1i	g1i	PROPN
ap-3488	319	23	.	.	PUNCT
ap-3488	320	1	because	because	SCONJ
ap-3488	320	2	v1i	v1i	NOUN
ap-3488	320	3	receives	receive	VERB
ap-3488	320	4	information	information	NOUN
ap-3488	320	5	only	only	ADV
ap-3488	320	6	from	from	ADP
ap-3488	320	7	v0	v0	PROPN
ap-3488	320	8	,	,	PUNCT
ap-3488	320	9	according	accord	VERB
ap-3488	320	10	to	to	ADP
ap-3488	320	11	the	the	DET
ap-3488	320	12	lemmas	lemma	NOUN
ap-3488	320	13	above	above	ADV
ap-3488	320	14	and	and	CCONJ
ap-3488	320	15	theorem	theorem	VERB
ap-3488	320	16	1	1	NUM
ap-3488	320	17	we	we	PRON
ap-3488	320	18	know	know	VERB
ap-3488	320	19	that	that	SCONJ
ap-3488	320	20	limt→∞	limt→∞	ADP
ap-3488	320	21	g−1	g−1	PROPN
ap-3488	320	22	1i	1i	NUM
ap-3488	320	23	g0	g0	NOUN
ap-3488	320	24	=	=	PUNCT
ap-3488	321	1	ḡ1i,0	ḡ1i,0	PROPN
ap-3488	321	2	.	.	PUNCT
ap-3488	322	1	(	(	PUNCT
ap-3488	322	2	2	2	NUM
ap-3488	322	3	.	.	PUNCT
ap-3488	322	4	)	)	PUNCT
ap-3488	323	1	for	for	ADP
ap-3488	323	2	km	km	PROPN
ap-3488	323	3	,	,	PUNCT
ap-3488	323	4	the	the	DET
ap-3488	323	5	elements	element	NOUN
ap-3488	323	6	in	in	ADP
ap-3488	323	7	this	this	DET
ap-3488	323	8	set	set	NOUN
ap-3488	323	9	are	be	AUX
ap-3488	323	10	denoted	denote	VERB
ap-3488	323	11	by	by	ADP
ap-3488	323	12	vmi	vmi	PROPN
ap-3488	323	13	,	,	PUNCT
ap-3488	323	14	1	1	NUM
ap-3488	323	15	≤	≤	NUM
ap-3488	323	16	i	i	PRON
ap-3488	323	17	≤	≤	ADV
ap-3488	323	18	cm	cm	NOUN
ap-3488	323	19	where	where	SCONJ
ap-3488	323	20	cm	cm	PROPN
ap-3488	323	21	is	be	AUX
ap-3488	323	22	the	the	DET
ap-3488	323	23	cardinality	cardinality	NOUN
ap-3488	323	24	of	of	ADP
ap-3488	323	25	this	this	DET
ap-3488	323	26	set	set	NOUN
ap-3488	323	27	.	.	PUNCT
ap-3488	324	1	vmi	vmi	PROPN
ap-3488	324	2	receives	receive	VERB
ap-3488	324	3	information	information	NOUN
ap-3488	324	4	from	from	ADP
ap-3488	324	5	the	the	DET
ap-3488	324	6	nodes	node	NOUN
ap-3488	324	7	which	which	PRON
ap-3488	324	8	are	be	AUX
ap-3488	324	9	elements	element	NOUN
ap-3488	324	10	of	of	ADP
ap-3488	324	11	⋃	⋃	PROPN
ap-3488	324	12	kn	kn	PROPN
ap-3488	324	13	,	,	PUNCT
ap-3488	324	14	n≤m−1	n≤m−1	PROPN
ap-3488	324	15	and	and	CCONJ
ap-3488	324	16	have	have	AUX
ap-3488	324	17	achieved	achieve	VERB
ap-3488	324	18	the	the	DET
ap-3488	324	19	desired	desire	VERB
ap-3488	324	20	configurations	configuration	NOUN
ap-3488	324	21	.	.	PUNCT
ap-3488	325	1	we	we	PRON
ap-3488	325	2	use	use	VERB
ap-3488	325	3	j	j	PROPN
ap-3488	325	4	to	to	PART
ap-3488	325	5	denote	denote	VERB
ap-3488	325	6	the	the	DET
ap-3488	325	7	index	index	NOUN
ap-3488	325	8	numbers	number	NOUN
ap-3488	325	9	of	of	ADP
ap-3488	325	10	these	these	DET
ap-3488	325	11	robots	robot	NOUN
ap-3488	325	12	,	,	PUNCT
ap-3488	325	13	that	that	ADV
ap-3488	325	14	is	is	ADV
ap-3488	325	15	,	,	PUNCT
ap-3488	325	16	vnjj	vnjj	NOUN
ap-3488	325	17	∈	∈	PROPN
ap-3488	325	18	knj	knj	PROPN
ap-3488	325	19	⊂⋃	⊂⋃	PROPN
ap-3488	325	20	kn	kn	PROPN
ap-3488	325	21	,	,	PUNCT
ap-3488	325	22	n≤m−1	n≤m−1	PROPN
ap-3488	325	23	.	.	PUNCT
ap-3488	326	1	then	then	ADV
ap-3488	326	2	with	with	ADP
ap-3488	326	3	the	the	DET
ap-3488	326	4	control	control	NOUN
ap-3488	326	5	law	law	NOUN
ap-3488	326	6	,	,	PUNCT
ap-3488	326	7	vmi	vmi	PROPN
ap-3488	326	8	will	will	AUX
ap-3488	326	9	converge	converge	VERB
ap-3488	326	10	to	to	ADP
ap-3488	326	11	the	the	DET
ap-3488	326	12	desired	desire	VERB
ap-3488	326	13	configuration	configuration	NOUN
ap-3488	326	14	relative	relative	ADJ
ap-3488	326	15	to	to	ADP
ap-3488	326	16	vnjj	vnjj	NOUN
ap-3488	326	17	,	,	PUNCT
ap-3488	326	18	so	so	ADV
ap-3488	326	19	lim	lim	PROPN
ap-3488	326	20	t→∞	t→∞	X
ap-3488	327	1	g−1	g−1	PROPN
ap-3488	327	2	mig0	mig0	PROPN
ap-3488	328	1	=	=	SYM
ap-3488	329	1	lim	lim	PROPN
ap-3488	329	2	t→∞	t→∞	X
ap-3488	329	3	g−1	g−1	ADJ
ap-3488	329	4	mignjjg	mignjjg	NOUN
ap-3488	329	5	−1	−1	NOUN
ap-3488	329	6	njj	njj	PROPN
ap-3488	329	7	g0	g0	PROPN
ap-3488	329	8	=	=	PROPN
ap-3488	329	9	(	(	PUNCT
ap-3488	329	10	lim	lim	PROPN
ap-3488	329	11	t→∞	t→∞	X
ap-3488	329	12	g−1	g−1	PROPN
ap-3488	329	13	mi	mi	PROPN
ap-3488	329	14	ḡnjj	ḡnjj	NOUN
ap-3488	329	15	)	)	PUNCT
ap-3488	329	16	(	(	PUNCT
ap-3488	329	17	ḡ−1	ḡ−1	PROPN
ap-3488	329	18	njj	njj	PROPN
ap-3488	329	19	ḡ0	ḡ0	PROPN
ap-3488	329	20	)	)	PUNCT
ap-3488	329	21	=	=	SYM
ap-3488	330	1	ḡ−1	ḡ−1	NOUN
ap-3488	330	2	(	(	PUNCT
ap-3488	330	3	njj),miḡ(njj),0	njj),miḡ(njj),0	ADV
ap-3488	330	4	=	=	SYM
ap-3488	330	5	ḡmi,0	ḡmi,0	X
ap-3488	330	6	.	.	PUNCT
ap-3488	331	1	the	the	DET
ap-3488	331	2	topology	topology	NOUN
ap-3488	331	3	graph	graph	NOUN
ap-3488	331	4	is	be	AUX
ap-3488	331	5	a	a	DET
ap-3488	331	6	finite	finite	ADJ
ap-3488	331	7	graph	graph	NOUN
ap-3488	331	8	,	,	PUNCT
ap-3488	331	9	so	so	ADV
ap-3488	331	10	all	all	DET
ap-3488	331	11	the	the	DET
ap-3488	331	12	robots	robot	NOUN
ap-3488	331	13	will	will	AUX
ap-3488	331	14	converge	converge	VERB
ap-3488	331	15	to	to	ADP
ap-3488	331	16	the	the	DET
ap-3488	331	17	desired	desire	VERB
ap-3488	331	18	configuration	configuration	NOUN
ap-3488	331	19	relative	relative	ADJ
ap-3488	331	20	to	to	ADP
ap-3488	331	21	v0	v0	PROPN
ap-3488	331	22	.	.	PUNCT
ap-3488	332	1	then	then	ADV
ap-3488	332	2	for	for	ADP
ap-3488	332	3	any	any	DET
ap-3488	332	4	vi	vi	NOUN
ap-3488	332	5	,	,	PUNCT
ap-3488	332	6	vj	vj	INTJ
ap-3488	332	7	,	,	PUNCT
ap-3488	332	8	we	we	PRON
ap-3488	332	9	have	have	VERB
ap-3488	332	10	lim	lim	PROPN
ap-3488	332	11	t→∞	t→∞	X
ap-3488	333	1	g−1	g−1	PROPN
ap-3488	333	2	i	i	PRON
ap-3488	333	3	gj	gj	NOUN
ap-3488	334	1	=	=	PROPN
ap-3488	334	2	lim	lim	PROPN
ap-3488	334	3	t→∞	t→∞	X
ap-3488	335	1	g−1	g−1	PROPN
ap-3488	335	2	i	i	PROPN
ap-3488	335	3	g0	g0	NOUN
ap-3488	335	4	g	g	PROPN
ap-3488	335	5	−1	−1	NOUN
ap-3488	335	6	0	0	NUM
ap-3488	335	7	gj	gj	NOUN
ap-3488	335	8	=	=	NOUN
ap-3488	336	1	ḡ−1	ḡ−1	NOUN
ap-3488	336	2	0i	0i	X
ap-3488	336	3	ḡ0j	ḡ0j	PROPN
ap-3488	336	4	=	=	PUNCT
ap-3488	336	5	ḡij	ḡij	PROPN
ap-3488	336	6	.	.	PUNCT
ap-3488	337	1	then	then	ADV
ap-3488	337	2	the	the	DET
ap-3488	337	3	formation	formation	NOUN
ap-3488	337	4	in	in	ADP
ap-3488	337	5	equation	equation	NOUN
ap-3488	337	6	9	9	NUM
ap-3488	337	7	is	be	AUX
