Jtam-A4.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 54, 1, pp. 149-161, Warsaw 2016 DOI: 10.15632/jtam-pl.54.1.149 MODELLING AND SIMULATION STUDIES ON THE MOBILE ROBOT WITH SELF-LEVELING CHASSIS Jacek Bałchanowski Wrocław University of Technology, Faculty of Mechanical Engineering, Wrocław, Poland e-mail: jacek.balchanowski@pwr.edu.pl The mobile robot presented in the article is a hybrid system combining efficient travel on wheels on a flat terrain with the capability of surmounting obstacles by walking. The research is focused ondesigning a control systemmaintaining the robot chassis at a constant position to the ground. The aims of this research are: creation of the computational model of the control system for the levelling system of designed mobile robots and realization of simulation studies on the robots travel in terrain with obstacles. The simulations aimed at determination of basic dynamic and kinematic properties. Keywords: mobile robot, simulation studies, self-leveling chassis 1. Introduction The research onmobile robots has intensified in the recent years, especially tomeet the demand for automating the transport process and for inspection (chemically, biologically) of contamina- ted areas and those exposed to hazard of fire explosions (Tchoń et al., 2000; Trojnacki et al., 2008). Studies focusedonmobile robotshavebeencarried out inmany research centers (universities, military and industrial centers). Theydealwithwheeled robots,walking robots, tracking robots, crawling robots, flying robots, floating robots and their hybrids.The researchhasbeen calculated on variety of such vehicles differing in their way of traveling: wheeled systems (WalkPartner, see Halme et al., 2003), tracked systems (INSPECTORRobot, see Hołdanowicz, 2008), walking systems (PetMan, see Boston Dynamic, 2014), floating and flying systems (Hermes RO 900, see Elbit Systems, 2014). The dominant contemporary form of vehicles motion is riding on wheels. In an urban area, where the surface is smooth, thewheels are themost effective. However, thebiggest disadvantage is that they have no ability to overcome obstacles in form of a substrate discontinuity – curbs, stairs, slopes. The most common form of motion by living organisms of the Earth is treading. This type of transportation is especially effective with moving around non-urbanized irregular surfaces containing obstacles (Bałchanowski and Gronowicz, 2012a,b; Zielińska,2003). Mobile wheel-legged robots are hybrids that combine efficient travelling on a flat terrain by wheels with the capability of surmounting obstacles by walking. Amajor challenge in designing such systems is to develop its wheel suspension allowing the robot both to move on wheels and towalk, and automatically level its chassis during travelling on anuneven surface (Bałchanowski and Gronowicz, 2012a,b; Gronowicz and Szrek, 2009a,b; Szrek andWójtowicz, 2010). One such system is a wheel-legged mobile robot (Fig. 1) designed and built at Wroclaw University of Technology (Bałchanowski, 2012; Bałchanowski and Gronowicz, 2012a,b). The robot is equippedwith a unique wheel suspensionwhich allows it to drive, walk, rise, lower and self-level the chassis. In this paper, the design of this device is described. 150 J. Bałchanowski Fig. 1. A general view of a mobile robot and a view of the walking phase 2. Design of a mobile robot In the framework of the project realized at Wroclaw University of Technology the design of a robotwhose schematic is shown in Fig. 2 has been developed. It is assumed that thewheels with suspensions are symmetrically arranged in relation to the longitudinal and transverse axis of the robot. Such a position of the wheels ensures a level playing field for driving of the front and rear axles. The major design challenge was to develop a suspension mechanism which should provide the robot with ability to walk with a view system to overcome obstacles on the track and enabling automatic self-levelling of the chassis (Fig. 3). Fig. 2. A general scheme of the wheel-leggedmobile robot (1-4 – wheel suspensions, 0 – ground, k – chasis) Fig. 3. A schematic showing the execution of suspension imotions: hip – lifting, h i w – ejecting Modelling and simulation studies on the mobile robot... 