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1 34 7 Vol. 34, No ACTA AUTOMATICA SINICA July, , ,, δ,,, δ,.,,,.,,, TP24 Wheel-terrain Geometric Contact Angle Estimation of All-terrain Mobile Robots SONG Xiao-Kang 1, 2 WANG Yue-Chao 1 TAN Da-Long 1 WU Zhen-Wei 1 Abstract A real-time estimate method of wheel-terrain geometric contact angle for all-terrain mobile robots is studied in this paper. For a six-wheeled all-terrain mobile robot with a passive-compliant mechanism, the wheel-terrain geometric contact angle δ is defined to reflect the effects of terrain profile and the contact relationship between the driven wheel and the terrain. The robot is treated as a series-parallel multi-rigid body system. The kinematical model of the robot body considering the unevenness of the terrain and wheel slips is developed based on closed velocity chain. Since δ is hardly measured directly by on-board sensors, this paper proposes a model-based estimate method by using common on-board sensor data to on-line estimate the contact angle δ. The Kalman filter is used to fuse noisy sensor data. The experimental results demonstrate the availability and effectiveness of this method. Key words All-terrain mobile robots, wheel-terrain geometric contact angle, kinematics modeling, Kalman filter,.,, [1 3] [4] [5 6].,,,,., [7]., [8],.,,, Received April 10, 2007; in revised form December 5, 2007 ( ) Supported by National Natural Science Foundation of China ( ) Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang Graduate University, Chinese Academy of Sciences, Beijing DOI: /SP.J , : 1), ; 2),,.,,,.,,.,,. [9],,,,,.,,,,,. Tarokh [10] Rocky7,

2 7 : 779 (Contact angle),,,,. Iagnemma [11] (Vehicle-ground contact angle),,., Iagnemma,.,.,,,. (Jet Propulsion Laboratory, JPL) Sohl [12],, ; Shibly [13],.,,, Iagnemma [14 15],,.,,,,,,,, Iagnemma,,.,.,,,,.,,.,,,,. Fig A six-wheeled all-terrain mobile robot,, , R ; D ; B 1 B 2 ; O 1 O 4 2 4, ; S 1 S 4, S 3 S 6 ; A i (i = 1, 2,, 6),. D z β 1 β 2,,, β 1 = β, β 2 = β; B1 B2 z ρ 1 ρ 2. β ρ 1 ρ 2,, β = ρ 1 = ρ 2 = 0;,. θ i, i = 1,, 6; ψ j, j = 1, 3, 4, 6; 2,. D-H. 1 ( 1 ). Fig. 2 2 The robot s coordinate system on the right side

3 C i, i = 1,, 6, 3. C i z, x, y. A i,. z Ai z Ci δ i., C i z Ai, z Ai z Ci, δ i (t t) i C i (t t), t i C i (t), ξ i, rθ i, t rθ i + ξ i, η i ζ i. Fig. 3 3 C i Coordinate frame of wheel-terrain contact point Fig. 4 C i Wheel slips,. R W u = [x y z φ x φ y φ z ] T,, [x y z] T, φ x φ y φ z.,., C i R.,,,. u β ρ ( ρ 1 ρ 2 ) ψ j δ i, θ i ξ i η ζ i,,,, ẊX +D i φ+d 1i β+d2i ρ = M i rθ i +M iξi +N i η i (1),, ; ẊX = [ẋ ẏ ż] T ; φ = [ φ x φy φz ] T ; r ; D i = 0 r z r y, r z 0 r x r y r x 0 ; D 1i = [r z 0 r x ] T,, β ; D 2i = [r ρz 0 r ρx ] T,, ρ ; M i N i 3 1, i ξ i η i, M T i M i = N T i N i = 1 (2) M T i N i = 0 (3),, R, R,, i φ + C 1i β + C2i ρ + C 3j ψ j + C 4i δi = O i ζi (4) (4), R, R ; φ = [ φ x φy φz ] T ; β ρ ; ψ j ; ζi ; C 1i C 2i C 3j C 4i O i β ρ ψ j δ i ζ i R, C T 1iC 1i = C T 2iC 2i = 1 (5)