ap-3488	337	8	achieved	achieve	VERB
ap-3488	337	9	.	.	PUNCT
ap-3488	338	1	4	4	X
ap-3488	338	2	.	.	X
ap-3488	338	3	simulation	simulation	NOUN
ap-3488	338	4	let	let	VERB
ap-3488	338	5	us	we	PRON
ap-3488	338	6	consider	consider	VERB
ap-3488	338	7	a	a	DET
ap-3488	338	8	group	group	NOUN
ap-3488	338	9	of	of	ADP
ap-3488	338	10	6	6	NUM
ap-3488	338	11	unicycle	unicycle	NOUN
ap-3488	338	12	-	-	PUNCT
ap-3488	338	13	type	type	NOUN
ap-3488	338	14	robots	robot	NOUN
ap-3488	338	15	which	which	PRON
ap-3488	338	16	are	be	AUX
ap-3488	338	17	located	locate	VERB
ap-3488	338	18	in	in	ADP
ap-3488	338	19	a	a	DET
ap-3488	338	20	global	global	ADJ
ap-3488	338	21	frame	frame	NOUN
ap-3488	338	22	,	,	PUNCT
ap-3488	338	23	and	and	CCONJ
ap-3488	338	24	we	we	PRON
ap-3488	338	25	suppose	suppose	VERB
ap-3488	338	26	that	that	SCONJ
ap-3488	338	27	each	each	DET
ap-3488	338	28	robot	robot	NOUN
ap-3488	338	29	could	could	AUX
ap-3488	338	30	know	know	VERB
ap-3488	338	31	its	its	PRON
ap-3488	338	32	own	own	ADJ
ap-3488	338	33	position	position	NOUN
ap-3488	338	34	and	and	CCONJ
ap-3488	338	35	orientation	orientation	NOUN
ap-3488	338	36	in	in	ADP
ap-3488	338	37	the	the	DET
ap-3488	338	38	frame	frame	NOUN
ap-3488	338	39	via	via	ADP
ap-3488	338	40	gps	gps	PROPN
ap-3488	338	41	or	or	CCONJ
ap-3488	338	42	via	via	ADP
ap-3488	338	43	a	a	DET
ap-3488	338	44	camera	camera	NOUN
ap-3488	338	45	which	which	PRON
ap-3488	338	46	is	be	AUX
ap-3488	338	47	installed	instal	VERB
ap-3488	338	48	above	above	ADP
ap-3488	338	49	the	the	DET
ap-3488	338	50	work	work	NOUN
ap-3488	338	51	area	area	NOUN
ap-3488	338	52	.	.	PUNCT
ap-3488	339	1	the	the	DET
ap-3488	339	2	initial	initial	ADJ
ap-3488	339	3	pose	pose	NOUN
ap-3488	339	4	of	of	ADP
ap-3488	339	5	each	each	PRON
ap-3488	339	6	is	be	AUX
ap-3488	339	7	p	p	NOUN
ap-3488	339	8	=	=	PUNCT
ap-3488	339	9	(	(	PUNCT
ap-3488	339	10	x	x	X
ap-3488	339	11	,	,	PUNCT
ap-3488	339	12	y	y	PROPN
ap-3488	339	13	,	,	PUNCT
ap-3488	339	14	θ	θ	PROPN
ap-3488	339	15	)	)	PUNCT
ap-3488	339	16	where	where	SCONJ
ap-3488	339	17	(	(	PUNCT
ap-3488	339	18	x	x	NOUN
ap-3488	339	19	,	,	PUNCT
ap-3488	339	20	y	y	NOUN
ap-3488	339	21	)	)	PUNCT
ap-3488	339	22	represents	represent	VERB
ap-3488	339	23	the	the	DET
ap-3488	339	24	robot	robot	NOUN
ap-3488	339	25	position	position	NOUN
ap-3488	339	26	in	in	ADP
ap-3488	339	27	figure	figure	NOUN
ap-3488	339	28	5	5	NUM
ap-3488	339	29	.	.	PUNCT
ap-3488	339	30	trajectories	trajectory	NOUN
ap-3488	339	31	of	of	ADP
ap-3488	339	32	the	the	DET
ap-3488	339	33	6	6	NUM
ap-3488	339	34	robots	robot	NOUN
ap-3488	339	35	.	.	PUNCT
ap-3488	340	1	the	the	DET
ap-3488	340	2	global	global	ADJ
ap-3488	340	3	frame	frame	NOUN
ap-3488	340	4	and	and	CCONJ
ap-3488	340	5	angle	angle	NOUN
ap-3488	340	6	θ	θ	PROPN
ap-3488	340	7	indicates	indicate	VERB
ap-3488	340	8	the	the	DET
ap-3488	340	9	orientation	orientation	NOUN
ap-3488	340	10	of	of	ADP
ap-3488	340	11	the	the	DET
ap-3488	340	12	robot	robot	NOUN
ap-3488	340	13	.	.	PUNCT
ap-3488	341	1	the	the	DET
ap-3488	341	2	six	six	NUM
ap-3488	341	3	initial	initial	ADJ
ap-3488	341	4	poses	pose	NOUN
ap-3488	341	5	are	be	AUX
ap-3488	341	6	given	give	VERB
ap-3488	341	7	by	by	ADP
ap-3488	341	8	p1	p1	PROPN
ap-3488	341	9	=	=	SYM
ap-3488	341	10	(	(	PUNCT
ap-3488	341	11	0	0	NUM
ap-3488	341	12	,	,	PUNCT
ap-3488	341	13	0	0	NUM
ap-3488	341	14	,	,	PUNCT
ap-3488	341	15	0	0	NUM
ap-3488	341	16	)	)	PUNCT
ap-3488	341	17	,	,	PUNCT
ap-3488	341	18	p2	p2	PROPN
ap-3488	341	19	=	=	SYM
ap-3488	341	20	(	(	PUNCT
ap-3488	341	21	5	5	NUM
ap-3488	341	22	,	,	PUNCT
ap-3488	341	23	3	3	NUM
ap-3488	341	24	,	,	PUNCT
ap-3488	341	25	0	0	NUM
ap-3488	341	26	)	)	PUNCT
ap-3488	341	27	,	,	PUNCT
ap-3488	341	28	p3	p3	PROPN
ap-3488	341	29	=	=	SYM
ap-3488	341	30	(	(	PUNCT
ap-3488	341	31	−1	−1	NOUN
ap-3488	341	32	,	,	PUNCT
ap-3488	341	33	6	6	NUM
ap-3488	341	34	,	,	PUNCT
ap-3488	341	35	π/6	π/6	NUM
ap-3488	341	36	)	)	PUNCT
ap-3488	341	37	,	,	PUNCT
ap-3488	341	38	p4	p4	NOUN
ap-3488	341	39	=	=	SYM
ap-3488	341	40	(	(	PUNCT
ap-3488	341	41	6,−5,−π/2	6,−5,−π/2	NUM
ap-3488	341	42	)	)	PUNCT
ap-3488	341	43	,	,	PUNCT
ap-3488	341	44	p5	p5	NOUN
ap-3488	341	45	=	=	SYM
ap-3488	341	46	(	(	PUNCT
ap-3488	341	47	0,−5	0,−5	PROPN
ap-3488	341	48	,	,	PUNCT
ap-3488	341	49	π/3	π/3	NUM
ap-3488	341	50	)	)	PUNCT
ap-3488	341	51	,	,	PUNCT
ap-3488	341	52	p3	p3	PROPN
ap-3488	341	53	=	=	SYM
ap-3488	341	54	(	(	PUNCT
ap-3488	341	55	−5,−4,−π/2	−5,−4,−π/2	PROPN
ap-3488	341	56	)	)	PUNCT
ap-3488	341	57	.	.	PUNCT
ap-3488	342	1	and	and	CCONJ
ap-3488	342	2	the	the	DET
ap-3488	342	3	desired	desire	VERB
ap-3488	342	4	formation	formation	NOUN
ap-3488	342	5	is	be	AUX
ap-3488	342	6	a	a	DET
ap-3488	342	7	regular	regular	ADJ
ap-3488	342	8	hexagon	hexagon	NOUN
ap-3488	342	9	with	with	ADP
ap-3488	342	10	side	side	ADJ
ap-3488	342	11	length	length	NOUN
ap-3488	342	12	of	of	ADP
ap-3488	342	13	2	2	NUM
ap-3488	342	14	.	.	PUNCT
ap-3488	343	1	let	let	VERB
ap-3488	343	2	c	c	NOUN
ap-3488	343	3	=	=	SYM
ap-3488	343	4	1	1	NUM
ap-3488	343	5	,	,	PUNCT
ap-3488	343	6	the	the	DET
ap-3488	343	7	sample	sample	NOUN
ap-3488	343	8	time	time	NOUN
ap-3488	343	9	is	be	AUX
ap-3488	343	10	0.1	0.1	NUM
ap-3488	343	11	s	s	NOUN
ap-3488	343	12	,	,	PUNCT
ap-3488	343	13	and	and	CCONJ
ap-3488	343	14	the	the	DET
ap-3488	343	15	maximum	maximum	ADJ
ap-3488	343	16	angular	angular	ADJ
ap-3488	343	17	velocity	velocity	NOUN
ap-3488	343	18	of	of	ADP
ap-3488	343	19	the	the	DET
ap-3488	343	20	wheels	wheel	NOUN
ap-3488	343	21	is	be	AUX
ap-3488	343	22	ωmax	ωmax	VERB
ap-3488	343	23	=	=	ADJ
ap-3488	344	1	5π	5π	NUM
ap-3488	344	2	/	/	SYM
ap-3488	344	3	s.	s.	PROPN
ap-3488	345	1	the	the	DET
ap-3488	345	2	communication	communication	NOUN
ap-3488	345	3	topology	topology	NOUN
ap-3488	345	4	is	be	AUX
ap-3488	345	5	given	give	VERB
ap-3488	345	6	in	in	ADP
ap-3488	345	7	figure	figure	NOUN
ap-3488	345	8	4	4	NUM
ap-3488	345	9	.	.	PUNCT
ap-3488	345	10	using	use	VERB
ap-3488	345	11	matlab	matlab	PROPN
ap-3488	345	12	,	,	PUNCT
ap-3488	345	13	the	the	DET
ap-3488	345	14	results	result	NOUN
ap-3488	345	15	are	be	AUX
ap-3488	345	16	obtained	obtain	VERB
ap-3488	345	17	as	as	SCONJ
