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2010 8th IEEE International Conference on ThB3.4 Control and Automation Xiamen, China, June 9-11, 2010 Control Methods of Mobile Robot Rough-Terrain Trajectory Tracking Yang. Yi, Graduate Student Member, IEEE, Fu. Mengyin, Zhu. Hao, Xiong. Guangming and Sun. Changsheng Abstract—This paper presents control methods and dynamic feedback linearization paradigm. In [3], the authors simulation experiments of wheeled skid-steering mobile robot applied experimental results to enable Fuzzy Logic modelling trajectory tracking on the rough terrain. According to dynamics of the vehicle-ground interactions in an integrated manner. analysis of the robot, a motion constraint of the robot is put These results illustrate the complexity of modelling forward. To address the issue of uncertain disturbance factors systematically the ground conditions and the necessity of during the robot running on the rough terrain, a practical fuzzy lateral control law is presented, and the globally asymptotically using two variables in identifying the surface properties. In stable of the control law is proven. At the same time, according [4], the authors described relevant rover safety and health to the requirement of the robot motion control, the longitudinal issues and presents an approach to maintaining vehicle safety control law and the sensor pan-tilt control law are also proposed. in a navigational context. Fuzzy logic approaches to Using virtual prototype technology, the mobile robot and the reasoning about safe attitude and traction management are experimental field are established on the ADAMS and presented. In [5], the authors introduced a model-based MATLAB co-simulation platform, and the robot trajectory tracking in the simulation environment is performed. The control for fast autonomous mobile robots on soft soils. This simulation experimental results indicate that the control control strategy takes into account slip and skid effects to methods are robust and effective for the mobile robot running extend the mobility over planar granular soils. Different from on the rough terrain. above researches, which control the robots on the tarmac, grass, sand, gravel or soil, this paper focuses on the motion I. INTRODUCTION control for skid-steering vehicles on the bumpy and rocklike A UTONOMOUS automobile technology is a rapidly developing field, with interest in both academia and industry[1]. Outdoor navigation of autonomous vehicles, terrain, and presents novel and effective trajectory tracking control methods, including the longitudinal, lateral, and sensors pan-tilt control law. Furthermore, based on especially for rough-terrain driving, has already been a new ADAMS&MATLAB co-simulation platform, iRobot research focus. DARPA Grand Challenge and LAGR ATRV2 is modelled and the bumpy off-road terrain is program stand for the top development level in this research constructed, at the same time, trajectory tracking control region. Rough-terrain driving research offers a challenge that methods are validated effectively on this platform. the in-vehicle control system must be able to handle rough and curvy roads, and quickly varying terrain types, such as II. MOBILE ROBOT DYNAMIC ANALYSIS gravel, loose sand, and mud puddles – while stably tracking trajectories between closely spaced hazards. The vehicle must To research on the motion of skid-steering robots, the be able to recover from large disturbances, without 4-wheeled differentially driven robot, which is moving on the intervention[1]. horizontal road normally without longitudinal wheel slippage, Since robotics autonomous navigation tasks in outdoor is analyzed for kinematics and dynamics. As shown in Fig. 1 environment can be effectively performed by skid-steering (a), global Descartes frame and in-vehicle Descartes frame vehicles, these vehicles are being widely used in military are established. In Global frame OXYZ , its origin O is affairs, academia research, space exploration and so on. In [2], sited on the horizontal plane where the robot is running, and a model-based nonlinear controller is designed, following the Z axis is orthogonal to the plane; in in-vehicle frame oxyz , its origin o is located at the robot center of mass, z axis is Manuscript received October 29, 2009. This work was supported in part orthogonal to the chassis of robot, x axis is parallel to the by National Natural Science Foundation of China (NSFC 60773044) and rectilinear translation orientation of the robot and y axis is Certain National Defence Key Research Foundation, The PLA General Armament Department (****0178) . orthogonal to the translation orientation in the plane of the Yang. Yi is with Beijing Institute of Technology, Beijing, 100081, chassis. The robot wheelbase is A and the distance between CHINA. (corresponding author to provide phone: 86-10-6891-4570; fax: 86-10-6891-4570; e-mail: yang_yi@bit.edu.cn). the left and right wheels is B . According to the relation Fu. Mengyin is with Beijing Institute of Technology, Beijing, 100081, between OXYZ and oxyz , the kinematics equation is as CHINA. (e-mail: youngeecn@126.com). Zhu. Hao is with Beijing Institute of Technology, Beijing, 100081, follows. CHINA. Xiong. Guangming is with Beijing Institute of Technology, Beijing, 100081, CHINA. 