4 7 : 781 C T 3jC 3j = C T 4iC 4i = O T i O i = 1 (6) O T i C 4i = C T 3jC 4i = C T 3jC 1i = 0 (7) D-H, (1) (4),, (1) (4),. 2 δ i i C i z Ci i A i z Ai,. δ i = 0. δ i,. δ i,. δ i,., δ i,,,, 1 ( ). 1, (4) δ 1 = C T φ 41 C T 41C 11 β = cos(β) sin(ψ 1 ) φ x cos(ψ 1 ) φ y + sin(β) sin(ψ 1 ) φ z + cos(ψ 1 ) β (8) δ 1 (t) = δ 1 (t 1) + δ 1 t = δ 1 (t 1) C T 41 φ t C T 41C 11 β t = δ 1 (t 1) + cos(β) sin(ψ 1 ) t φ x cos(ψ 1 ) t φ y + sin(β) sin(ψ 1 ) φ z t+ cos(ψ 1 ) 1 β x = [δ 1 φx φy φz β ρ] T z = [ φ x φy φz β ρ] T (8) (9) (10) (11) { x k = Ax k 1 + w k 1 z k = Hx k + v k (12), w v,, : P (w) N(0, QQ), P (v) N(0, RR),, δ i Kalman {ˆx k = Aˆx k 1 ˆP k = A P (13) k A T + QQ x k = ˆx k + K k (z k Hˆx k ) K k = ˆP k H T (H ˆP k H T + RR) 1 (14) P = (I K k H) ˆP k,,,,. 3, δ i., φ xm φ ym φ zm, β ρ 1 ρ 2, ψ j θ i, β ρ 1 ρ 2. : 1) ; 2) 30 cm.,, , C i z Ai,., cm.,,., C i z Ci, A i z Ai,,., ;.., [11],

5 自 782 动化学报 34 卷关系, 不仅与地形表面的几何变化有关, 还与机器人本体的姿态有关, 如当机器人处于同一个斜面上时, 轮地几何接触角为 0, 但地形坡度并不为 0, 因此两者之间并不完全相同. 图6 机器人在平坦硬质地面直线前进时右前轮轮地几何接触角的变化曲线 Fig. 6 The curve of estimated wheel-terrain contact angle of right-front wheel when moving straightly on a flat terrain 图 5 机器人 Fig. 5 The robot 图 7 机器人 Fig. 7 The robot 4 结论图8 机器人跨越高度为 30 cm 的台阶形障碍物时右前轮轮地几何接触角的变化曲线 Fig. 8 The curve of estimated wheel-terrain contact angle of right-front wheel when moving straightly on a uneven terrain with a sidestep-shaped obstacle of about 30 cm height 全地形移动机器人的精确运动控制是一个具有挑战性的问题, 与一般平坦地形下的移动机器人具有很大差异, 地形复杂性所带来的影响不可忽略. 本文以一个六轮全地形移动机器人为对象, 从车轮与地形相互作用的角度出发, 将机器人看作为一个串并联多刚体系统, 考虑车轮与地形的几何接触关系以及车轮平面滑移, 基于速度闭链理论建立了机器人整体运动学模型. 在机器人运动学模型中, 通过轮地几何接触角 δ 来反映地形不平坦给机器人运动带来的影响, 并针对 δ 难以直接测量的问题提出了一种基于模型的卡尔曼滤波估计方法, 对轮地几何接触角进行实时估计. 但当地形的几何轮廓发生突然变化时, 轮地几何接触角会随之发生突变, 此时卡尔曼滤波算法估计的值相对于真实值会有一定滞后. 通过估计轮地几何接触角, 可反映出驱动轮与地形之间的几何接触关系, 为机器人运动学的精确求解和车轮滑移分析奠定了基础, 有利于进一