ap-3488	345	18	shown	show	VERB
ap-3488	345	19	in	in	ADP
ap-3488	345	20	figure	figure	NOUN
ap-3488	345	21	5	5	NUM
ap-3488	345	22	and	and	CCONJ
ap-3488	345	23	6	6	NUM
ap-3488	345	24	.	.	PUNCT
ap-3488	346	1	we	we	PRON
ap-3488	346	2	observe	observe	VERB
ap-3488	346	3	that	that	SCONJ
ap-3488	346	4	the	the	DET
ap-3488	346	5	six	six	NUM
ap-3488	346	6	robots	robot	NOUN
ap-3488	346	7	achieve	achieve	VERB
ap-3488	346	8	the	the	DET
ap-3488	346	9	desired	desire	VERB
ap-3488	346	10	hexagonal	hexagonal	ADJ
ap-3488	346	11	formation	formation	NOUN
ap-3488	346	12	:	:	PUNCT
ap-3488	346	13	robot-1	robot-1	NUM
ap-3488	346	14	has	have	VERB
ap-3488	346	15	no	no	DET
ap-3488	346	16	information	information	NOUN
ap-3488	346	17	source	source	NOUN
ap-3488	346	18	,	,	PUNCT
ap-3488	346	19	so	so	SCONJ
ap-3488	346	20	it	it	PRON
ap-3488	346	21	remains	remain	VERB
ap-3488	346	22	static	static	ADJ
ap-3488	346	23	.	.	PUNCT
ap-3488	347	1	other	other	ADJ
ap-3488	347	2	robots	robot	NOUN
ap-3488	347	3	perform	perform	VERB
ap-3488	347	4	the	the	DET
ap-3488	347	5	trajectories	trajectory	NOUN
ap-3488	347	6	according	accord	VERB
ap-3488	347	7	to	to	ADP
ap-3488	347	8	the	the	DET
ap-3488	347	9	posture	posture	NOUN
ap-3488	347	10	of	of	ADP
ap-3488	347	11	their	their	PRON
ap-3488	347	12	information	information	NOUN
ap-3488	347	13	source	source	NOUN
ap-3488	347	14	robots	robot	NOUN
ap-3488	347	15	.	.	PUNCT
ap-3488	348	1	robots	robot	NOUN
ap-3488	348	2	4	4	NUM
ap-3488	348	3	,	,	PUNCT
ap-3488	348	4	5	5	NUM
ap-3488	348	5	and	and	CCONJ
ap-3488	348	6	6	6	NUM
ap-3488	348	7	achieve	achieve	VERB
ap-3488	348	8	the	the	DET
ap-3488	348	9	desired	desire	VERB
ap-3488	348	10	configurations	configuration	NOUN
ap-3488	348	11	after	after	ADP
ap-3488	348	12	robots	robot	NOUN
ap-3488	348	13	2	2	NUM
ap-3488	348	14	and	and	CCONJ
ap-3488	348	15	3	3	NUM
ap-3488	348	16	because	because	SCONJ
ap-3488	348	17	of	of	ADP
ap-3488	348	18	the	the	DET
ap-3488	348	19	communication	communication	NOUN
ap-3488	348	20	topology	topology	NOUN
ap-3488	348	21	shape	shape	NOUN
ap-3488	348	22	.	.	PUNCT
ap-3488	349	1	figure	figure	NOUN
ap-3488	349	2	6	6	NUM
ap-3488	349	3	shows	show	VERB
ap-3488	349	4	the	the	DET
ap-3488	349	5	evolution	evolution	NOUN
ap-3488	349	6	of	of	ADP
ap-3488	349	7	the	the	DET
ap-3488	349	8	angles	angle	NOUN
ap-3488	349	9	between	between	ADP
ap-3488	349	10	the	the	DET
ap-3488	349	11	forward	forward	ADJ
ap-3488	349	12	direction	direction	NOUN
ap-3488	349	13	of	of	ADP
ap-3488	349	14	each	each	DET
ap-3488	349	15	robot	robot	NOUN
ap-3488	349	16	and	and	CCONJ
ap-3488	349	17	the	the	DET
ap-3488	349	18	x	x	NOUN
ap-3488	349	19	-	-	NOUN
ap-3488	349	20	axis	axis	NOUN
ap-3488	349	21	of	of	ADP
ap-3488	349	22	the	the	DET
ap-3488	349	23	global	global	ADJ
ap-3488	349	24	frame	frame	NOUN
ap-3488	349	25	.	.	PUNCT
ap-3488	350	1	we	we	PRON
ap-3488	350	2	see	see	VERB
ap-3488	350	3	that	that	SCONJ
ap-3488	350	4	the	the	DET
ap-3488	350	5	six	six	NUM
ap-3488	350	6	angles	angle	NOUN
ap-3488	350	7	turn	turn	NOUN
ap-3488	350	8	to	to	ADP
ap-3488	350	9	the	the	DET
ap-3488	350	10	same	same	ADJ
ap-3488	350	11	value	value	NOUN
ap-3488	350	12	after	after	ADP
ap-3488	350	13	some	some	DET
ap-3488	350	14	regulations	regulation	NOUN
ap-3488	350	15	of	of	ADP
ap-3488	350	16	the	the	DET
ap-3488	350	17	configurations	configuration	NOUN
ap-3488	350	18	,	,	PUNCT
ap-3488	350	19	which	which	PRON
ap-3488	350	20	indicates	indicate	VERB
ap-3488	350	21	the	the	DET
ap-3488	350	22	coordination	coordination	NOUN
ap-3488	350	23	of	of	ADP
ap-3488	350	24	the	the	DET
ap-3488	350	25	robots	robot	NOUN
ap-3488	350	26	’	'	PUNCT
ap-3488	350	27	orientations	orientation	NOUN
ap-3488	350	28	.	.	PUNCT
ap-3488	351	1	the	the	DET
ap-3488	351	2	rotation	rotation	NOUN
ap-3488	351	3	velocities	velocity	NOUN
ap-3488	351	4	become	become	VERB
ap-3488	351	5	0	0	NUM
ap-3488	351	6	at	at	ADP
ap-3488	351	7	the	the	DET
ap-3488	351	8	end	end	NOUN
ap-3488	351	9	.	.	PUNCT
ap-3488	352	1	5	5	X
ap-3488	352	2	.	.	X
ap-3488	352	3	conclusions	conclusion	NOUN
ap-3488	352	4	in	in	ADP
ap-3488	352	5	this	this	DET
ap-3488	352	6	paper	paper	NOUN
ap-3488	352	7	,	,	PUNCT
ap-3488	352	8	we	we	PRON
ap-3488	352	9	have	have	AUX
ap-3488	352	10	studied	study	VERB
ap-3488	352	11	the	the	DET
ap-3488	352	12	problem	problem	NOUN
ap-3488	352	13	of	of	ADP
ap-3488	352	14	formation	formation	NOUN
ap-3488	352	15	control	control	NOUN
ap-3488	352	16	for	for	ADP
ap-3488	352	17	a	a	DET
ap-3488	352	18	group	group	NOUN
ap-3488	352	19	of	of	ADP
ap-3488	352	20	unicycle	unicycle	NOUN
ap-3488	352	21	-	-	PUNCT
ap-3488	352	22	type	type	NOUN
ap-3488	352	23	robots	robot	NOUN
ap-3488	352	24	using	use	VERB
ap-3488	352	25	a	a	DET
ap-3488	352	26	lie	lie	NOUN
ap-3488	352	27	group	group	NOUN
ap-3488	352	28	.	.	PUNCT
ap-3488	353	1	a	a	DET
ap-3488	353	2	local	local	ADJ
ap-3488	353	3	control	control	NOUN
ap-3488	353	4	law	law	NOUN
ap-3488	353	5	based	base	VERB
ap-3488	353	6	on	on	ADP
ap-3488	353	7	se(2	se(2	PROPN
ap-3488	353	8	)	)	PUNCT
ap-3488	353	9	for	for	ADP
ap-3488	353	10	the	the	DET
ap-3488	353	11	robots	robot	NOUN
ap-3488	353	12	is	be	AUX
ap-3488	353	13	proposed	propose	VERB
ap-3488	353	14	,	,	PUNCT
ap-3488	353	15	and	and	CCONJ
ap-3488	353	16	the	the	DET
ap-3488	353	17	stability	stability	NOUN
ap-3488	353	18	is	be	AUX
ap-3488	353	19	analyzed	analyze	VERB
ap-3488	353	20	.	.	PUNCT
ap-3488	354	1	the	the	DET
ap-3488	354	2	problem	problem	NOUN
ap-3488	354	3	is	be	AUX
ap-3488	354	4	investigated	investigate	VERB
ap-3488	354	5	under	under	ADP
ap-3488	354	6	a	a	DET
ap-3488	354	7	rooted	rooted	ADJ
ap-3488	354	8	directed	direct	VERB
ap-3488	354	9	acyclic	acyclic	ADJ
ap-3488	354	10	communication	communication	NOUN
ap-3488	354	11	topology	topology	NOUN
ap-3488	354	12	for	for	ADP
ap-3488	354	13	a	a	DET
ap-3488	354	14	group	group	NOUN
ap-3488	354	15	of	of	ADP
ap-3488	354	16	unicycle	unicycle	NOUN
ap-3488	354	17	-	-	PUNCT
ap-3488	354	18	type	type	NOUN
ap-3488	354	19	robots	robot	NOUN
ap-3488	354	20	,	,	PUNCT
ap-3488	354	21	and	and	CCONJ
ap-3488	354	22	the	the	DET