151 The wheel suspension is a complex mechanism with 4 degrees of freedom in relation to the body. Such amechanism (Fig. 3)must ensure the full range of motion in order to fulfill the task of driving (turning and twisting wheels – two degrees of freedom) as well as lifting and ejecting the wheels (two degrees of freedom). As a result of the design work on the suspension structure and then on the geometric syn- thesis, main dimensions of system have been chosen (Bałchanowski, 2012; Bałchanowski and Gronowicz, 2012c; Gronowicz et al., 2012; Sperzyński et al., 2010; Szrek andWójtowicz, 2010). A view of the right front side of the robot with wheel suspension mechanism 1 robot is given in Fig. 4. For a single suspension, the lifting of the wheel hip is realized by a linear actuator q i p. The ejecting of the wheel hiw is by means of linear actuators q i w. Fig. 4. The kinematic scheme of mobile robot suspension (front right side) The robot is designed for inspection work both outdoors and indoors (e.g. buildings, pro- duction halls, etc.). Since it is designed tomove inside rooms, to pass through typical doorways (less than 0.9m wide) and to be able to surmount an obstacle with a height equal to that of a typical stair step (the wheel lifting height greater than 0.2m), its overall dimensions have to be limited. The chosen axle base ra is 0.8m and the wheels base rw is 0.65m (Fig. 2). The rest of basic parameters of geometric wheel suspension 1 is shown in Table 1. Table 1.Geometric parameters of wheel suspension 1 Parameter Value Parameter Value Parameter Value xA1 0.11m yA1 −0.65m zA1 0m xB1 −0.04m yB1 −0.65m zB1 −0.152m xG1 0.518m yG1 −0.65m zG1 0.005m DS1 0.253m A1F 0.17m A1C 0.303m CS1 0.5m CD 0.162m h0 0.335m The lifting and ejection can be achieved with linear drives, e.g. electric actuators LINAK LA36. Solid rubber-steel wheels with a motor and a gear integrated with a hub (GOLDENMOTOR HUB24E) have been chosen as the travelling drives (Bałchanowski, 2012; Bałchanowski and Gronowicz, 2012a,b). The main specifications of the wheel drives as well as the lift and ejection-protrusion actuators are shown in Table 2. On the basis of the developed conceptual design and documentation, a prototype of amobile wheel-legged robot has beenmade (Fig. 1). When driving on uneven ground, the robot chassis is rotated along the longitudinal and transverse axes. The implementation of the levelling aims tomaintain a constant orientation of 152 J. Bałchanowski Table 2.Main parameters of the drives Actuator LINAKLA36 qw,qp (stroke length) 0.35-0.5m vw,vp (speed) 0.068m/s Fw,Fp (force) 1700N ms (mass) 4.9kg Wheel GOLDENMOTORHUB24 dqn/dt (angular velocity) 13.08rad/s (125rpm) Mn (nominal torque) 13.5Nm kr (radial stiffness) 9.5 ·10 5N/m mk (mass) 5kg rk (radius of wheel) 0.105m the robot body above the ground according to the scheme shown in Figs. 2 and 3, whichmeans maintaining the value of the given angles of orientation αx =0 αy =0 Raising or lowering the individual wheels can bring the robot to the assumed level. This function can be accomplished solely by lifting the chassis by means of the lifting actuators qip (Fig. 4), while the other drives (ejection, turn and rolling) remain fixed. For the given values of wheels radii rk and suspension height h0, the height h i k of the robot chassis above the groundmay be presented in the form (Fig. 3) hik = rk+h0+h i p(q i p) (2.1) The graph in Fig. 5 shows changes of the height hip for the suspension as a function of the actuator extension qip (Bałchanowski andGronowicz, 2012a,b,c). For theadopted actuator stroke qip =0.35-0.5m (Table 2), the defined range of changes of the wheel lifting h i p is 0¬hip ¬ 0.26m=hp (2.2) where hp is the maximum height of the suspension lifting. Fig. 5. Elevation of the robot chassis hik versus extension of the lifting actuator q i p Themaximumvalue of thewheel lifting height hp determines the possibility of overcoming a certain unevenness.Themechanism shown in side and front views onuneven ground is presented inFig. 