Motion planning for cooperating mobile manipulators

We address the problem of motion planning for nonholonomic cooperating mobile robots manipulating and transporting objects while holding them in a stable grasp. We present a general approach for solving optimal control problems based on the calculus of variations. We specialize this approach to solving the motion planning problem and obtaining trajectories and actuator forces/torques for any maneuver in the presence of obstacles. The approach allows geometric constraints such as joint limits, kinematic constraints such as nonholonomic velocity constraints, and dynamic constraints such as frictional constraints and contact force constraints to be incorporated into the planning scheme. The application of this method is illustrated by computing motion plans for several examples and these motions plans are implemented on an experimental testbed.

[1]  L. Dubins.  On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[2]  D. Jacobson,et al.  A transformation technique for optimal control problems with a state variable inequality constraint , 1969 .

[3]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[4]  J. Meditch,et al.  Applied optimal control , 1972, IEEE Transactions on Automatic Control.

[5]  R. Brockett.  Control Theory and Singular Riemannian Geometry , 1982 .

[6]  T. Flash,et al.  The coordination of arm movements: an experimentally confirmed mathematical model , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[7]  L. Shepp,et al.  OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS , 1990 .

[8]  Claude Samson,et al.  Feedback control of a nonholonomic wheeled cart in Cartesian space , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[9]  J. Gregory,et al.  Constrained optimization in the calculus of variations and optimal control theory , 1992 .

[10]  S. Shankar Sastry,et al.  Stabilization of trajectories for systems with nonholonomic constraints , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[11]  S. Sastry,et al.  Trajectory generation for the N-trailer problem using Goursat normal form , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[12]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[13]  Vijay Kumar,et al.  Optimal trajectories and force distribution for cooperating arms , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[14]  Zvi Shiller,et al.  Time-energy optimal control of articulated systems with geometric path constraints , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[15]  Richard M. Murray,et al.  A motion planner for nonholonomic mobile robots , 1994, IEEE Trans. Robotics Autom..

[16]  Vijay Kumar,et al.  Two-arm manipulation: what can we learn by studying humans? , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[17]  S. Shankar Sastry,et al.  Steering Three-Input Nonholonomic Systems: The Fire Truck Example , 1995, Int. J. Robotics Res..

[18]  Milos Zefran,et al.  Optimal control of systems with unilateral constraints , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[19]  Vijay Kumar,et al.  Motion planning for multiple mobile manipulators , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[20]  Oussama Khatib,et al.  Coordination and decentralized cooperation of multiple mobile manipulators , 1996, J. Field Robotics.

[21]  Vijay R. Kumar,et al.  Continuous methods for motion planning , 1996 .

[22]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[23]  Vijay R. Kumar,et al.  Motion planning and control of cooperative robotic systems , 1998 .

[24]  J. March.  Introduction to the Calculus of Variations , 1999 .

[25]  Vijay Kumar,et al.  Optimal Gait Selection for Nonholonomic Locomotion Systems , 2000, Int. J. Robotics Res..