ap-3488	354	23	behavior	behavior	NOUN
ap-3488	354	24	of	of	ADP
ap-3488	354	25	the	the	DET
ap-3488	354	26	system	system	NOUN
ap-3488	354	27	is	be	AUX
ap-3488	354	28	discussed	discuss	VERB
ap-3488	354	29	.	.	PUNCT
ap-3488	355	1	some	some	DET
ap-3488	355	2	simulations	simulation	NOUN
ap-3488	355	3	of	of	ADP
ap-3488	355	4	a	a	DET
ap-3488	355	5	6	6	NUM
ap-3488	355	6	-	-	PUNCT
ap-3488	355	7	robot	robot	NOUN
ap-3488	355	8	system	system	NOUN
ap-3488	355	9	validate	validate	VERB
ap-3488	355	10	the	the	DET
ap-3488	355	11	7	7	NUM
ap-3488	355	12	youwei	youwei	NOUN
ap-3488	355	13	dong	dong	PROPN
ap-3488	355	14	,	,	PUNCT
ap-3488	355	15	ahmed	ahmed	PROPN
ap-3488	355	16	rahmani	rahmani	PROPN
ap-3488	355	17	acta	acta	PROPN
ap-3488	355	18	polytechnica	polytechnica	PROPN
ap-3488	355	19	figure	figure	NOUN
ap-3488	355	20	6	6	NUM
ap-3488	355	21	.	.	PUNCT
ap-3488	356	1	orientation	orientation	NOUN
ap-3488	356	2	of	of	ADP
ap-3488	356	3	the	the	DET
ap-3488	356	4	6	6	NUM
ap-3488	356	5	robots	robot	NOUN
ap-3488	356	6	.	.	PUNCT
ap-3488	357	1	proposed	propose	VERB
ap-3488	357	2	control	control	NOUN
ap-3488	357	3	laws	law	NOUN
ap-3488	357	4	.	.	PUNCT
ap-3488	358	1	the	the	DET
ap-3488	358	2	communication	communication	NOUN
ap-3488	358	3	topology	topology	NOUN
ap-3488	358	4	was	be	AUX
ap-3488	358	5	supposed	suppose	VERB
ap-3488	358	6	fixed	fix	VERB
ap-3488	358	7	.	.	PUNCT
ap-3488	359	1	the	the	DET
ap-3488	359	2	case	case	NOUN
ap-3488	359	3	of	of	ADP
ap-3488	359	4	switching	switch	VERB
ap-3488	359	5	topology	topology	NOUN
ap-3488	359	6	,	,	PUNCT
ap-3488	359	7	avoiding	avoid	VERB
ap-3488	359	8	obstacles	obstacle	NOUN
ap-3488	359	9	and	and	CCONJ
ap-3488	359	10	an	an	DET
ap-3488	359	11	experiment	experiment	NOUN
ap-3488	359	12	on	on	ADP
ap-3488	359	13	real	real	ADJ
ap-3488	359	14	robots	robot	NOUN
ap-3488	359	15	will	will	AUX
ap-3488	359	16	be	be	AUX
ap-3488	359	17	studied	study	VERB
ap-3488	359	18	in	in	ADP
ap-3488	359	19	our	our	PRON
ap-3488	359	20	future	future	ADJ
ap-3488	359	21	work	work	NOUN
ap-3488	359	22	.	.	PUNCT
ap-3488	360	1	list	list	NOUN
ap-3488	360	2	of	of	ADP
ap-3488	360	3	symbols	symbol	NOUN
ap-3488	360	4	u	u	PROPN
ap-3488	360	5	robot	robot	NOUN
ap-3488	360	6	’s	’s	PART
ap-3488	360	7	longitudinal	longitudinal	ADJ
ap-3488	360	8	velocity	velocity	NOUN
ap-3488	360	9	[	[	X
ap-3488	360	10	m	m	NOUN
ap-3488	360	11	/	/	SYM
ap-3488	360	12	s	s	PROPN
ap-3488	360	13	]	]	X
ap-3488	360	14	ω	ω	NUM
ap-3488	360	15	robot	robot	NOUN
ap-3488	360	16	’s	’s	PART
ap-3488	360	17	chassis	chassis	NOUN
ap-3488	360	18	instantaneous	instantaneous	ADJ
ap-3488	360	19	velocity	velocity	NOUN
ap-3488	360	20	of	of	ADP
ap-3488	360	21	rotation	rotation	NOUN
ap-3488	360	22	[	[	X
ap-3488	360	23	rad	rad	PROPN
ap-3488	360	24	/	/	SYM
ap-3488	360	25	s	s	PART
ap-3488	360	26	]	]	X
ap-3488	360	27	ω1	ω1	PROPN
ap-3488	360	28	,	,	PUNCT
ap-3488	360	29	ω2	ω2	ADJ
ap-3488	360	30	angular	angular	ADJ
ap-3488	360	31	velocity	velocity	NOUN
ap-3488	360	32	of	of	ADP
ap-3488	360	33	right	right	NOUN
ap-3488	360	34	and	and	CCONJ
ap-3488	360	35	left	leave	VERB
ap-3488	360	36	wheel	wheel	NOUN
ap-3488	361	1	[	[	X
ap-3488	361	2	rad	rad	PROPN
ap-3488	361	3	/	/	SYM
ap-3488	361	4	s	s	PART
ap-3488	361	5	]	]	X
ap-3488	361	6	rω	rω	VERB
ap-3488	361	7	radius	radius	NOUN
ap-3488	361	8	of	of	ADP
ap-3488	361	9	wheel	wheel	NOUN
ap-3488	361	10	[	[	X
ap-3488	361	11	m	m	X
ap-3488	361	12	]	]	X
ap-3488	361	13	l	l	NOUN
ap-3488	361	14	distance	distance	NOUN
ap-3488	361	15	between	between	ADP
ap-3488	361	16	the	the	DET
ap-3488	361	17	two	two	NUM
ap-3488	361	18	actuated	actuate	VERB
ap-3488	361	19	wheels	wheel	NOUN
ap-3488	362	1	[	[	X
ap-3488	363	1	m	m	X
ap-3488	363	2	]	]	X
ap-3488	363	3	p	p	X
ap-3488	364	1	=	=	PUNCT
ap-3488	364	2	[	[	X
ap-3488	364	3	xi	xi	X
ap-3488	364	4	,	,	PUNCT
ap-3488	364	5	yi	yi	PROPN
ap-3488	364	6	]	]	PUNCT
ap-3488	364	7	t	t	PRON
ap-3488	364	8	position	position	NOUN
ap-3488	364	9	of	of	ADP
ap-3488	364	10	robot	robot	NOUN
ap-3488	364	11	in	in	ADP
ap-3488	364	12	frame	frame	NOUN
ap-3488	364	13	fi	fi	NOUN
ap-3488	364	14	gi	gi	X
ap-3488	364	15	∈	∈	PROPN
ap-3488	364	16	se(2	se(2	PROPN
ap-3488	364	17	)	)	PUNCT
ap-3488	364	18	configuration	configuration	NOUN
ap-3488	364	19	of	of	ADP
ap-3488	364	20	local	local	ADJ
ap-3488	364	21	frame	frame	NOUN
ap-3488	364	22	attached	attach	VERB
ap-3488	364	23	to	to	ADP
ap-3488	364	24	roboti	roboti	VERB
ap-3488	364	25	relative	relative	ADJ
ap-3488	364	26	to	to	ADP
ap-3488	364	27	frame	frame	VERB
ap-3488	364	28	fi	fi	NOUN
ap-3488	364	29	gij	gij	ADJ
ap-3488	364	30	configuration	configuration	NOUN
ap-3488	364	31	of	of	ADP
ap-3488	364	32	robot	robot	NOUN
ap-3488	364	33	-	-	PUNCT
ap-3488	364	34	j	j	PROPN
ap-3488	364	35	relative	relative	ADJ
ap-3488	364	36	to	to	ADP
ap-3488	364	37	the	the	DET
ap-3488	364	38	local	local	ADJ
ap-3488	364	39	frame	frame	NOUN
ap-3488	364	40	attached	attach	VERB
ap-3488	364	41	to	to	ADP
ap-3488	364	42	robot	robot	NOUN
ap-3488	364	43	-	-	PUNCT
ap-3488	364	44	i	i	PRON
ap-3488	364	45	ḡij	ḡij	VERB
ap-3488	364	46	desired	desire	VERB
ap-3488	364	47	configuration	configuration	NOUN
ap-3488	364	48	of	of	ADP
ap-3488	364	49	robot	robot	NOUN
ap-3488	364	50	-	-	PUNCT
ap-3488	364	51	j	j	PROPN
ap-3488	364	52	relative	relative	ADJ
ap-3488	364	53	to	to	ADP
ap-3488	364	54	robot	robot	NOUN
ap-3488	364	55	-	-	PUNCT
ap-3488	364	56	i	i	NOUN
ap-3488	364	57	b	b	NOUN
ap-3488	364	58	=	=	SYM
ap-3488	364	59	(	(	PUNCT
ap-3488	364	60	0	0	NUM
ap-3488	364	61	,	,	PUNCT
ap-3488	364	62	r	r	NOUN
ap-3488	364	63	)	)	PUNCT
ap-3488	364	64	the	the	DET
ap-3488	364	65	centre	centre	NOUN
ap-3488	364	66	of	of	ADP
ap-3488	364	67	a	a	DET
ap-3488	364	68	circle	circle	NOUN
ap-3488	364	69	of	of	ADP
ap-3488	364	70	which	which	PRON
ap-3488	364	71	the	the	DET
ap-3488	364	72	radius	radius	NOUN
ap-3488	364	73	is	be	AUX
ap-3488	364	74	|r|	|r|	NOUN
ap-3488	364	75	a	a	NOUN
ap-3488	364	76	=	=	X
ap-3488	365	1	[	[	X
ap-3488	365	2	x	x	NOUN
ap-3488	365	3	,	,	PUNCT
ap-3488	365	4	y]t	y]t	NOUN
ap-3488	365	5	position	position	NOUN
ap-3488	365	6	of	of	ADP
ap-3488	365	7	robot	robot	NOUN