978-1-4244-5196-8/10/$26.00 ©2010 IEEE 731 ThB3.4 centripetal force f cen , the equation of which is, f cen cos E f y 3 f y 4 f y1 f y 2 (4) JJJK In (4), E is the angle between Coo and y axis. Accordingly, when the centripetal acceleration is considered, assume E | 0 , then the equation of the tractive force of the robot is, mg hma y ma y xco Ps mgA ª § a y · º 2 (a) (b) ° Foutside ( ) Pr «1 ¨ ¸ » Fig. 1. Dynamics analysis of the robot and the motion ° 2 B 2R 4 B « © g Ps ¹ » ° ¬ ¼ constraint about Co ® ma y xco Ps mgA ª § a y · º 2 ° mg hma y ªX º ª x cos T y sin T º ª cos T sin T º ª x º ° Finside ( ) Pr «1 ¨ ¸ » 2 B 2R 4 B « © g Ps ¹ » « » « x sin T y cos T » « sin T ° ¬ ¼ cos T » « y » (1) ¯ ¬Y ¼ ¬ ¼ ¬ ¼¬ ¼ (5) The derivative of equation (1) with respect to time is where h is the height of the robot center of mass, that is the ªX º sin T º ª x yT º ªcos T distance between the robot center of mass and the ground, and « » « sin T « » ¬Y ¼ ¬ cos T » « y xT » ¼¬ ¼ (2) R is the radius of the robot turning [6]. In the paper, as the motion of the robot is instantaneous ªcos T sin T º ª a x º fixed-axis rotation, obviously, the straight line motion of the « sin T cos T » « a » ¬ ¼¬ y¼ robot can be expressed as R f . Co is the instantaneous In the above equations, X , Y , X , Y represent the center of the rotation, and the coordinates of Co can be absolute longitudinal and lateral velocity, and the absolute T ªy x ºT longitudinal and lateral acceleration respectively; T is the expressed as ª xco yco º « . In Fig. 1 (b), the real ¬ ¼ ¬T T»¼ angle between x axis and X axis. x, y , T denote the line arrowheads represent the transfer orientations of the four longitudinal, lateral and angular velocity in in-vehicle frame wheels of the robot, when Co moves within the wheelbase respectively, a x , a y are the longitudinal and lateral range of the robot; the dashed arrowheads stand for the acceleration respectively in in-vehicle frame. transfer orientations of the four wheels of the robot, when Co , 4 4 c that is Co , moves beyond the wheelbase range of the robot. ° ma x ¦ Fxi ¦ f xi ° i 1 i 1 Clearly, if Co moves out of the wheelbase range, the lateral ° 4 ® ma y ¦ f yi transfer orientations of four wheels are the same, as a result, (3) the motion of the robot will be out of control. The motion ° i 1 constraint is as follows, ° J T ( B / 2)(( F F ) ( F F )) M ° x1 x3 x2 x4 r ªX º ¯ « » Let Pr and Ps be the coefficient of longitudinal rolling > sin T cos T l@ «Y » 0 (l A 2 ) (6) «T » resistance and the coefficient of lateral friction respectively. ¬ ¼ The equations of the robot motion can be shown as (3), where J is the moment of inertia of the robot; Fxi denotes the where l is the distance from Co to y axis. According to tractive force produced by the i -th wheel, and composes the outside tractive force Foutside and the inside Finside ; f xi is Fig. 1 (a), it is l Aa y cos E 2 Ps g that can be obtained. Therefore, the constraint of the motion, shown as follow, is the longitudinal resistance of the i -th wheel; f yi is the imperative. lateral resistance of the i -th wheel; M r is the resistive ( x ) 2 R Ps g or (T ) 2 R P s g (7) moment around the center of o . During the turning of the robot, the robot is subject to the In this paper, a description of trajectory space[7] is presented according to the robot’s dynamic analysis, which is 732 ThB3.4 defined as the two-dimensional space of the robot’s turning objects include the longitudinal velocity, the lateral velocity, angular speed T and longitude velocity Vlong , (Vlong x) . and the angles of sensor pan-tilts. As shown in Fig. 3, in an off-road environment, the robot This kind of description is very useful during motion control. uses laser range finder (LRF) with one degree of freedom Consider equation (7): (Vlong (t )) 2 / R P s g or (DOF) pan-tilt (only tilt) to scan bumpy situation of the close front ground, on which the robot is moving, and employs (T (t )) 2 R Ps g , it is easy to get | Vlong (t ) | Ps gR or stereo vision with two DOF pan-tilt to perceive drivable situation of far front ground. With the data accessed from | T (t ) | Ps