









































  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 
 
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. 

CONTROL OF 
SATELLITES WITH 

ONBOARD ROBOTIC 
MANIPULATORS 

ROBERT BUCKELEW, ETHAN CATALANELLO, 
ANNALISA SCACCHIOLI (FACULTY ADVISOR) 

 
 
 

✵ ABSTRACT 
Free-floating satellites with onboard robotic 

manipulators are subjected to widely varying loads 
resulting from the motion of the robotic manipula-
tors. As there are no fixed supports in space, these 
loads will cause the satellite to move. By modelling 
the motion of the onboard robotic arms, determin-
ing the necessary reaction loads (which must be sup-
plied by the satellite to keep the arm fixed), and sim-
ulating the resulting satellite dynamics, we designed 
a model of a satellite-arm system. We found that a 
Proportional-Integral-Derivative (PID) control 
scheme, with disturbance-estimating capabilities, 
was effective in maintaining satellite position and ori-
entation during the operation of the onboard ro-
botic manipulator. The MATLAB-based Simulink 
modeling environment was used to perform the sim-
ulations of satellite dynamics and control. 

 

1 INTRODUCTION 
The operational success of several fields, in-

cluding communication technology and space ex-
ploration, is dependent on a functional space satel-
lite infrastructure. An advanced satellite network, 
such as a constellation of communications satellites, 
will require routine maintenance to maximize its 
functional lifetime[1]. The Defense Advanced Re-
search Projects Agency (DARPA) has proposed tech-
nology to perform robotic servicing of on-orbit sat-
ellites[2]. The project is titled Robotic Servicing of Ge-
osynchronous Satellites (RSGS) and involves satellite-

mounted robotic arms which can perform opera-
tions on other satellites. Potential missions for the 
“nurse” satellite include inspection, installation, and 
repair of on-orbit satellites as well as their relocation 
to new orbits. 
 In general, the motion of robotic manipula-
tors and the body to which they are mounted are 
coupled—that is, the motion of one tends to influ-
ence the motion of the other. The magnitude of this 
effect depends on the inertial properties of the bod-
ies and the interaction forces involved. In a micro-
gravity environment such as Low Earth Orbit (LEO), 
no dissipative reaction forces exist unlike those pre-
sent in operations performed on and near the Earth’s 
surface. Therefore, the motion of satellite-mounted 
robotic manipulators will have significant effects on 
satellite attitude (the direction the satellite is point-
ing) [3]. 
 It is desirable to reduce the effects of robotic 
manipulator disturbances on satellite position and 
attitude using an attitude control system (ACS). An 
ACS measures satellite position and orientation with 
respect to reference values. It uses mechanical actu-
ators (e.g., reaction wheels, gas jet thrusters) to re-
ject disturbances. In this project, we model the dy-
namics of the FREND Mark II robotic arm and simu-
late the motion of a base satellite subjected to dis-
turbances from the robotic arm motion. Additionally, 
we designed a control scheme using a basic PID 
(Proportional-Integral-Derivative) controller. PID 
controllers feature three gains—proportional, inte-
gral, and derivative—which determine the control in-
put signal based on the magnitude, time integration, 
and time rate of change of the error signal respec-
tively. The goal is to reduce the perturbations arising 
from operation of the robotic arm, resulting in a sat-
ellite that maintains its position and attitude. While 
extensive work has been performed in this area uti-
lizing complex, nonlinear controls, we wanted to 
evaluate the effectiveness of a much simpler, linear 
control scheme, as it was assumed the perturbations 
arising from the robotic arm would be very small. We 
believed that these small perturbations would be 
well approximated by linear control theory, and thus 
that linear controllers would be sufficient at stabiliz-
ing the system. This belief/idea, combined with the 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

development of the modular simulation for control 
design, serves as the novel contribution of our pro-
ject. We have created an environment that allows for 
control refinement without requiring rigorous math-
ematical proofs. 
 

2 METHODOLOGY  

 The robotic arm proposed by DARPA for the 
Robotic Servicing of Geosynchronous Satellites 
(RSGS) program is the FREND Mark II (hereafter re-
ferred to as the FREND), a 7-joint 3D manipulator 
which will be responsible for performing operations 
on the “patient” satellite. An illustration of the FREND 
arm is shown in FIGURE 1. 