ap-3488	365	8	gi	gi	VERB
ap-3488	365	9	in	in	ADP
ap-3488	365	10	frame	frame	NOUN
ap-3488	366	1	o′x	o′x	INTJ
ap-3488	366	2	′y	′y	NOUN
ap-3488	366	3	′	′	NUM
ap-3488	367	1	θ	θ	PROPN
ap-3488	367	2	orientation	orientation	NOUN
ap-3488	367	3	of	of	ADP
ap-3488	367	4	robot	robot	NOUN
ap-3488	367	5	gi	gi	NOUN
ap-3488	367	6	relative	relative	ADJ
ap-3488	367	7	to	to	ADP
ap-3488	367	8	axis	axis	NOUN
ap-3488	367	9	o′x	o′x	NUM
ap-3488	367	10	′	′	NUM
ap-3488	367	11	ϕ	ϕ	PROPN
ap-3488	367	12	angle	angle	NOUN
ap-3488	367	13	∠abx	∠abx	NOUN
ap-3488	367	14	′	′	NUM
ap-3488	367	15	∈	∈	PROPN
ap-3488	368	1	[	[	X
ap-3488	368	2	−π	−π	X
ap-3488	368	3	,	,	PUNCT
ap-3488	368	4	π	π	X
ap-3488	368	5	]	]	X
ap-3488	368	6	l	l	NOUN
ap-3488	368	7	distance	distance	NOUN
ap-3488	368	8	between	between	ADP
ap-3488	368	9	a	a	DET
ap-3488	368	10	and	and	CCONJ
ap-3488	368	11	b	b	NOUN
ap-3488	368	12	d	d	NOUN
ap-3488	368	13	distance	distance	NOUN
ap-3488	368	14	between	between	ADP
ap-3488	368	15	a	a	DET
ap-3488	368	16	and	and	CCONJ
ap-3488	368	17	o′	o′	PROPN
ap-3488	368	18	β̄	β̄	PROPN
ap-3488	368	19	angle	angle	NOUN
ap-3488	368	20	formed	form	VERB
ap-3488	368	21	by	by	ADP
ap-3488	368	22	−→ba	−→ba	ADJ
ap-3488	368	23	and	and	CCONJ
ap-3488	368	24	robot	robot	NOUN
ap-3488	368	25	’s	’s	PART
ap-3488	368	26	orientation	orientation	NOUN
ap-3488	368	27	,	,	PUNCT
ap-3488	368	28	∈	∈	PROPN
ap-3488	369	1	[	[	X
ap-3488	369	2	−π	−π	X
ap-3488	369	3	,	,	PUNCT
ap-3488	369	4	π	π	X
ap-3488	369	5	]	]	X
ap-3488	369	6	α	α	PROPN
ap-3488	369	7	angle	angle	NOUN
ap-3488	369	8	arcsin(r	arcsin(r	NUM
ap-3488	369	9	/	/	SYM
ap-3488	369	10	l	l	NOUN
ap-3488	369	11	)	)	PUNCT
ap-3488	369	12	∈	∈	PROPN
ap-3488	370	1	[	[	X
ap-3488	370	2	−π/2	−π/2	PROPN
ap-3488	370	3	,	,	PUNCT
ap-3488	370	4	π/2	π/2	NUM
ap-3488	370	5	]	]	PUNCT
ap-3488	371	1	ψ	ψ	X
ap-3488	371	2	angle	angle	NOUN
ap-3488	371	3	∠bao′	∠bao′	ADP
ap-3488	371	4	∈	∈	PROPN
ap-3488	371	5	[	[	X
ap-3488	371	6	0	0	NUM
ap-3488	371	7	,	,	PUNCT
ap-3488	371	8	π/2	π/2	NUM
ap-3488	371	9	]	]	PUNCT
ap-3488	372	1	acknowledgements	acknowledgement	NOUN
ap-3488	372	2	youwei	youwei	PROPN
ap-3488	372	3	dong	dong	PROPN
ap-3488	372	4	was	be	AUX
ap-3488	372	5	sponsored	sponsor	VERB
ap-3488	372	6	by	by	ADP
ap-3488	372	7	the	the	DET
ap-3488	372	8	china	china	PROPN
ap-3488	372	9	scholarship	scholarship	PROPN
ap-3488	372	10	council	council	PROPN
ap-3488	372	11	.	.	PUNCT
ap-3488	373	1	many	many	ADJ
ap-3488	373	2	thanks	thank	NOUN
ap-3488	373	3	to	to	ADP
ap-3488	373	4	members	member	NOUN
ap-3488	373	5	of	of	ADP
ap-3488	373	6	the	the	DET
ap-3488	373	7	math	math	NOUN
ap-3488	373	8	stack	stack	PROPN
ap-3488	373	9	exchange	exchange	NOUN
ap-3488	373	10	community	community	NOUN
ap-3488	373	11	,	,	PUNCT
ap-3488	373	12	anonymous	anonymous	ADJ
ap-3488	373	13	and	and	CCONJ
ap-3488	373	14	otherwise	otherwise	ADV
ap-3488	373	15	,	,	PUNCT
ap-3488	373	16	for	for	ADP
ap-3488	373	17	helpful	helpful	ADJ
ap-3488	373	18	comments	comment	NOUN
ap-3488	373	19	and	and	CCONJ
ap-3488	373	20	suggestions	suggestion	NOUN
ap-3488	373	21	.	.	PUNCT
ap-3488	374	1	references	reference	NOUN
ap-3488	374	2	[	[	X
ap-3488	374	3	1	1	NUM
ap-3488	374	4	]	]	X
ap-3488	374	5	r.	r.	PROPN
ap-3488	374	6	dong	dong	PROPN
ap-3488	374	7	,	,	PUNCT
ap-3488	374	8	z.	z.	PROPN
ap-3488	374	9	geng	geng	PROPN
ap-3488	374	10	.	.	PUNCT
ap-3488	375	1	consensus	consensus	NOUN
ap-3488	375	2	based	base	VERB
ap-3488	375	3	formation	formation	NOUN
ap-3488	375	4	control	control	NOUN
ap-3488	375	5	laws	law	NOUN
ap-3488	375	6	for	for	ADP
ap-3488	375	7	systems	system	NOUN
ap-3488	375	8	on	on	ADP
ap-3488	375	9	lie	lie	NOUN
ap-3488	375	10	groups	group	NOUN
ap-3488	375	11	.	.	PUNCT
ap-3488	376	1	in	in	ADP
ap-3488	376	2	systems	system	NOUN
ap-3488	376	3	&	&	CCONJ
ap-3488	376	4	control	control	PROPN
ap-3488	376	5	letters	letter	NOUN
ap-3488	376	6	62:104–111	62:104–111	PROPN
ap-3488	376	7	,	,	PUNCT
ap-3488	376	8	2013	2013	NUM
ap-3488	376	9	.	.	PUNCT
ap-3488	377	1	doi:10.1016	doi:10.1016	PROPN
ap-3488	377	2	/	/	SYM
ap-3488	377	3	j.sysconle.2012.11.005	j.sysconle.2012.11.005	PROPN
ap-3488	377	4	.	.	PUNCT
ap-3488	378	1	[	[	X
ap-3488	378	2	2	2	NUM
ap-3488	378	3	]	]	PUNCT
ap-3488	378	4	a.	a.	NOUN
ap-3488	378	5	gautam	gautam	PROPN
ap-3488	378	6	,	,	PUNCT
ap-3488	378	7	s.	s.	PROPN
ap-3488	378	8	mohan	mohan	PROPN
ap-3488	378	9	.	.	PUNCT
ap-3488	379	1	a	a	DET
ap-3488	379	2	review	review	NOUN
ap-3488	379	3	of	of	ADP
ap-3488	379	4	research	research	NOUN
ap-3488	379	5	in	in	ADP
ap-3488	379	6	multi	multi	ADJ
ap-3488	379	7	-	-	ADJ
ap-3488	379	8	robot	robot	ADJ
ap-3488	379	9	systems	system	NOUN
ap-3488	379	10	.	.	PUNCT
ap-3488	380	1	in	in	ADP
ap-3488	380	2	industrial	industrial	ADJ
ap-3488	380	3	and	and	CCONJ
ap-3488	380	4	information	information	NOUN
ap-3488	380	5	systems(iciis	systems(iciis	PROPN
ap-3488	380	6	)	)	PUNCT
ap-3488	380	7	,	,	PUNCT
ap-3488	380	8	pp	pp	ADP
ap-3488	380	9	.	.	PUNCT
ap-3488	381	1	1–5	1–5	X
ap-3488	381	2	.	.	X
ap-3488	381	3	chennai	chennai	PROPN
ap-3488	381	4	,	,	PUNCT
ap-3488	381	5	aug	aug	PROPN
ap-3488	381	6	2012	2012	NUM
ap-3488	381	7	.	.	PUNCT
ap-3488	382	1	doi:10.1109	doi:10.1109	VERB
ap-3488	382	2	/	/	SYM
ap-3488	382	3	iciinfs.2012.6304778	iciinfs.2012.6304778	PROPN
ap-3488	382	4	.	.	PUNCT
ap-3488	383	1	[	[	X
ap-3488	383	2	3	3	X
ap-3488	383	3	]	]	X
ap-3488	383	4	k.-k	k.-k	PROPN
ap-3488	383	5	.	.	PUNCT
ap-3488	384	1	oh	oh	INTJ
ap-3488	384	2	,	,	PUNCT
ap-3488	384	3	h.-s	h.-s	PROPN
ap-3488	384	4	.	.	PUNCT
ap-3488	385	1	ahn	ahn	PROPN
ap-3488	385	2	.	.	PUNCT
ap-3488	385	3	formation	formation	NOUN
ap-3488	385	4	control	control	NOUN
ap-3488	385	5	of	of	ADP
ap-3488	385	6	mobile	mobile	ADJ
ap-3488	385	7	agents	agent	NOUN
ap-3488	385	8	based	base	VERB
ap-3488	385	9	on	on	ADP
ap-3488	385	10	distributed	distribute	VERB
ap-3488	385	11	position	position	NOUN
ap-3488	385	12	estimation	estimation	NOUN
ap-3488	385	13	.	.	PUNCT
ap-3488	386	1	in	in	ADP
ap-3488	386	2	ieee	ieee	NOUN
ap-3488	386	3	transactions	transaction	NOUN
ap-3488	386	4	on	on	ADP
ap-3488	386	5	automatic	automatic	ADJ
ap-3488	386	6	control	control	NOUN