g / R , then take another constraint into laser and vision sensors, the passable path can be planned, consideration, Vlong TR , now a figure of the robot’s and the velocities of left side and right side of the robot can be controlled to track the path, consequently, the robot off-road V T space (see Fig. 2.) can be obtained. The boundary running is completed. curve in the figure satisfies Vlong (t ) T (t ) Ps g . When the Trajectory Curvature Radius robot’s V T state is in the shadow region, that’s to say Vlong (t ) T (t ) Ps g , the robot is safe, which means the Road Roughness Fuzzy hazardous situation like side slippage won’t occur. As a result, Longitudinal Control equation (7) is crucial for control decision making. Law Sensor System Process Time Velocity Requirement Fig. 4. The longitudinal control law of the robot A. Longitudinal Control Law In this section, a kind of humanoid driving longitudinal control law based on fuzzy logic is proposed. First, the effect factors to the longitudinal velocity are classified. As shown in Fig. 4, these factors include curvature radius of trajectory, road roughness, process time of sensors and speed Fig. 2. The V T space of motion control of the robot. (In this requirement. Based on the four factors and the analysis of figure, Ps 0.49 and g 9.8m / s 2 ) kinematics and dynamics, the longitudinal velocity equation can be given, III. TRAJECTORY TRACKING CONTROL LAWS DESIGN Vlong P cv ( rc ) Prr ( Rrough ) Pt (Tsen ) Pv (Vre )Vre Autonomous mobile robot achieves outdoor navigation by (8) three processes, including the environment information where Vlong is longitude velocity command, Pcv , Prr , Pt acquired by the perception module, the control decision made by the planner module, and the motion plan performed by the and Pv are the weight factors of the curvature radius of motion control module[8]. Consequently, for safe and accurate trajectory rc , road roughness Rrough , processing time of outdoor navigation it is vital to harmonize the three modules performance. In this paper, the emphasis is focused on the sensors Tsen and speed requirement Vre respectively. The decision of control laws of the robot, and these controlled weight factors can vary within [0,1] . B. Lateral Control Law Autonomous vehicle off-road driving is a special control problem because mathematical models are highly complex and can’t be accurately linearized. Fuzzy logic control, however, is robust and efficient for non-linear system control[9], and a well-tested method for dealing with this kind of system, provides good results, and can incorporate human Fig. 3. Off-road driving of the robot procedural knowledge into control algorithms. Also, fuzzy 733 ThB3.4 logic lets us mimic human driving behavior to some extent[10]. indicated in terms of triangle and rectangle membership Therefore, the paper has presented a kind of novel fuzzy functions: lateral control law for the robot off-road running. Part One: the space of ed is divided into LB , LS , MC , In the paper, the lateral control law is designed for the purpose of position tracking by adjusting navigation RS , RB . According to the result of the ed division, the orientation to reduce position error. phenotype rules of the lateral fuzzy control law hold. Part Two: the space of T e is also divided into LB , LS , MC , RS , RB . According to the result of the T e division, the recessive rules of the control law are obtained. It is necessary to explain that the phenotype rules are the basis of the recessive rules, namely each phenotype rule possesses a group of relevant recessive rules. Each phenotype rule has already established their own expectation orientation angle T e , that is to say the robot is expected to run on this orientation angle, T e , and this angle is the very center angle of this group recessive rules. When the center angle, T e , of each group recessive rules is varying, the division of T e of each group recessive rules changes accordingly. Fig. 5. Plots of membership functions of ed and Te . The upper plot All of the control rules can be expressed as continuous stands for P ( ed ) . > 0.1,0.1@ is the range of the center region, functions, f LB , f LS , f MC , f RS , f RB , consequently, the P ( ed ) 1.0 in this region. The lower plot expresses P (Te ) , which global continuity of the control rules is established. is indicated with triangle membership function. In this figure, the The functions, f LB , f LS , f RS , f RB , which express the colorful bands represent the continuous changing course of e . d rule functions of the non center region of ed , are as Definition: When the robot moves toward the trajectory, follows: the orientation angle of the robot is positive, whichever of