6.Themaximumangles of theground inclinationαmaxx along the robot longitudinalxaxis as well as αmaxy along the robot transverse y axis, can be determined from the relationship αmaxx =arctan hp rw =21.8◦ αmaxy =arctan hp ra =18.0◦ Modelling and simulation studies on the mobile robot... 153 Fig. 6. Side and front views of the robot on uneven ground. The schematic shows the maximum angles of the ground inclinationαmaxx and α max y along the robot longitudinal x and transverse y axis If the area has larger values of the inclination angles, then the lifting mechanisms do not provide sufficient levelling of the chassis. 3. Numerical model of the mobile robot In order to perform simulations, a computational model of the wheel-legged robot shown in Fig. 7, has been created in the LMS DADS (Haug, 1989) dynamic analysis system. The robot has 22 DOF, with the body having 6 DOF and each wheel suspension having 4 DOF relative to the body. Sixteen kinematic excitations are defined in the robot: 8 rotational excitations qin and qis (wheel rolling and turning) as well as 8 linear excitations q i p and q i w (wheel lifting and ejecting) for each suspension (i=1,2,3,4) (Bałchanowski, 2012; Bałchanowski andGronowicz, 2012a,b). Fig. 7. The model of the wheel-leggedmobile robot (main view) Thewheel/base interactions aremodelledusinga tire/ground interaction forcemodel (TIRE) (Haug, 1989). Themass of the wheels is quite large due to the fact that themotor and gear are incorporated in the hub, and because of their high radial and longitudinal stiffness (Table 2). The total weight (deadweight+payload) of thewheeled-legged robot is estimated at 100kg. The mass and geometry of the suspension, wheel and actuator parts are assumed as in the design. The weight of the body (comprising deadweight of the frame bearer, steering system, batteries, current generator as well as payload) is appropriatelymatched to obtain the assumed total weight of 100kg, with the center of gravity located in the body center. 154 J. Bałchanowski 3.1. Design of the control system for the levelling mechanism of the robot chassis When the robot travels on an uneven substrate, the robot chassis changes its orientation relative to the ground. The changes in orientation of the chassis are described by the angles of inclination αx (the angle of the body rotation relative to the robot transverse axis) and the steering angle αy (the angle of the body rotation relative to the robot longitudinal axis, Fig. 2). In a real robot, both angles (Fig. 1) are measured using inclinometers (Bałchanowski and Gronowicz, 2012b; Gronowicz and Szrek, 2009a,b; Szrek andWójtowicz, 2010). Theplane of the robot chassis will be twisted as a result of rotationsαx andαy. The twisting can bedescribedbymeans ofh1,h2,h3 andh4 vertical displacements of pointsP1,P2,P3 andP4 (Figs. 2 and 8). For anglesαx,αy, the position of pointsP1 in the global coordinate system xyz, described by the vector rPi = [xPi,yPi,zPi] T, can be calculated using the following formula rPi =AxAy k rPi (3.1) where i is the number of suspension, i=1, . . . ,4,Ax –matrices of rotation from thek-th system to the xyz system about the angleαx along the x‘ axis,Ay –matrices of rotation from the k-th system to the xyz system about the angle αy along the y axis Ax =      1 0 0 0 0 cosαx −sinαx 0 0 sinαx cosαx 0 0 0 0 1      Ay =      cosαy 0 sinαy 0 0 1 0 0 −sinαy 0 cosαy 0 0 0 0 1      and krPi – position vector of point Pi on the chassis in the xkykzk coordinate system krP1 = [ra/2,rw/2,0,1] T krP2 = [ra/2,−rw/2,0,1] T krP3 = [−ra/2,rw/2,0,1] T krP4 = [−ra/2,−rw/2,0,1] T Finally, the value of hi is described by the zPi coordinate of the vector rPi from formula (3.1) hi = zPi i=1, . . . ,4 (3.2) In order to bring the robot chassis plane to the level, the points P1, P2, P3 and P4 need to be moved to the designated values of h1, h2, h3, h4. The displacements hi are the disruptions for the leveling control system of the robot chassis. The control system has to set the proper wheel elevation hi using the linear actuators q i p to bring the robot chassis to the level (αx = 0 and αy =0). Fig. 8. The scheme of the robot chassis orientation angles This requires controlling of only wheel lifting drives qip i.e., forcing the suspension displace- ment of qip by using forces F i p from the actuators. For a mobile robot on four wheels equipped with mechanisms for raising and lowering, the all-wheel task of setting a specific orientation of the chassis for uneven ground can be realized in Modelling and simulation studies on the mobile robot... 