ap-3488	386	7	58(3):737	58(3):737	NUM
ap-3488	386	8	–	–	PUNCT
ap-3488	386	9	742	742	NUM
ap-3488	386	10	,	,	PUNCT
ap-3488	386	11	march	march	PROPN
ap-3488	386	12	2013	2013	NUM
ap-3488	386	13	.	.	PUNCT
ap-3488	387	1	doi:10.1109	doi:10.1109	VERB
ap-3488	387	2	/	/	SYM
ap-3488	387	3	tac.2012.2209269	tac.2012.2209269	NOUN
ap-3488	387	4	.	.	PUNCT
ap-3488	388	1	[	[	X
ap-3488	388	2	4	4	X
ap-3488	388	3	]	]	X
ap-3488	388	4	h.	h.	PROPN
ap-3488	388	5	mehrjerdi	mehrjerdi	PROPN
ap-3488	388	6	,	,	PUNCT
ap-3488	388	7	j.	j.	PROPN
ap-3488	388	8	ghommam	ghommam	PROPN
ap-3488	388	9	,	,	PUNCT
ap-3488	388	10	m.	m.	NOUN
ap-3488	388	11	saad	saad	PROPN
ap-3488	388	12	.	.	PUNCT
ap-3488	389	1	nonlinear	nonlinear	ADJ
ap-3488	389	2	coordination	coordination	NOUN
ap-3488	389	3	control	control	NOUN
ap-3488	389	4	for	for	ADP
ap-3488	389	5	a	a	DET
ap-3488	389	6	group	group	NOUN
ap-3488	389	7	of	of	ADP
ap-3488	389	8	mobile	mobile	ADJ
ap-3488	389	9	robots	robot	NOUN
ap-3488	389	10	using	use	VERB
ap-3488	389	11	a	a	DET
ap-3488	389	12	virtual	virtual	ADJ
ap-3488	389	13	structure	structure	NOUN
ap-3488	389	14	.	.	PUNCT
ap-3488	390	1	in	in	ADP
ap-3488	390	2	mechatronics	mechatronic	NOUN
ap-3488	390	3	21:1147–1155	21:1147–1155	NUM
ap-3488	390	4	,	,	PUNCT
ap-3488	390	5	2011	2011	NUM
ap-3488	390	6	.	.	PUNCT
ap-3488	391	1	doi:10.1016	doi:10.1016	PROPN
ap-3488	391	2	/	/	SYM
ap-3488	391	3	j.mechatronics.2011.06.006	j.mechatronics.2011.06.006	PROPN
ap-3488	391	4	.	.	PUNCT
ap-3488	392	1	[	[	X
ap-3488	392	2	5	5	NUM
ap-3488	392	3	]	]	PUNCT
ap-3488	392	4	w.	w.	PROPN
ap-3488	392	5	ren	ren	PROPN
ap-3488	392	6	.	.	PUNCT
ap-3488	393	1	consensus	consensus	NOUN
ap-3488	393	2	based	base	VERB
ap-3488	393	3	formation	formation	NOUN
ap-3488	393	4	control	control	NOUN
ap-3488	393	5	strategies	strategy	NOUN
ap-3488	393	6	for	for	ADP
ap-3488	393	7	multi	multi	ADJ
ap-3488	393	8	-	-	ADJ
ap-3488	393	9	vehicle	vehicle	NOUN
ap-3488	393	10	systems	system	NOUN
ap-3488	393	11	.	.	PUNCT
ap-3488	394	1	in	in	ADP
ap-3488	394	2	proceedings	proceeding	NOUN
ap-3488	394	3	of	of	ADP
ap-3488	394	4	the	the	DET
ap-3488	394	5	2006	2006	NUM
ap-3488	394	6	american	american	PROPN
ap-3488	394	7	control	control	PROPN
ap-3488	394	8	conference	conference	PROPN
ap-3488	394	9	,	,	PUNCT
ap-3488	394	10	pp	pp	X
ap-3488	394	11	.	.	PUNCT
ap-3488	394	12	4237–4242	4237–4242	NUM
ap-3488	394	13	.	.	PUNCT
ap-3488	394	14	minnesota	minnesota	PROPN
ap-3488	394	15	,	,	PUNCT
ap-3488	394	16	june	june	PROPN
ap-3488	394	17	2006	2006	NUM
ap-3488	394	18	.	.	PUNCT
ap-3488	395	1	doi:10.1109	doi:10.1109	PROPN
ap-3488	395	2	/	/	SYM
ap-3488	395	3	acc.2006.1657384	acc.2006.1657384	PROPN
ap-3488	395	4	.	.	PUNCT
ap-3488	396	1	[	[	X
ap-3488	396	2	6	6	NUM
ap-3488	396	3	]	]	PUNCT
ap-3488	396	4	s.	s.	PROPN
ap-3488	396	5	mastellone	mastellone	PROPN
ap-3488	396	6	,	,	PUNCT
ap-3488	396	7	j.	j.	PROPN
ap-3488	396	8	s.	s.	PROPN
ap-3488	396	9	mejía	mejía	PROPN
ap-3488	396	10	,	,	PUNCT
ap-3488	396	11	d.	d.	PROPN
ap-3488	396	12	m.	m.	PROPN
ap-3488	396	13	stipanović	stipanović	PROPN
ap-3488	396	14	,	,	PUNCT
ap-3488	396	15	m.	m.	NOUN
ap-3488	396	16	w.	w.	PROPN
ap-3488	396	17	song	song	PROPN
ap-3488	396	18	.	.	PUNCT
ap-3488	397	1	formation	formation	NOUN
ap-3488	397	2	control	control	NOUN
ap-3488	397	3	and	and	CCONJ
ap-3488	397	4	coordinated	coordinated	ADJ
ap-3488	397	5	tracking	tracking	NOUN
ap-3488	397	6	via	via	ADP
ap-3488	397	7	asymptotic	asymptotic	ADJ
ap-3488	397	8	decoupling	decoupling	NOUN
ap-3488	397	9	for	for	ADP
ap-3488	397	10	lagrangian	lagrangian	ADJ
ap-3488	397	11	multi	multi	ADJ
ap-3488	397	12	-	-	ADJ
ap-3488	397	13	agent	agent	ADJ
ap-3488	397	14	systems	system	NOUN
ap-3488	397	15	.	.	PUNCT
ap-3488	398	1	in	in	ADP
ap-3488	398	2	automatica	automatica	PROPN
ap-3488	398	3	47:2355–2363	47:2355–2363	NUM
ap-3488	398	4	,	,	PUNCT
ap-3488	398	5	2011	2011	NUM
ap-3488	398	6	.	.	PUNCT
ap-3488	399	1	doi:10.1016	doi:10.1016	PROPN
ap-3488	399	2	/	/	SYM
ap-3488	399	3	j.automatica.2011.08.030	j.automatica.2011.08.030	PROPN
ap-3488	399	4	.	.	PUNCT
ap-3488	400	1	[	[	X
ap-3488	400	2	7	7	X
ap-3488	400	3	]	]	X
ap-3488	400	4	r.	r.	PROPN
ap-3488	400	5	olfati	olfati	PROPN
ap-3488	400	6	-	-	PUNCT
ap-3488	400	7	saber	saber	NOUN
ap-3488	400	8	,	,	PUNCT
ap-3488	400	9	r.	r.	PROPN
ap-3488	400	10	m.	m.	PROPN
ap-3488	400	11	murray	murray	PROPN
ap-3488	400	12	.	.	PUNCT
ap-3488	401	1	distributed	distribute	VERB
ap-3488	401	2	cooperative	cooperative	ADJ
ap-3488	401	3	control	control	NOUN
ap-3488	401	4	of	of	ADP
ap-3488	401	5	multiple	multiple	ADJ
ap-3488	401	6	vehicle	vehicle	NOUN
ap-3488	401	7	formations	formation	NOUN
ap-3488	401	8	using	use	VERB
ap-3488	401	9	8	8	NUM
ap-3488	401	10	http://dx.doi.org/10.1016/j.sysconle.2012.11.005	http://dx.doi.org/10.1016/j.sysconle.2012.11.005	PROPN
ap-3488	401	11	http://dx.doi.org/10.1109/iciinfs.2012.6304778	http://dx.doi.org/10.1109/iciinfs.2012.6304778	NOUN
ap-3488	401	12	http://dx.doi.org/10.1109/tac.2012.2209269	http://dx.doi.org/10.1109/tac.2012.2209269	ADP
ap-3488	401	13	http://dx.doi.org/10.1016/j.mechatronics.2011.06.006	http://dx.doi.org/10.1016/j.mechatronics.2011.06.006	PROPN
ap-3488	401	14	http://dx.doi.org/10.1109/acc.2006.1657384	http://dx.doi.org/10.1109/acc.2006.1657384	VERB
ap-3488	401	15	http://dx.doi.org/10.1016/j.automatica.2011.08.030	http://dx.doi.org/10.1016/j.automatica.2011.08.030	PROPN
ap-3488	401	16	vol	vol	NOUN
ap-3488	401	17	.	.	PUNCT
ap-3488	402	1	56	56	NUM
ap-3488	402	2	no	no	NOUN
ap-3488	402	3	.	.	PUNCT
ap-3488	403	1	1/2016	1/2016	NUM
ap-3488	403	2	formation	formation	NOUN
ap-3488	403	3	control	control	NOUN
ap-3488	403	4	of	of	ADP
ap-3488	403	5	multiple	multiple	ADJ
ap-3488	403	6	unicycle	unicycle	NOUN
ap-3488	403	7	-	-	PUNCT
ap-3488	403	8	type	type	NOUN
ap-3488	403	9	robots	robot	NOUN
ap-3488	403	10	using	use	VERB
ap-3488	403	11	lie	lie	NOUN
ap-3488	403	12	group	group	NOUN
ap-3488	403	13	structural	structural	ADJ
ap-3488	403	14	potential	potential	ADJ
ap-3488	403	15	functions	function	NOUN
ap-3488	403	16	.	.	PUNCT
ap-3488	404	1	in	in	ADP
ap-3488	404	2	ifac	ifac	NOUN