the two regions, namely left error region and right error region of kTe kt (T e T e ) T ktT tr (9) the tracking position, the robot is in. When the robot moves Ts against the trajectory, the angle is negative. When the robot motion is parallel to the trajectory, the angle is zero. In (9), Te is the expectation tracking-angle in the current In the course of trajectory tracking of the robot, position position error region, and it monotonically increase about ed . error ed and orientation error T e , which are the error values ked ed between the robot and the trajectory, are the inputs of the Te can be given by this equation: Te arctan , lateral controller. First, the error inputs, including the position Vlong error and the orientation error, are pre-processed to improve ked P DL ( ed )k DL PDS ( ed )k DS , where PDL stands for steady precision of the trajectory tracking, and restrain oscillation of that. The error E can be written as the large error region, including LB and RB , membership E E 'E , where E is the result of smoothing filter degree of ed , and P DS represents the small error region, about E , i.e. E i ¦ ei n ; 'E forecasts the error including LS and RS , membership degree of ed . Ttr is i n 1 the estimation of the trajectory-angle rate. kT can be worked produced in the next system sample time, e i out by this equation: kT PT L (T e )kT L PT S (T e )kT S , 'E ¦ kei ei n ( i ! n ) . As a result, e i n 1 where PT L stands for the large error region, including LB i E ¦ (1 kei ) ei n ( i ! n ) , n 4 , kei f ei ( x, Ts ) , Ts and RB , membership degree of Te , and PT S denotes the i n 1 represents system sample time. Second, the error inputs, after small error region, including LS and RS , membership being pre-processed, are fuzzyfication-processed. As shown degree of T e . k DL , kT L and k DS , kT S express the standard in Fig. 5, degree of membership P ( ed ) and P (T e ) are coefficients of the large error region of ed or Te and that of 734 ThB3.4 the small error region of ed or Te respectively. kt is the the robot and the trajectory when the robot just enters the proportional coefficients of the system sample time TS . center region. R | 2O can be worked out by D2 f MC is deduced as follows: geometry, and in addition, the value of D is very small, so the process of approaching trajectory can be represented as When the robot moves into the center region at the 'O orientation of D , the motion state of the robot can be divided 'D D . O into two kinds of situations. Situation Two: When D 0 or D ! T cent . If the motion decision from the planner module were the same as Situation One, the motion will not meet (7). According to the above analysis, the error of tracking can not converge until the adjusted Te makes D be true of Situation One. Therefore, the purpose of control in Situation Two is to decrease Te . Based on the above deduction, f MC is as follow: kt (T e T e ) T ktT tr (10) Ts edT cent where Te , O is the variety range of ed in the O center region, > 0.1m,0@ or >0,0.1m@ . T is the output of (9) Fig. 6. Tracking trajectory of the robot. In this Figure, the red dashdotted line stands for the trajectory tracked by the robot. The and (10), at the same time, T is subject to (7), consequently, different color dotted lines represent the bounderies of the different error regions of ed . T 2 R P g is required by the control rules. s Situation One: Assume that D has decreased into the rule The execution sequence of the control rules is as follows: admission angular range of center region, i.e. First, the phenotype control rules are enabled, namely to 0 d D d T cent , where T cent , which is subject to (7), is the estimate which error region ( LB , LS , MC , RS , RB ) critical angle of center region. To make the robot approach the current ed of the robot belongs to, and to enable the the trajectory smoothly, the planner module requires the robot relevant recessive rules; Second, the relevant recessive rules to move along a certain circle path. As the robot moves along are executed, at the same time, Te is established in time. the circle path in Fig. 6, the values of ed and T e decrease The lateral control law can be shown as Fig. 7. In this synchronously. In Fig. 6, O is the variety range of ed in the figure, the different color concentric circle bands represent center region. D is the angle between the orientation of the different position error ed . From the outermost circle band to the center round, the values of ed is decreasing. The red center round stands for MC of ed , that is the center region of ed . At the center point of the red round, ed 0. According to the above definition, the orientation range of the robot is S , S @ , and the two 0 degree