155 many ways (Fig. 9) for different settings of the wheel height hik in the permissible range of the stroke hp. In the proposed algorithm of automatic positioning and orientation of the chassis, in order to obtain one solution, it is assumed that the suspensions of three wheels are active and the forth one is the leading wheel with a predetermined height hl (Fig. 10). Fig. 9. A schematic showing examples of robot positions on uneven ground for different settings of the wheel heights hi∗k and h i∗∗ k Fig. 10. The robot on the uneven ground with leading wheel 2 in side and front views. A schematic showing the maximum angles of ground inclination αhx, α l x and α h y, α l y In the work, it is assumed that the leading wheel is wheel 2 (left front). For such a proposed method of levelling, only one solution of searched heights hi will always be obtained for a given position of the body. The height hl of the leading wheel can be set in the range of 0¬hl ¬hp (3.3) For the adopted height hl, the leading wheel possible changes in the orientation angles can be determined by formulas (Fig. 10) αhy =arctan hl ra αly =arctan hp−hl ra αhx =arctan hl rw αlx =arctan hp−hl rw (3.4) The height hl can be dynamically determined depending on the nature of themobile robot ride and the existing uneven ground. In driving the robot on grounds with a positive angle (uphill), in order to increase the possibility of levelling the body, hl should have values close to zero in order to get the angle αly according to (3.4), reaching its maximum value. When driving the robot on the groundwith a negative angle (down),hl value should be close to hp to obtain the angle α h y reaching the maximum value. When driving in the area with an undetermined uneven ground, hl should have a value of hp/2. 156 J. Bałchanowski As a result of the control model with leading wheel 2 (front left) having the fixed height hl while levelling displacement of the body, the values hi should be corrected about the value hl hc1 =h1−hl h c 3 =h3−hl h c 4 =h4−hl (3.5) The corrected values hci will be disruptions to the regulators which control the raising of active wheel 1, 3 and 4 (front right, rear left and right). The regulators of the active wheels will reset the disruption hci to zero. In the structure of the levelling algorithm, there are three active regulators that control the raising and lowering of the active wheels 1, 3 and 4. In Fig. 11, a block algorithm of the platform levelling system of the robot chassis is shown. Fig. 11. A general diagram of the levelling control system The inclinometersmounted on the robot bodymeasure the distortions in formof orientation angles αrx, α r y of twisting of the chassis while driving. These values will be used for calculation from formula (3.5) thedisplacementhci needed to bring the chassis to the level. Theoutput of the regulator wheel is the force F ip which causes the displacement q i p of the actuator which controls raising and lowering of the active wheel i. The proposed control system has a closed structure with three feedback loops controlling the elevation hik. The regulators control the actuators q i p by determination of the active force F ip. The heights h c 1, h c 3, h c 4 of the active wheels 1, 3, 4 relative to the chassis will be controlled in closed loops. In this control system, an external control loop computes the difference between the prescri- bed robot chassis elevation hsi (h s i =0 in the case of levelling) and the actual chassis elevation h c i calculated on the basis of the anglesαrx,α r y read from the chassis location. The computed eleva- tion deviation∆hpasses throughproportional controllerswith constantsK1,K2,K3, generating a signal specifying the required demand for the active lifting force F ip, which is applied to the driving link of the robot. The control system incorporates blocks limiting the generated value of the force F ip to the maximum values (−F max p