The Robotics, Vision, and Control Toolbox, a 
third-party MATLAB-based toolbox for robotics ap-
plications (hereafter referred to as “the Toolbox”) 
was used to develop a model of the FREND and to 
perform dynamics calculations. The results of these 
dynamics calculations, based on the FREND model, 
were used as inputs to the satellite dynamics simula-
tion. These results effectively modeled the disturb-
ances to the satellite arising from the motion of the 
robotic arm. 
 
 
 

FREND Arm Modelling 
 The Toolbox is capable of modelling and 
performing calculations on any robotic arm so long 
as the arm’s relevant parameters are provided. The 
relevant parameters are inertial parameters, includ-
ing the mass and inertia matrix and Denavit-Harten-
berg parameters (which describe arm geometry). 
The Denavit-Hartenberg parameters used in the 
FREND model were defined according to the defini-
tions shown in FIGURE 2 and measurements taken from 
FIGURE 3. The Denavit-Hartenberg parameters are 
shown in SUPPLEMENTAL TABLE S1. 

FIGURE 1: DARPA rendering of the FREND Mark II arm[4] 

IT IS DESIRABLE TO REDUCE 

THE EFFECTS OF ROBOTIC  
MANIPULATOR DISTURBANCES 

ON SATELLITE POSITION AND 

ATTITUDE USING AN ATTITUDE 

CONTROL SYSTEM (ACS). 

 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

None of the required parameters for the 
FREND were publicly accessible, so the measure-
ments were approximated using pixel measure-
ments from schematics and images that were pub-
licly available. Knowing this information, an image 
editing software can be used to analyze the sche-
matic in FIGURE 3 in order to define a pixel scale which 
relates real-world dimensions to pixel dimensions. 
The geometry of the arm was then calculated from 
the schematic in FIGURE 3 and used to compute the in-
ertia tensor. Each link is assumed to be a cylinder of 

solid aluminum having a density of 2700 𝑘𝑘𝑘𝑘
𝑚𝑚3 and a 

center of mass located at the geometric center. This 
assumption of material composition represents a 
“worst case scenario” as the actual arm is not   solid 
aluminum[4]. The computed dynamic parameters are 
shown in SUPPLEMENTAL TABLE S2 and then inertia matrices 
are shown in SUPPLEMENTAL TABLE S3. 

ABOVE: 
FIGURE 2: Graphic definition of  
Denavit-Hartenberg parameters[5]  

RIGHT: 
FIGURE 3:  Schematic of the FREND Mark II showing 
the relative orientations of link reference frames[4] 

 

 

 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

[a] Gravity was neglected in our simulation because the satellite is in space. 

 

 The Toolbox features a function that can numerically evaluate the robot dynamics equation (EQUATION (1)). 
This is a system of coupled differential equations that relates the joints’ angular kinematics (𝑞𝑞, �̇�𝑞, �̈�𝑞) of the robotic 
arm joints to the joint torques (𝑄𝑄) and other external loads (end effector wrench 𝑊𝑊 and gravity torque 𝐺𝐺(𝑞𝑞)[a]) 
acting on the arm. Solving these differential equations yields the joint torques and the reaction loads at the base 
of the arm. 
 

𝑄𝑄(𝑞𝑞, �̇�𝑞, �̈�𝑞) = 𝑀𝑀(𝑞𝑞)�̈�𝑞 + 𝐶𝐶(𝑞𝑞, �̇�𝑞)�̇�𝑞 + 𝐹𝐹(�̇�𝑞) + 𝐺𝐺(𝑞𝑞) + 𝐽𝐽(𝑞𝑞)𝑇𝑇𝑊𝑊   
 
The parameters of EQUATION (1) are defined in TABLE 1 below. 
 
 

The joint torques 𝑄𝑄(𝑞𝑞, �̇�𝑞, �̈�𝑞) obtained through the solution of the differential equation can be utilized to solve for 
the reaction forces as well as the moments the arm will induce on the satellite. Thus, these loads will be utilized in 
the simulation as the external disturbance the satellite is subjected to. 
 