axes of Te stand for the 0 degree orientation of the left and right region of the trajectory respectively, at the same time, S axis and 2 S axis of Te are two common axes of the orientation of 2 the robot in the left and right region of the trajectory. In the upper sub-region of 0 degree axes, the orientation of the Fig. 7. Plot of the lateral control law of the robot. These dasheds stand robot is toward the trajectory, and in the lower sub-region, the for the parts of the performance result of the control law. orientation of the robot is against the trajectory. The result of 735 ThB3.4 the control rules converges to the center of the concentric ed (t )T cent circle bands according to the direction of the arrowheads in T e (t ) (14) Fig. 7. Based on the analysis of the figure, the global O Combine equation (11) and (14), then asymptotic stability of the lateral control law can be e T established, and iff ed 0 & T e 0 , the robot reaches the e d V long O sin( d cent ) . In this region, d e is very small, only equilibrium zero. The proving process is shown as ed Tcent consequently, will also be very small, follow: O e T e T then sin( d cent ) | d cent is derived. Therefore, O O ed Tcent Vlong Tcent e Vlong e , and then d O O d VlongT cent e (t ) e ( t ) exp{ } , where t1 is the time when d d 1 O the robot enters the center region. In other word, ed Fig. 8. Trajectory Tracking of the mobile robot converges to 0 exponentially. Then, according to e T Proof: From the kinematic model (see Fig. 8.), it can be Te ( t ) d cent , T e (t ) converges to 0 . So the origin is the seen that the position error of the robot ed satisfies the O following equation, only equilibrium in the ed T e phase space. Vlong (t ) sin(T e (t )) (11) ed (t ) C. LRF Pan-Tilt and Stereo Vision Pan-Tilt Control a. When the robot is in the non center region, a controller is designed to control the robot’s lateral movement: ked ed (t ) T e (t ) arctan (12) Vlong (t ) Combines equation (11) and (12), then Fig. 9. LRF Pan-Tilt and Stereo Vision Pan-Tilt motion ked ed (t ) Perception is the key to high-speed off-road driving. A ed (t ) Vlong (t )sin(arctan(T e (t ))) 2 vehicle needs to have maximum data coverage on regions in § k e (t ) · its trajectory, but must also sense these regions in time to 1 ¨ ed d ¸ ¨ V (t ) ¸ react to obstacles in its path. In off-road conditions, the © long ¹ vehicle is not guaranteed a traversable path through the (13) environment, thus better sensor coverage provides improved As the sign of ed is always opposite that of ed , ed will safety when traveling. Therefore, it is important for off-road converge to 0 . In equation (11), ed (t ) | Vlong (t ) , and driving to apply active sensing technology. In the paper, the angular control of the sensor pan-tilts assisted in achieving ed (t ) | ked ed (t ) can formed by equation (13). Therefore the active sensing of the robot. Equation (15) represents the the convergence rate of ed is between linear and exponential. relation between the measurement angles, i.e. M c , J c and When the robot is far away from the trajectory, it’s heading J l , of the sensors mounted on the robot and the motion state, S i.e. T e and x , of the robot. for trajectory vertically, then Te , ed (t ) Vlong (t ) , 2 ed (t ) Vlong (t ) ed (t0 ) ; when the robot is near the ªM c º ª kM c 0 0 º ªT e º «J » « »« » «0 kJ c 0 » « x » (15) trajectory, ed | 0 , then in equation (12), « c» «J l » ¬ ¼ «0 ¬ 0 kJ c » « x » ¼¬ ¼ 2 § ke ed ( t ) · 1 ¨ d ¸ ¨ Vlong ( t ) ¸ |1 , ed (t ) ked ed (t ) . Now consider In (15), Mc , J c are the pan angle and tilt angle of the © ¹ equation (12), since ed converges to 0 , according to the stereo vision respectively. Jl is the tilt angle of the LRF. kM c , arctan function, T e converges to 0 . property of kJ c and kJ l are the experimental coefficients between the b. When the robot enters the center region, another measurement angles and the motion state, and they are given controller is designed, by practical experiments of the sensors and connected with 736 ThB3.4 the measurement range requirement of off-road driving. At track two different kinds of trajectories, including the straight the same time, the coordinates of the scanning center are line path, sinusoidal path and circle path. In Test One, the xec xc hc cot J c cos M c , yec yc hc cot J c sin M c ; tracking trajectory consists of the straight line path and sinusoidal path, in which the wavelength of the sinusoidal and xel xl hl cot J l , yel 0 . In the above equations, path is 5S m , the amplitude is 3m . The simulation result of xc , yc , xl , yl , respectively, are the coordinates of the Test One is shown in Fig. 12. In Test Two, the tracking sense center points of the