Multilevel Path Planning for Nonholonomic Robots Using Semiholonomic Subsystems

We present a new and complete multilevel approachfor solving path- planning problems for nonholonomic robots. At the first level, a path is found that disrespects (some of) the nonholonomic constraints. At each of the next levels, a new path is generated by transformation of the path generated at the previous level. The transformation is such that more nonholonomic constraints are respected than at the previous level. At the final level, all nonholonomic constraints are respected. We present two techniques for these transformations. The first, which we call the pick and link technique, repeatedly picks pieces from the given path, and tries to replace them by more feasible ones. The second technique restricts the free configuration space to a "tube" around the given path, and a road map that captures the free-space connectivity within this tube is constructed by the prob abilistic path planner. From this road map we retrieve a new, more feasible path. In the intermediate levels, we plan paths for what we refer to as semiholonomic subsystems. Such systems are obtained by taking real (physical) systems, and removing some of their nonholonomic constraints. In this paper, we apply the scheme to carlike robots pulling trail ers, that is, tractor-trailer robots. In this case, the real system is the tractor-trailer robot, and the ignored constraints in the semiholo nomic subsystems are the kinematic ones on the trailers. These are the constraints of rolling without slipping, on the trailer's wheels. Experimental results are given that illustrate the time efficiency of the resulting planner. In particular, we show that using the multilevel scheme leads to significantly better performance (in computation time and path shape) than direct transformations to feasible paths.

[1]  Philippe Martin,et al.  Flatness and motion planning : the car with n trailers. , 1992 .

[2]  Lydia E. Kavraki,et al.  Probabilistic roadmaps for path planning in high-dimensional configuration spaces , 1996, IEEE Trans. Robotics Autom..

[3]  S. Shankar Sastry,et al.  Steering car-like systems with trailers using sinusoids , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[4]  Jean-Claude Latombe,et al.  Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[5]  Zexiang Li,et al.  Optimal Nonholonomic Motion Planning for a Falling Cat , 1993 .

[6]  Jean-Paul Laumond,et al.  Singularities and Topological Aspects in Nonholonomic Motion Planning , 1993 .

[7]  John F. Canny,et al.  Using skeletons for nonholonomic path planning among obstacles , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[8]  Pierre Ferbach,et al.  A method of progressive constraints for nonholonomic motion planning , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

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

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

[11]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[12]  S. Sastry,et al.  Steering nonholonomic systems using sinusoids , 1990, 29th IEEE Conference on Decision and Control.

[13]  Mark H. Overmars,et al.  Motion Planning for Carlike Robots Using a Probabilistic Learning Approach , 1997, Int. J. Robotics Res..

[14]  Jean-Paul Laumond,et al.  Topological property of trajectories computed from sinusoidal inputs for nonholonomic chained form systems , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[15]  S. LaValle,et al.  Motion Planning , 2008, Springer Handbook of Robotics.

[16]  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.

[17]  R. Murray,et al.  Trajectory generation for the N-trailer problem using Goursat normal form , 1995 .

[18]  H. Sussmann,et al.  Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[19]  Jules Vleugels,et al.  Exact motion planning for tractor-trailer robots , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[20]  S. Sekhavat,et al.  Collision-free motion planning for a nonholonomic mobile robot with trailers , 1994 .

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