Probabilistic motion planning for parallel mechanisms

Despite the increasing interest in parallel mechanisms during the last years, few researchers have addressed the motion planning problem for such systems. The few existing techniques lie in a representation of the workspace of the mechanism (or its boundary). However, obtaining this representation is generally too difficult, only partial solutions exist for particular cases. In this paper we propose a general approach based on probabilistic motion planning techniques. This approach does not need any modeling of the robot's workspace. It combines random sampling techniques with simple but general geometric algorithms that guide the sampling toward feasible configurations satisfying the closure constraints of the parallel mechanism. The efficiency and the generality of the method are demonstrated onto several complex mechanisms mode up with serial or parallel associations of Stewart platforms, or created with several redundant robots manipulating an object.

[1]  Lydia E. Kavraki,et al.  A probabilistic roadmap approach for systems with closed kinematic chains , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[2]  J.-P. Laumond,et al.  Move3D: A generic platform for path planning , 2001, Proceedings of the 2001 IEEE International Symposium on Assembly and Task Planning (ISATP2001). Assembly and Disassembly in the Twenty-first Century. (Cat. No.01TH8560).

[3]  D. Stewart,et al.  A platform with 6 degrees of freedom , 1966 .

[4]  D. Stewart.  A Platform with Six Degrees of Freedom , 1965 .

[5]  Jean-Claude Latombe,et al.  A Single-Query Bi-Directional Probabilistic Roadmap Planner with Lazy Collision Checking , 2001, ISRR.

[6]  Jean-Pierre Merlet,et al.  Parallel Robots: Open Problems , 2000 .

[7]  Dinesh Manocha,et al.  Spherical shell: a higher order bounding volume for fast proximity queries , 1998 .

[8]  Jian Wang,et al.  Workspace evaluation of Stewart platforms , 1994, Adv. Robotics.

[9]  Thierry Siméon,et al.  A random loop generator for planning the motions of closed kinematic chains using PRM methods , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[10]  Thierry Siméon,et al.  Visibility-based probabilistic roadmaps for motion planning , 2000, Adv. Robotics.

[11]  Steven M. LaValle,et al.  RRT-connect: An efficient approach to single-query path planning , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[12]  Bhaskar Dasgupta,et al.  The Stewart platform manipulator: a review , 2000 .

[13]  Clément Gosselin,et al.  Stiffness mapping for parallel manipulators , 1990, IEEE Trans. Robotics Autom..

[14]  A. Sali,et al.  Modeling of loops in protein structures , 2000, Protein science : a publication of the Protein Society.

[15]  Bhaskar Dasgupta,et al.  Singularity-free path planning for the Stewart platform manipulator , 1998 .

[16]  Sylvie Charentus.  Modélisation et commande d'un robot manipulateur redondant composé de plusieurs plateformes de Stewart , 1990 .

[17]  Jean-Pierre Merlet,et al.  Determination of the orientation workspace of parallel manipulators , 1995, J. Intell. Robotic Syst..

[18]  Nancy M. Amato,et al.  MAPRM: a probabilistic roadmap planner with sampling on the medial axis of the free space , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

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

[20]  Daniel Vallejo,et al.  OBPRM: an obstacle-based PRM for 3D workspaces , 1998 .

[21]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[22]  Lydia E. Kavraki,et al.  Path planning using lazy PRM , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[23]  Jean-Pierre Merlet.  Manipulateurs paralleles, 6eme partie : determination des espaces de travail en orientation , 1993 .

[24]  Mark H. Overmars,et al.  The Gaussian sampling strategy for probabilistic roadmap planners , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

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