stereo vision and LRF in in-vehicle trajectory contains the straight line path and circle path, in which the radius of the circle path is 5m . The simulation frame. As shown in Fig. 9, hc and hl are their height value, result of Test Two is shown in Fig. 13. to the ground, accordingly. In Fig. 12, which is the same as Fig. 13, sub-figure a is the The angular control and the longitudinal control are simulation data recorded by ADAMS. In sub-figure a, the achieved by PI controllers, and they are the same as the upper-left part is the 3D animation figure of the robot reference [1]. IV. SIMULATION TESTS Fig. 11. The simulation test ground in ADAMS Fig. 10. ATRV2 and its model in ADAMS off-road driving on the simulation platform, in which the white path shows the motion trajectory of the robot. The A. Simulation Platform Build upper-right part is the velocity magnitude figure of the robot. In this section, ADAMS and MATLAB co-simulation It is indicated that the velocity of the robot is adjusted platform is built up. Based on the analysis of the simulation according to the longitudinal control law. In addition, it is result, the design of experiments in real world can become clear that the longitudinal control law, whose change mainly more reasonable and safer. is due to the curvature radius of the path and the road First, based on the characteristics of the robot, ATRV2, the roughness, can assist the lateral control law to track the simulation model is accomplished, as shown in Fig. 10. trajectory more accurately. In Test One, the average velocity Second, according to the test data of the tires of ATRV2, the approximately is 1.2m / s , and in Test Two, the average attribute of the tires and the connection character between the tires and the ground are set. The ADAMS sensor interface velocity approximately is 1.0m / s . The lower-left part is the module can be used to define the motion state sensors figure of the height of the robot mass center during the parameters, which can provide the information of position tracking of the robot. In the figure, the road roughness can be and orientation of the ATRV2 model during its moving. implied. The lower-right part shows that the kinetic energy It is road roughness that affects the dynamic performance magnitude is required by the robot motion in the course of of vehicles, the state of driving and the dynamic load of road. tracking. In Sub-figure b, the angle data of the stereo vision Therefore, the abilities of overcoming the stochastic road pan rotation is indicated. The pan rotation angle varies roughness of vehicles are the key to test the performance of according to the trajectory. Sub-figure c is the error statistic the control law during off-road driving. In the paper, the figure of trajectory tracking. As is shown, the error values simulation terrain model is built up by Gaussian-distributed almost converge to 0 . The factors, which produce these pseudo random number sequence and power spectral density errors, include the roughness and the curvature variation of function. the trajectory. In Fig. 13 (d), the biggest error is yielded at the Assign a certain value to the road roughness and adjust the start point due to the start error between the start point and the parameters of the special points on the road according to the trajectory. Sub-figure d is the trajectory tracking figure, test design, and the simulation test ground is shown in Fig. 11. which contains the objective trajectory and real tracking trajectory. It is obvious that the robot is able to recover from B. Simulation Tests large disturbances, without intervention, and accomplish the In this section, the control law is validated with the tracking accurately. ADAMS&MATLAB co-simulation platform. Based on the position-orientation information provided by V. CONCLUSIONS the simulation sensors and the control law, the lateral, The ADAMS&MATLAB co-simulation platform longitudinal motion of the robot and the sensors pan-tilts facilitates control method design, and dynamics modeling and motion are achieved. The test is designed to make the robot 737 ThB3.4 a a b c b c d d Fig. 12. Plots of the result of Test One (Ts 0.05 s ) Fig. 13. Plots of the result of Test Two (Ts 0.05 s ) analysis of the robot on the rough terrain. According to the [5] D. Lhomme-Desages, Ch. Grand, J-C. Guinot, “Model-based Control of a fast Rover over natural Terrain,” PUBLISHED IN THE practical requirement, the various terrain roughness and PROCEEDINGS OF CLAWAR’06: INT. CONF. ON CLIMBING obstacles can be configured with modifying the relevant AND WALKING ROBOTS, SEPT 2006. parameters of the simulation platform. In the simulation [6] J. Y. 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