ap-3488	404	3	world	world	PROPN
ap-3488	404	4	congress	congress	PROPN
ap-3488	404	5	.	.	PUNCT
ap-3488	404	6	barcelona	barcelona	PROPN
ap-3488	404	7	,	,	PUNCT
ap-3488	404	8	2002	2002	NUM
ap-3488	404	9	.	.	PUNCT
ap-3488	405	1	[	[	X
ap-3488	405	2	8	8	X
ap-3488	405	3	]	]	PUNCT
ap-3488	405	4	k.	k.	PROPN
ap-3488	405	5	d.	d.	PROPN
ap-3488	405	6	listmann	listmann	PROPN
ap-3488	405	7	,	,	PUNCT
ap-3488	405	8	m.	m.	NOUN
ap-3488	405	9	v.	v.	ADP
ap-3488	405	10	masalawala	masalawala	PROPN
ap-3488	405	11	,	,	PUNCT
ap-3488	405	12	j.	j.	PROPN
ap-3488	405	13	adamy	adamy	PROPN
ap-3488	405	14	.	.	PUNCT
ap-3488	406	1	consensus	consensus	NOUN
ap-3488	406	2	for	for	ADP
ap-3488	406	3	formation	formation	NOUN
ap-3488	406	4	control	control	NOUN
ap-3488	406	5	of	of	ADP
ap-3488	406	6	nonholonomic	nonholonomic	ADJ
ap-3488	406	7	mobile	mobile	ADJ
ap-3488	406	8	robots	robot	NOUN
ap-3488	406	9	,	,	PUNCT
ap-3488	406	10	in	in	ADP
ap-3488	406	11	robotics	robotic	NOUN
ap-3488	406	12	and	and	CCONJ
ap-3488	406	13	automation	automation	NOUN
ap-3488	406	14	.	.	PUNCT
ap-3488	407	1	in	in	ADP
ap-3488	407	2	mathematical	mathematical	ADJ
ap-3488	407	3	physics	physics	NOUN
ap-3488	407	4	,	,	PUNCT
ap-3488	407	5	pp	pp	ADJ
ap-3488	407	6	.	.	PUNCT
ap-3488	407	7	3886–3891	3886–3891	NUM
ap-3488	407	8	.	.	PUNCT
ap-3488	407	9	kobe	kobe	PROPN
ap-3488	407	10	,	,	PUNCT
ap-3488	407	11	may	may	PROPN
ap-3488	407	12	2009	2009	NUM
ap-3488	407	13	.	.	PUNCT
ap-3488	408	1	doi:10.1109	doi:10.1109	VERB
ap-3488	408	2	/	/	SYM
ap-3488	408	3	robot.2009.5152865	robot.2009.5152865	PROPN
ap-3488	408	4	.	.	PUNCT
ap-3488	409	1	[	[	X
ap-3488	409	2	9	9	NUM
ap-3488	409	3	]	]	PUNCT
ap-3488	409	4	p.	p.	NOUN
ap-3488	409	5	morin	morin	NOUN
ap-3488	409	6	,	,	PUNCT
ap-3488	409	7	c.	c.	PROPN
ap-3488	409	8	samson	samson	PROPN
ap-3488	409	9	.	.	PUNCT
ap-3488	410	1	control	control	NOUN
ap-3488	410	2	of	of	ADP
ap-3488	410	3	nonholonomic	nonholonomic	ADJ
ap-3488	410	4	mobile	mobile	ADJ
ap-3488	410	5	robots	robot	NOUN
ap-3488	410	6	based	base	VERB
ap-3488	410	7	on	on	ADP
ap-3488	410	8	the	the	DET
ap-3488	410	9	transverse	transverse	NOUN
ap-3488	410	10	function	function	NOUN
ap-3488	410	11	approach	approach	NOUN
ap-3488	410	12	.	.	PUNCT
ap-3488	411	1	in	in	ADP
ap-3488	411	2	transactions	transaction	NOUN
ap-3488	411	3	on	on	ADP
ap-3488	411	4	robotics	robotic	NOUN
ap-3488	411	5	25(5):1058–1073	25(5):1058–1073	NUM
ap-3488	411	6	,	,	PUNCT
ap-3488	411	7	oct	oct	PROPN
ap-3488	411	8	2009	2009	NUM
ap-3488	411	9	.	.	PUNCT
ap-3488	412	1	doi:10.1109	doi:10.1109	VERB
ap-3488	412	2	/	/	SYM
ap-3488	412	3	tro.2009.2014123	tro.2009.2014123	NUM
ap-3488	412	4	.	.	PUNCT
ap-3488	413	1	[	[	X
ap-3488	413	2	10	10	NUM
ap-3488	413	3	]	]	X
ap-3488	413	4	r.	r.	PROPN
ap-3488	413	5	m.	m.	PROPN
ap-3488	413	6	murray	murray	PROPN
ap-3488	413	7	,	,	PUNCT
ap-3488	413	8	z.	z.	PROPN
ap-3488	413	9	li	li	PROPN
ap-3488	413	10	,	,	PUNCT
ap-3488	413	11	s.	s.	PROPN
ap-3488	413	12	s.	s.	PROPN
ap-3488	413	13	sastry	sastry	PROPN
ap-3488	413	14	.	.	PUNCT
ap-3488	414	1	a	a	DET
ap-3488	414	2	mathematical	mathematical	ADJ
ap-3488	414	3	introduction	introduction	NOUN
ap-3488	414	4	to	to	ADP
ap-3488	414	5	robotic	robotic	ADJ
ap-3488	414	6	manipulation	manipulation	NOUN
ap-3488	414	7	.	.	PUNCT
ap-3488	415	1	crc	crc	PROPN
ap-3488	415	2	press	press	PROPN
ap-3488	415	3	,	,	PUNCT
ap-3488	415	4	1994	1994	NUM
ap-3488	415	5	.	.	PUNCT
ap-3488	416	1	[	[	X
ap-3488	416	2	11	11	NUM
ap-3488	416	3	]	]	X
ap-3488	416	4	f.	f.	PROPN
ap-3488	416	5	w.	w.	PROPN
ap-3488	416	6	warner	warner	PROPN
ap-3488	416	7	.	.	PUNCT
ap-3488	417	1	foundations	foundation	NOUN
ap-3488	417	2	of	of	ADP
ap-3488	417	3	differentiable	differentiable	ADJ
ap-3488	417	4	manifolds	manifold	NOUN
ap-3488	417	5	and	and	CCONJ
ap-3488	417	6	lie	lie	NOUN
ap-3488	417	7	groups	group	NOUN
ap-3488	417	8	.	.	PUNCT
ap-3488	418	1	london	london	PROPN
ap-3488	418	2	:	:	PUNCT
ap-3488	418	3	scott	scott	PROPN
ap-3488	418	4	,	,	PUNCT
ap-3488	418	5	foresman	foresman	NOUN
ap-3488	418	6	and	and	CCONJ
ap-3488	418	7	company	company	NOUN
ap-3488	418	8	,	,	PUNCT
ap-3488	418	9	1983	1983	NUM
ap-3488	418	10	.	.	PUNCT
ap-3488	419	1	[	[	X
ap-3488	419	2	12	12	NUM
ap-3488	419	3	]	]	X
ap-3488	419	4	p.	p.	NOUN
ap-3488	419	5	coelho	coelho	PROPN
ap-3488	419	6	,	,	PUNCT
ap-3488	419	7	u.	u.	PROPN
ap-3488	419	8	nunes	nunes	PROPN
ap-3488	419	9	.	.	PUNCT
ap-3488	420	1	lie	lie	PROPN
ap-3488	420	2	algebra	algebra	NOUN
ap-3488	420	3	application	application	NOUN
ap-3488	420	4	to	to	ADP
ap-3488	420	5	mobile	mobile	ADJ
ap-3488	420	6	robot	robot	NOUN
ap-3488	420	7	control	control	NOUN
ap-3488	420	8	:	:	PUNCT
ap-3488	420	9	a	a	DET
ap-3488	420	10	tutorial	tutorial	NOUN
ap-3488	420	11	.	.	PUNCT
ap-3488	421	1	in	in	ADP
ap-3488	421	2	robotica	robotica	PROPN
ap-3488	421	3	21:483–493	21:483–493	NUM
ap-3488	421	4	,	,	PUNCT
ap-3488	421	5	2003	2003	NUM
ap-3488	421	6	.	.	PUNCT
ap-3488	422	1	doi:10.1017	doi:10.1017	NOUN
ap-3488	422	2	/	/	SYM
ap-3488	422	3	s0263574703005149	s0263574703005149	NOUN
ap-3488	422	4	.	.	PUNCT
ap-3488	423	1	[	[	X
ap-3488	423	2	13	13	NUM
ap-3488	423	3	]	]	PUNCT
ap-3488	423	4	j.	j.	PROPN
ap-3488	423	5	f.	f.	PROPN
ap-3488	423	6	cariñena	cariñena	PROPN
ap-3488	423	7	,	,	PUNCT
ap-3488	423	8	j.	j.	PROPN
ap-3488	423	9	clemente	clemente	PROPN
ap-3488	423	10	-	-	PUNCT
ap-3488	423	11	gallardo	gallardo	PROPN
ap-3488	423	12	,	,	PUNCT
ap-3488	423	13	a.	a.	PROPN
ap-3488	423	14	ramos	ramos	PROPN
ap-3488	423	15	.	.	PUNCT
ap-3488	424	1	motion	motion	NOUN
ap-3488	424	2	on	on	ADP
ap-3488	424	3	lie	lie	NOUN
ap-3488	424	4	groups	group	NOUN
ap-3488	424	5	and	and	CCONJ
ap-3488	424	6	its	its	PRON
ap-3488	424	7	applications	application	NOUN
ap-3488	424	8	in	in	ADP
ap-3488	424	9	control	control	NOUN
ap-3488	424	10	theory	theory	NOUN
ap-3488	424	11	.	.	PUNCT
ap-3488	425	1	in	in	ADP
ap-3488	425	2	mathematical	mathematical	ADJ
ap-3488	425	3	physics	physics	NOUN
ap-3488	425	4	51:159–70	51:159–70	NOUN
ap-3488	425	5	,	,	PUNCT
ap-3488	425	6	jul	jul	PROPN
ap-3488	425	7	2003	2003	NUM
ap-3488	425	8	.	.	PUNCT
ap-3488	426	1	doi:10.1016	doi:10.1016	PROPN