Satellite Modelling 

To model the effects of robotic arm motion on satellite position and attitude, we utilized the Aerospace 
Blockset’s “6DOF” (six degree-of-freedom) block in the MATLAB-based Simulink modeling environment. This 
block implements the equations of motion described in EQUATIONS (2) and (3), which are the differential equations 
describing translational motion and angular motion, respectively. The parameters of these equations are defined 
explicitly in SUPPLEMENTAL TABLE S5.  

 

�̈�𝑥 =
∑ 𝐹𝐹𝑗𝑗(𝑡𝑡)𝑁𝑁
𝑗𝑗=1

𝑚𝑚
 

�̈�𝜃(𝑡𝑡) = 𝐼𝐼−1 ���𝑀𝑀(𝑡𝑡) + 𝑟𝑟𝑗𝑗 × 𝐹𝐹𝑗𝑗(𝑡𝑡)� − �̇�𝜃(𝑡𝑡) × �𝐼𝐼�̇�𝜃(𝑡𝑡)�
𝑁𝑁

𝑗𝑗=1
�  

 
 

𝑞𝑞, �̇�𝑞, �̈�𝑞 JOINT ANGULAR POSITION, VELOCITY, and ACCELERATION respectively  

𝑄𝑄 VECTOR OF GENERALIZED JOINT TORQUES – torques required at each joint to achieve the motion described by (𝑞𝑞, �̇�𝑞, �̈�𝑞) 

𝑀𝑀(𝑞𝑞) JOINT-SPACE INERTIA MATRIX – describes the moment of inertia of each link in matrix form 

𝐶𝐶(𝑞𝑞, �̇�𝑞) CORIOLIS AND CENTRIPETAL COUPLING MATRIX – describes centripetal forces due to rotation of the links 

𝐹𝐹(�̇�𝑞) FRICTION MATRIX – describes torques from friction present in the joints 

𝐺𝐺(𝑞𝑞) GRAVITY LOAD – describes torques originating from gravity acting on the links 

𝐽𝐽(𝑞𝑞) MANIPULATOR JACOBIAN MATRIX – describes the sensitivity of the end effector to the motion of each joint 

𝑊𝑊 END EFFECTOR WRENCH – describes the load on the end effector 

TABLE 1: Definition of terms in EQUATION (1) 

(1) 

(2) 
 
 

(3) 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

 Since there is no satellite design specified for the RSGS program, we assumed a generic small satellite 
configuration. We take the satellite to be a rectangular prism of 2𝑚𝑚 × 1𝑚𝑚 × 1𝑚𝑚 with two thin rectangular solar 
arrays fixed at opposing ends 3𝑚𝑚 × 1.5𝑚𝑚 × .0055𝑚𝑚 located . 5𝑚𝑚 from the satellite body. The density of the satellite 

was assumed to be 200 𝑘𝑘𝑘𝑘
𝑚𝑚3, which is an approximate mass density for spacecraft of this size[9] and the solar panels 

were assumed to be identical to those manufactured by Spectrolab, a manufacturer of satellites for use in space, 

and have a planar density of 2.06 𝑘𝑘𝑘𝑘
𝑚𝑚2 

[10]. This means that the entire satellite has a mass of 𝑚𝑚 = 411.9305362785 𝑘𝑘𝑘𝑘, 

and the inertia tensor is shown below:  
 

𝐼𝐼 = (303.02687565826 0 0 0 170.14297228667 0 0 0 199.55068127826 )𝑘𝑘𝑘𝑘 ∙ 𝑚𝑚2 
 

 

Controller Modelling 
Recall that our objective is to maintain the 

translational position as well as the angular position 
(or attitude) of the satellite throughout operation of 
the on-board robotic arm. To accomplish satellite 
position and attitude control, PID controllers, which 
represents a basic function for the control of linear 
systems, were implemented for each of the six de-
grees of freedom, namely the three translational co-
ordinates (𝑥𝑥,𝑦𝑦, 𝑧𝑧) of satellite position and the three 
Euler angles (𝜙𝜙,𝜃𝜃,𝜓𝜓) defining satellite roll, pitch, and 
yaw, respectively. The optimal values of the PID con-
troller gains, 𝐾𝐾𝑃𝑃, 𝐾𝐾𝐼𝐼, and 𝐾𝐾𝐷𝐷 are determined automat-
ically using the MATLAB PID Tuner tool. The optimal 
gains for the RSGS model satellite are shown in SUP-

PLEMENTAL TABLE S4.  
 

