范国梁, 王云宽. 基于几何方法的多智能体群体刚性运动的路径规划[J]. 机器人, 2005, 27(4): 362-366..
FAN Guo-liang, WANG Yun-kuan. Path Planning of Swarm Rigid Motion for Multi Intelligent Agents Based on Geometric Methods. ROBOT, 2005, 27(4): 362-366..
Abstract:Based on geometric mathods, rigid body motion is studied on SE(3). As to the path planning problem of multi intelligent agents with known boundary conditions, virtual structure is adopted. Under the kinetic energy function, the optimal path is deduced on SE(3). The resulting trajectories are smooth and invariable to the interia frame. The mathod can be used widely to the motion planning of multi intelligent agents.
[1] Desai J,Ostrowski J P, Kumar V, et al. Controlling formations of multiple mobile robots[A]. Proceedings of the 1998 IEEE International Conference on Robotics and Automation [C]. USA: IEEE ,1998. 2864-2869. [2] Balch T, Arkin R, Gulag F. Behavior-based formation control for multirobotic teams [J]. IEEE Transactions on Robotics and Automation,1998, 14(6): 926-934. [3] Olfati-Saber R,Murray R M. Distributed cooperative control of multiple vehicle formations using structural potential functions[A]. International Federation of Automatic Control World Congress[C] . Barcelona, Spain: 2002. 454-459. [4] Leonard N E,Fiorelli E. Virtual leaders, artificial potentials, and coordinated control of groups[A]. Proceedings of the 40th IEEE Conference on Decision and Control [C]. USA: IEEE, 2001. 2968-2973. [5] Park F C,Ravani B. Bezier curves on Riemannian manifolds and Lie groups with kinematics application[J]. American Society of Mechanical Engineers Journal of Mechanical Design, 1995, 17 (1): 36-40. [6] Jutler B. Visualization of moving objects using dual quaternion curves[J]. Computers and Graphics, 1994,18(3): 315-326. [7] Srinivasan L,Ge Q J. Fine tuning of rational B-spline motions[J]. American Society of Mechanical Engineers Journal of Mechanical Design, 1998, 120(1): 46-51. [8] Carmo M P. Riemannian Geometry[M]. Boston: Birkhauser,1992. [9] Murray R M, Li Z, Sastry S. A Mathematical Introduction to Robotic Manipulation[M]. Boca Raton: Chemical Rubber Company Press,1994. [10] Crouch P, Leite F S. The dynamic interpolation problem: on Riemannian manifolds, Lie group, and symmetric spaces[J]. Dynamic Control Systems, 1995, 1(2): 177-202. [11] 蔡自兴.机器人学[M].北京:清华大学出版社,2000. [12] 日本机器人学会.机器人技术手册[M].北京:科学出版社,1996.