ap-3488	426	2	/	/	SYM
ap-3488	426	3	s0034	s0034	PROPN
ap-3488	426	4	-	-	PUNCT
ap-3488	426	5	4877(03)80010	4877(03)80010	NOUN
ap-3488	426	6	-	-	PUNCT
ap-3488	426	7	1	1	NUM
ap-3488	426	8	.	.	PUNCT
ap-3488	427	1	[	[	X
ap-3488	427	2	14	14	NUM
ap-3488	427	3	]	]	X
ap-3488	427	4	g.	g.	PROPN
ap-3488	427	5	s.	s.	PROPN
ap-3488	427	6	chirikjian	chirikjian	PROPN
ap-3488	427	7	.	.	PUNCT
ap-3488	428	1	information	information	NOUN
ap-3488	428	2	theory	theory	NOUN
ap-3488	428	3	on	on	ADP
ap-3488	428	4	lie	lie	NOUN
ap-3488	428	5	groups	group	NOUN
ap-3488	428	6	and	and	CCONJ
ap-3488	428	7	mobile	mobile	ADJ
ap-3488	428	8	robotics	robotic	NOUN
ap-3488	428	9	applications	application	NOUN
ap-3488	428	10	.	.	PUNCT
ap-3488	429	1	in	in	ADP
ap-3488	429	2	ieee	ieee	PROPN
ap-3488	429	3	international	international	ADJ
ap-3488	429	4	conference	conference	NOUN
ap-3488	429	5	on	on	ADP
ap-3488	429	6	robotics	robotic	NOUN
ap-3488	429	7	and	and	CCONJ
ap-3488	429	8	automation	automation	NOUN
ap-3488	429	9	,	,	PUNCT
ap-3488	429	10	pp	pp	ADP
ap-3488	429	11	.	.	PUNCT
ap-3488	430	1	2751–2757	2751–2757	NOUN
ap-3488	430	2	.	.	PUNCT
ap-3488	431	1	alaska	alaska	PROPN
ap-3488	431	2	,	,	PUNCT
ap-3488	431	3	2010	2010	NUM
ap-3488	431	4	.	.	PUNCT
ap-3488	432	1	doi:10.1109	doi:10.1109	VERB
ap-3488	432	2	/	/	SYM
ap-3488	432	3	robot.2010.5509791	robot.2010.5509791	NUM
ap-3488	432	4	.	.	PUNCT
ap-3488	433	1	[	[	X
ap-3488	433	2	15	15	NUM
ap-3488	433	3	]	]	PUNCT
ap-3488	434	1	z.	z.	PROPN
ap-3488	434	2	peng	peng	PROPN
ap-3488	434	3	.	.	PUNCT
ap-3488	435	1	formation	formation	NOUN
ap-3488	435	2	control	control	NOUN
ap-3488	435	3	of	of	ADP
ap-3488	435	4	multi	multi	PROPN
ap-3488	435	5	nonhonomic	nonhonomic	ADJ
ap-3488	435	6	wheeled	wheel	VERB
ap-3488	435	7	mobile	mobile	ADJ
ap-3488	435	8	robots	robot	NOUN
ap-3488	435	9	.	.	PUNCT
ap-3488	436	1	ph.d	ph.d	PROPN
ap-3488	436	2	.	.	PUNCT
ap-3488	437	1	thesis	thesis	PROPN
ap-3488	437	2	,	,	PUNCT
ap-3488	437	3	ecole	ecole	X
ap-3488	437	4	centrale	centrale	X
ap-3488	437	5	de	de	X
ap-3488	437	6	lille	lille	PROPN
ap-3488	437	7	,	,	PUNCT
ap-3488	437	8	june	june	PROPN
ap-3488	437	9	2013	2013	NUM
ap-3488	437	10	.	.	PUNCT
ap-3488	438	1	[	[	X
ap-3488	438	2	16	16	NUM
ap-3488	438	3	]	]	X
ap-3488	438	4	g.	g.	PROPN
ap-3488	438	5	wen	wen	PROPN
ap-3488	438	6	.	.	PUNCT
ap-3488	439	1	distributed	distribute	VERB
ap-3488	439	2	cooperative	cooperative	ADJ
ap-3488	439	3	control	control	NOUN
ap-3488	439	4	for	for	ADP
ap-3488	439	5	multi	multi	ADJ
ap-3488	439	6	-	-	ADJ
ap-3488	439	7	agent	agent	ADJ
ap-3488	439	8	systems	system	NOUN
ap-3488	439	9	.	.	PUNCT
ap-3488	440	1	ph.d	ph.d	PROPN
ap-3488	440	2	.	.	PUNCT
ap-3488	441	1	thesis	thesis	PROPN
ap-3488	441	2	,	,	PUNCT
ap-3488	441	3	ecole	ecole	X
ap-3488	441	4	centrale	centrale	X
ap-3488	441	5	de	de	X
ap-3488	441	6	lille	lille	PROPN
ap-3488	441	7	,	,	PUNCT
ap-3488	441	8	october	october	PROPN
ap-3488	441	9	2012	2012	NUM
ap-3488	441	10	.	.	PUNCT
ap-3488	442	1	[	[	X
ap-3488	442	2	17	17	NUM
ap-3488	442	3	]	]	X
ap-3488	442	4	b.	b.	PROPN
ap-3488	442	5	siciliano	siciliano	PROPN
ap-3488	442	6	,	,	PUNCT
ap-3488	442	7	o.	o.	PROPN
ap-3488	442	8	khatib	khatib	PROPN
ap-3488	442	9	.	.	PUNCT
ap-3488	443	1	handbook	handbook	NOUN
ap-3488	443	2	of	of	ADP
ap-3488	443	3	robotics	robotic	NOUN
ap-3488	443	4	.	.	PUNCT
ap-3488	444	1	springer	springer	NOUN
ap-3488	444	2	,	,	PUNCT
ap-3488	444	3	2008	2008	NUM
ap-3488	444	4	.	.	PUNCT
ap-3488	445	1	9	9	NUM
ap-3488	445	2	http://dx.doi.org/10.1109/robot.2009.5152865	http://dx.doi.org/10.1109/robot.2009.5152865	NOUN
ap-3488	445	3	http://dx.doi.org/10.1109/tro.2009.2014123	http://dx.doi.org/10.1109/tro.2009.2014123	NOUN
ap-3488	445	4	http://dx.doi.org/10.1017/s0263574703005149	http://dx.doi.org/10.1017/s0263574703005149	NOUN
ap-3488	445	5	http://dx.doi.org/10.1016/s0034-4877(03)80010-1	http://dx.doi.org/10.1016/s0034-4877(03)80010-1	PROPN
ap-3488	445	6	http://dx.doi.org/10.1109/robot.2010.5509791	http://dx.doi.org/10.1109/robot.2010.5509791	PROPN
ap-3488	445	7	acta	acta	PROPN
ap-3488	445	8	polytechnica	polytechnica	PROPN
ap-3488	445	9	56(1):1–9	56(1):1–9	PROPN
ap-3488	445	10	,	,	PUNCT
ap-3488	445	11	2016	2016	NUM
ap-3488	445	12	1	1	NUM
ap-3488	445	13	introduction	introduction	NOUN
ap-3488	445	14	2	2	NUM
ap-3488	445	15	preliminary	preliminary	ADJ
ap-3488	445	16	and	and	CCONJ
ap-3488	445	17	problem	problem	NOUN
ap-3488	445	18	statement	statement	NOUN
ap-3488	445	19	2.1	2.1	NUM
ap-3488	445	20	lie	lie	NOUN
ap-3488	445	21	groups	group	NOUN
ap-3488	445	22	2.2	2.2	NUM
ap-3488	445	23	lie	lie	NOUN
ap-3488	445	24	algebra	algebra	NOUN
ap-3488	445	25	associated	associate	VERB
ap-3488	445	26	with	with	ADP
ap-3488	445	27	a	a	DET
ap-3488	445	28	lie	lie	NOUN
ap-3488	445	29	group	group	NOUN
ap-3488	445	30	2.3	2.3	NUM
ap-3488	445	31	graph	graph	NOUN
ap-3488	445	32	theory	theory	NOUN
ap-3488	445	33	2.4	2.4	NUM
ap-3488	445	34	problem	problem	NOUN
ap-3488	445	35	statement	statement	NOUN
ap-3488	445	36	2.5	2.5	NUM
ap-3488	445	37	kinematic	kinematic	ADJ
ap-3488	445	38	model	model	NOUN
ap-3488	445	39	on	on	ADP
ap-3488	445	40	a	a	DET
ap-3488	445	41	lie	lie	NOUN
ap-3488	445	42	group	group	NOUN
ap-3488	445	43	3	3	NUM
ap-3488	445	44	formation	formation	NOUN
ap-3488	445	45	control	control	NOUN
ap-3488	445	46	law	law	NOUN
ap-3488	445	47	on	on	ADP
ap-3488	445	48	se(2	se(2	PROPN
ap-3488	445	49	)	)	PUNCT
ap-3488	445	50	3.1	3.1	NUM
ap-3488	445	51	controller	controller	NOUN
ap-3488	445	52	design	design	VERB
ap-3488	445	53	3.2	3.2	NUM
ap-3488	445	54	stability	stability	NOUN
ap-3488	445	55	analysis	analysis	NOUN
ap-3488	445	56	3.3	3.3	NUM
ap-3488	445	57	stability	stability	NOUN
ap-3488	445	58	of	of	ADP
ap-3488	445	59	formation	formation	NOUN
ap-3488	445	60	control	control	NOUN
ap-3488	445	61	4	4	NUM
ap-3488	445	62	simulation	simulation	NOUN
ap-3488	445	63	5	5	NUM
ap-3488	445	64	conclusions	conclusion	NOUN
ap-3488	445	65	list	list	NOUN
ap-3488	445	66	of	of	ADP
ap-3488	445	67	symbols	symbol	NOUN
ap-3488	445	68	acknowledgements	acknowledgement	NOUN
ap-3488	445	69	references	reference	NOUN