3 RESULTS  

As a result of this project, we have devel-
oped a multiple component model in which a user 
can define a robotic arm configuration and trajectory 
as well as the inertial parameters of a satellite. The 
user can then simulate the motion response of the 
satellite to disturbances arising from motion of the 
arm and employ a predictive control scheme to 
maintain a reference satellite position and attitude. 
A simplified Simulink block diagram demonstrating 
the fundamental logic behind the model is shown in 
FIGURE 4. As shown in the figure, the controller (which 
is a PID controller in this case) receives the transla-
tional position and angular position offset as well as 
an estimation of the incoming arm loads which it 
then uses to calculate the necessary control 
force/torque.

𝑥𝑥(𝑡𝑡) VECTOR OF SATELLITE POSITIONAL COORDINATES 

𝜃𝜃(𝑡𝑡) VECTOR OF SATELLITE ANGULAR POSITION COORDINATES 

𝐹𝐹𝑗𝑗(𝑡𝑡) VECTOR OF TRANSLATIONAL FORCE CAUSED BY ROBOTIC ARM 𝑗𝑗 

𝑀𝑀𝑗𝑗(𝑡𝑡) VECTOR OF MOMENTS CAUSED BY ROBOTIC ARM 𝑗𝑗 

𝑚𝑚 SATELLITE MASS 

𝐼𝐼 SATELLITE INERTIA TENSOR 

𝑟𝑟𝑗𝑗 VECTOR DEFINING THE BASE OF ARM 𝑗𝑗 RELATIVE TO THE SATELLITE COM 

TABLE 2: Definition of terms in EQUATIONS (2) and (3) 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

The objective of this work is to demonstrate 
the use of a PID controller with load estimative ca-
pacity in the control of position and attitude of satel-
lites with onboard robotic manipulators. The simula-
tion was run for multiple scenarios: without control, 
with non-predictive control, and with the load esti-
mating controller. For runs with the controller, it is 

assumed that the satellite has an ideal control actua-
tor onboard that can instantly induce the required 
torques or forces determined by the PID controller. 
It is important to note that this is a preliminary as-
sumption used to evaluate the effectiveness of the 
control scheme rather than to evaluate its perfor-
mance in a realistic application. The position and at-

 

 

LEFT: 
FIGURE 4: Simplified block dia-
gram describing the logical rela-
tions between the disturbance 
load, satellite, and controller  

BELOW: 
FIGURE 5:  Disturbance forces and 
moments acting on the satellite 
throughout the arm’s trajectory 

 

 

 

 

 

The forces and moments of the satellite disturbance load are plotted against time in FIGURE 5. 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

titude responses of the satellite both with and with-
out control are compared in FIGURE 6. The left side of 
FIGURE 6 shows the uncontrolled case: notice that the 
angular and translational positions diverge from the 
reference (initial condition). The controlled case is 
shown on the right side of FIGURE 6. Notice how the 
satellite’s deviation from the reference was drasti-
cally reduced compared to the uncontrolled case 
and that the satellite returned to the initial reference 
state (position of (0, 0, 0) and angular position of 
(0, 0, 0)) after the disturbance loads ceased. It is im-
portant to note that this simulation represents a 
“worst case scenario” for the satellite, as several as-
sumptions were made that negatively impact the 
control effectiveness. Despite these assumptions, 
the PID controller was very effective at stabilizing the 
system. Thus, we have succeeded in designing an ef-
fective controller for the satellite. 

4 DISCUSSION OF SIMULATION RESULTS 

The use of the Proportional-Integral-Deriva-
tive control scheme with load prediction resulted in 
a very accurate satellite response. The maximum de-
viations from reference position and attitude were 
. 07 𝑚𝑚𝑚𝑚 and 1.26° respectively. Without the use of 
the controller, the satellite motion would continue 
indefinitely following a disturbance. These results 
provide evidence that such a control scheme could 
effectively maintain satellite position and attitude 
during robotic servicing operations. The use of cal-
culated robotic arm disturbances as load predictions 
is a reasonable assumption when considering the ac-
tual implementation of robotic servicing missions. If 
a space organization were to implement satellite-
mounted robotic arms for maintenance purposes, 

FIGURE 6: Comparison of system response between uncontrolled (LEFT) and controlled (RIGHT) satellite position (TOP) and angu-
lar position (BOTTOM) 

 
 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

the simulation of the robot dynamics prior to the ex-
ecution of the mission would result in a more accu-
rately controlled system during operation, as the re-
sult of the simulation would be used as the load es-
timation. In addition to the load prediction, the PID 
controllers add robustness to the scheme, adjusting 
for additional perturbations arising from the opera-
tional environment. 

