Randomized path planning for linkages with closed kinematic chains

We extend randomized path planning algorithms to the case of articulated robots that have closed kinematic chains. This is an important class of problems, which includes applications such as manipulation planning using multiple open-chain manipulators that cooperatively grasp an object and planning for reconfigurable robots in which links might be arranged in a loop to ease manipulation or locomotion. Applications also exist in areas beyond robotics, including computer graphics, computational chemistry, and virtual prototyping. Such applications typically involve high degrees of freedom and a parameterization of the configurations that satisfy closure constraints is usually not available. We show how to implement key primitive operations of randomized path planners for general closed kinematics chains. These primitives include the generation of random free configurations and the generation of local paths. To demonstrate the feasibility of our primitives for general chains, we show their application to recently developed randomized planners and present computed results for high-dimensional problems.

[1]  Lydia E. Kavraki,et al.  Efficient database screening for rational drug design using pharmacophore-constrained conformational search , 1999, RECOMB.

[2]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[3]  Norman I. Badler,et al.  Inverse kinematics positioning using nonlinear programming for highly articulated figures , 1994, TOGS.

[4]  Ronan Boulic,et al.  Hierarchical kinematic behaviors for complex articulated figures , 1996 .

[5]  Jean-Claude Latombe,et al.  Planning motions with intentions , 1994, SIGGRAPH.

[6]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[7]  Nancy M. Amato,et al.  A Kinematics-Based Probabilistic Roadmap Method for Closed Chain Systems , 2001 .

[8]  Tsai-Yen Li,et al.  Assembly maintainability study with motion planning , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[9]  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.

[10]  Arthur G. Erdman,et al.  Mechanism Design : Analysis and Synthesis , 1984 .

[11]  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).

[12]  S. Basu,et al.  COMPUTING ROADMAPS OF SEMI-ALGEBRAIC SETS ON A VARIETY , 1999 .

[13]  Lydia E. Kavraki,et al.  A randomized kinematics‐based approach to pharmacophore‐constrained conformational search and database screening , 2000 .

[14]  S. LaValle.  Rapidly-exploring random trees : a new tool for path planning , 1998 .

[15]  H. Whitney.  Elementary Structure of Real Algebraic Varieties , 1957 .

[16]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

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

[18]  Clément Gosselin,et al.  Workspaces of Planar Parallel Manipulators , 1998 .

[19]  Steven M. LaValle,et al.  Rapidly-Exploring Random Trees: Progress and Prospects , 2000 .

[20]  Tucker R. Balch,et al.  Behavior-based formation control for multirobot teams , 1998, IEEE Trans. Robotics Autom..

[21]  Jean-Claude Latombe,et al.  On multi-arm manipulation planning , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[22]  J. Denavit,et al.  A kinematic notation for lower pair mechanisms based on matrices , 1955 .

[23]  Ferdinand Freudenstein,et al.  Kinematic Synthesis of Linkages , 1965 .

[24]  Craig D. McGray,et al.  The self-reconfiguring robotic molecule: design and control algorithms , 1998 .

[25]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[26]  Craig D. McGray,et al.  The self-reconfiguring robotic molecule , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[27]  Clément Gosselin,et al.  Workspaces of Planar Parallel Manipulators , 1998 .

[28]  Gregory S. Chirikjian,et al.  Useful metrics for modular robot motion planning , 1997, IEEE Trans. Robotics Autom..

[29]  Rachid Alami,et al.  A geometrical approach to planning manipulation tasks. The case of discrete placements and grasps , 1991 .

[30]  Gabriel Taubin,et al.  Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

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

[32]  Mark H. Yim,et al.  Locomotion With A Unit-Modular Reconfigurable Robot , 1995 .

[33]  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).