6 7 : 783. References 1 Volpe R, Balaram J, Ohm T, Ivlev R. The rocky 7 Mars rover prototype. In: Proceedings of the 1996 IEEE/RSJ International Conference on Intelligent Robots and Systems. Pasadena, USA: IEEE, Mishkin A H, Morrison J C, Nguyen T T, Stone H W, Cooper B K, Wilcox B H. Experiences with operations and autonomy of the Mars pathfinder microrover. In: Proceedings of the 1998 IEEE Aerospace Conference. Snowmass at Aspen, USA: IEEE, Schenker P S, Huntsberger T L, Pirjanian P, Baumgartner E T, Tunstel E. Planetary rover developments supporting Mars exploration, sample return and future human-robotic colonization. Autonomous Robots, 2003, 14(2-3): Weisbin C R, Blitch J, Lavery D, Krotkov E, Shoemaker C, Matthies L. Miniature robots for space and military missions. IEEE Robotics and Automation Magazine, 1999, 6(3): Astrand B, Baerveldt A J. An agriculture mobile robot with vision-based perception for mechanical weed control. Autonomous Robots, 2002, 13(1): Hellstrom T, Johansson T, Ringdahl O. Development of an autonomous forest machine for path tracking. In: Proceedings of the 4th International Conference on Field and Service Robotics. Berlin, Germany: Springer-Verlag, Song Xiao-Kang, Wang Yue-Chao, Tan Da-Long, Wu Zhen- Wei. Study on modeling and control of all-terrain mobile robots. Robot, 2007, 29(5): (,,,.., 2007, 29(5): ) 8 Ellery A. Environment-robot interaction the basis for mobility in planetary micro-rovers. Robotics and Autonomous Systems, 2005, 51(1): Wang Zuo-Wei, Liang Bin,Wu Hong-Xin. Kinematical modeling and analysis of six-wheel lunar rover. Journal of Astronautics, 2003, 24(5): (,,.., 2003, 24(5): ) 10 Tarokh M, McDermott G J. Kinematics modeling and analyses of articulated rovers. IEEE Transactions on Robotics, 2005, 21(4): Iagnemma K, Dubowsky S. Vehicle-ground contact angle estimation with application to mobile robot traction. In: Proceedings of the 7th International Conference on Advances on Robot Kinematics. Portoroz, Slovenia: IEEE, Sohl G, Jain A. Wheel-terrain contact modeling in the roams planetary rover simulation. In: Proceedings of ASME International Design Engineering Technical Conference. Long Beach, USA: DETC, Shibly H, Iagnemma K, Dubowsky S. An equivalent soil mechanics formulation for rigid wheels in deformable terrain, with application to planetary exploration rovers. Journal of Terramechanics, 2005, 42(1): Iagnemma K, Shibly H, Dubowsky S. On-line terrain estimation for planetary rovers. In: Proceedings of the 2002 IEEE International Conference on Robotics and Automation. Washington D. C., USA: IEEE, Iagnemma K, Kang S, Shibly H, Dubowsky S. Online terrain parameter estimation for wheeled mobile robots with application to planetary rovers. IEEE Transactions on Robotics, 2004, 20(5): songxiaokang@sia.cn (SONG Xiao-Kang Ph. D. candidate at Shenyang Institute of Automation, Chinese Academy of Sciences. His main research interest is all-terrain mobile robots. Corresponding author of this paper.).. ycwang@sia.cn (WANG Yue-Chao Professor at Shenyang Institute of Automation, Chinese Academy of Sciences. His main research interest is intelligent robots.).. dltan@sia.cn (TAN Da-Long Professor at Shenyang Institute of Automation, Chinese Academy of Sciences. His research interest covers intelligent control of robots and multi-robot systems.).. wuzw@sia.cn (WU Zhen-Wei Professor at Shenyang Institute of Automation, Chinese Academy of Sciences. His main research interest is robot control.)

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,,.,, : 1),,,,, 2),,,,, 3),,,,,,,,,, [6].,,, ( ),, [9], : 1), 2),,,,, 3),,, 2.,, [10].,,,,,,,,, [11]. 2.1,, [12],, ;, ; Fig. 1 1 Granular hier 36 7 Vol. 36, No. 7 2010 7 ACTA AUTOMATICA SINICA July, 2010 1, 2 1, 2, 3 1, 2,,,,,,, DOI,,, 10.3724/SP.J.1004.2010.00923 Distributed Simulation System Hierarchical Design Model Based on Quotient Space