 

5 CONCLUSIONS AND FUTURE WORK 
The goal of this project was to create a dy-

namics simulation of a robotic manipulator and sat-
ellite in order to develop a model-based control al-
gorithm for maintaining satellite position and orien-
tation. Even with a very basic PID feedback control 
scheme, the results of the simulation were very 
promising. The arm load estimation technique al-
lowed the controller to effectively eliminate transla-
tional and angular displacement. We believe that 
this research offers a framework for future investiga-
tion into more advanced control methods, including 
nonlinear approaches such at Lyapunov theory, 
which incorporates the nonlinear system model into 
the controls equation. We also hope to develop a 
more accurate satellite model that includes realistic 
actuators, such as reaction wheels and gas thrusters, 
to better evaluate the effectiveness of the control 
scheme. With this, we also hope to investigate vari-
ous satellite/arm designs and to determine which 
configuration is most effective. 

This was inspired by DAPRA’s Robotic Ser-
vicing of Geosynchronous Satellites (RSGS)[4] pro-
posal, which aims to extend the operational lives of 
satellites located in geostationary orbit through is-
sue diagnosis, repair, and upgrades. The implica-
tions of this proposal include lowering the cost of 
operation for geosynchronous satellites, thereby en-
couraging more private companies to contribute to 
space infrastructure. This, in turn, aligns closely with 
the NASA Space Technology Mission Directorate[18], 
as contributing to this Earth-based infrastructure will 
facilitate future missions carried out to the moon any 
beyond. We hope future work on this project will in-
centivize more private companies to begin develop-
ing autonomous, robotic satellite systems to further 
humanities reach beyond planet Earth∎  

6 ACKNOWLEDGEMENTS 
The authors would like to acknowledge the 

help of others who contributed to the success of this 
project. We thank our Aresty research advisor, Dr. 
Annalisa Scacchioli, for her continuous guidance 
and encouragement throughout the duration of the 
project. We thank Dr. Aaron Mazzeo for introducing 
us to the robotics toolbox. We thank Dr. Laurent 
Burlion for his discussion about control methodolo-
gies and satellite attitude dynamics. We thank Mike 
Vivar for his recommendation of the robotics 
toolbox. Finally, we thank our undergraduate peers, 
especially Michael Higgins and Aaron Pfister, for 
their continued interest in our project.  

 

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[1] F. Garcia, L. Peret, G. Verfaillie, Deployment and Mainte-

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vicing of Geosynchronous Satellites (RSGS).  
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NOUS-SATELLITES 

[3]  A. Antonello, P. Tsiotras, A. Valverde, Free-flying Spacecraft-
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[4]  Defense Advanced Research Projects Agency. (2019, May 
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[5]  P.I. Corke, “Robotics, Vision & Control”, Springer 2017, ISBN 
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[6]  MathWorks. 6DOF (Euler Angles).  
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[7]  P.C. Hughes, “Spacecraft Attitude Dynamics”, Dover Publica-
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[8]  Northrop Grumman. Space Logistics Services.  
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VICES/ 

[9]  Phipps, Claude & Albrecht, G. & Friedman, H. & Gavel, D. & 
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[10]  Spectrolab. Space Solar Panels.  
 HTTPS://WWW.SPECTROLAB.COM/DATASHEETS/PANEL/PANELS.PDF 

[11]  MathWorks. Open PID Tuner.  
HTTPS://WWW.MATHWORKS.COM/HELP/SLCONTROL/UG/DESIGNING-CON-

TROLLERS-WITH-THE-PID-TUNER.HTML 

[12]  G.F. Franklin, J.D. Powell, A. Emami-Naeini, “Feedback Con-
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[13]  MathWorks. Sgolayfilt.  
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https://www.darpa.mil/program/robotic-servicing-of-geosynchronous-satellites
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https://www.mathworks.com/help/slcontrol/ug/designing-controllers-with-the-pid-tuner.html
https://www.mathworks.com/help/slcontrol/ug/designing-controllers-with-the-pid-tuner.html
https://www.mathworks.com/help/signal/ref/sgolayfilt.html


  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

[14]  C.J. Damaren, A.H.J. de Ruiter, J.R. Forbes, “Spacecraft Dy-
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[15]  S.A. Rawashdeh, Attitude Analysis of Small Satellites Using 
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[16]  R. Hernandez-Alvarado, L.G. Garcia-Valdovinos, et. al., Neu-
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[17]  H.E.Soken, C. Hajiyev, S. Sakai, Robust Kalman filtering for 
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[18]  NASA. Space Technology Mission Directorate.  
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https://www.nasa.gov/directorates/spacetech/about_us/index.html


  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

8 SUPPLEMENTARY TABLES 

 
 

JOINT 𝑑𝑑 𝑎𝑎 𝛼𝛼 OFFSET 

1 0.3469785 0 −
𝜋𝜋
2 0 

2 0.2517295 0 −
𝜋𝜋
2 0 

3 0.8776515 0 
𝜋𝜋
2 0 

4 0.2122692 0 −
𝜋𝜋
2 0 

5 0.1592019 0 �
127
449� 0 

5A 0.6349236746 0 −�
127
449� 0 

5B 0.1074953 0 
𝜋𝜋
2 0 

6 0.1728089 0 −
𝜋𝜋
2 0 

7 0.2000229 0 0 0 

 
 
 
 

LINK 𝑚𝑚 (𝑘𝑘𝑘𝑘) 𝑟𝑟 (𝑚𝑚) 𝐿𝐿 (𝑚𝑚) 

1 2.45581930238976 0.0530673 0.3469785 

2 1.78167282722394 0.0530673 0.2517295 

3 8.64176380422475 0.0625922 0.8776515 

4 0.802308387477559 0.03877995 0.2122692 

5 0.540058000435033 0.0367389 0.1592019 

5A 2.15384119253858 0.0367389 0.6349236746 

5B 0.364654547302287 0.0367389 0.1074953 

6 0.425389148502536 0.0312961 0.1728089 

7 0.536125954214708 0.0326568 0.2000229 

 

SUPPLEMENTAL TABLE S1: Denavit-Hartenberg parameters for the FREND Mark II arm model. 

SUPPLEMENTAL TABLE S2: Mass, radius, and length of each cylindrical link object used 
in the definition of the FREND arm model 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

LINK 𝐼𝐼 (𝑘𝑘𝑘𝑘 ∙ 𝑚𝑚2) 

1 (0.00778041772567878 0 0 0 0.0116706265885182 0 0 0 0.00778041772567878 ) 

2 (0.0056446167813748 0 0 0 0.0084669251720622 0 0 0 0.0056446167813748 ) 

3 (0.0380886296066415 0 0 0 0.0571329444099623 0 0 0 0.0380886296066415 ) 

4 (0.00135740156152532 0 0 0 0.00203610234228798 0 0 0 0.00135740156152532 ) 

5 (0.00082005923636261 0 0 0 0.00085043340488162 0.00010738583988220 0 0.00010738583988220 0.001199714686025 ) 

5A 
(0.003270532724590 0 0 0 0.003391669964095 − 0.00042827260265995 0 

− 0.00042827260265995 0.004784661847380 ) 

5B (0.000553715210877318 0 0 0 0.000830572816315976 0 0 0 0.000553715210877318 ) 

6 (0.000468726352717391 0 0 0 0.000703089529076087 0 0 0 0.000468726352717391 ) 

7 (0.000643230468209275 0 0 0 0.000643230468209275 0 0 0 0.000964845702313913 ) 

 
 
 
 
 

 𝐾𝐾𝑃𝑃 𝐾𝐾𝐼𝐼 𝐾𝐾𝐷𝐷 

FORCE 617.061827129926 35.6866537699081 2667.42085820047 

MOMENT 102.843637854979 5.94777562634487 444.570143033412 

 

SUPPLEMENTAL TABLE S3: Inertia tensors for each link of the FREND Mk. II arm model 

SUPPLEMENTAL TABLE S3: Proportional, integral, and derivative gains for the force and moment PID controllers 


