Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems

We introduce the notion of kinematic controllability for second-order underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collision-free trajectories between zero velocity states can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by time-optimal time scaling. While this approach is well known for fully actuated systems, until now there has been no way to apply it to underactuated dynamic systems. The results in this paper form the basis for efficient collision-free trajectory planning for a class of underactuated mechanical systems including manipulators and vehicles in space and underwater environments.

[1]  I. Holopainen.  Riemannian Geometry , 1927, Nature.

[2]  Kang G. Shin,et al.  Minimum-time control of robotic manipulators with geometric path constraints , 1985 .

[3]  J. Bobrow,et al.  Time-Optimal Control of Robotic Manipulators Along Specified Paths , 1985 .

[4]  Friedrich Pfeiffer,et al.  A concept for manipulator trajectory planning , 1987, IEEE J. Robotics Autom..

[5]  H. Sussmann.  A general theorem on local controllability , 1987 .

[6]  Jean-Jacques E. Slotine,et al.  Improving the Efficiency of Time-Optimal Path-Following Algorithms , 1988, 1988 American Control Conference.

[7]  John F. Canny,et al.  An exact algorithm for kinodynamic planning in the plane , 1990, SCG '90.

[8]  Steven Dubowsky,et al.  On computing the global time-optimal motions of robotic manipulators in the presence of obstacles , 1991, IEEE Trans. Robotics Autom..

[9]  John F. Canny,et al.  An exact algorithm for kinodynamic planning in the plane , 1991, Discret. Comput. Geom..

[10]  Z. Shiller,et al.  Computation of Path Constrained Time Optimal Motions With Dynamic Singularities , 1992 .

[11]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

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

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

[14]  Richard M. Murray,et al.  Geometric phases and robotic locomotion , 1995, J. Field Robotics.

[15]  Hongyan Wang,et al.  Non-Uniform Discretization Approximations for Kinodynamic Motion Planning and its Applications , 1996 .

[16]  Jean-Paul Laumond,et al.  Algorithms for Robotic Motion and Manipulation , 1997 .

[17]  Naoji Shiroma,et al.  Motion planning for a 3-DOF robot with a passive joint , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[18]  Richard M. Murray,et al.  Configuration Controllability of Simple Mechanical Control Systems , 1997, SIAM Rev..

[19]  A. D. Lewis,et al.  When is a mechanical control system kinematic? , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[20]  Steven M. LaValle,et al.  Randomized Kinodynamic Planning , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

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

[22]  Naoji Shiroma,et al.  Collision-Free Trajectory Planning for a 3-DoF Robot with a Passive Joint , 2000, Int. J. Robotics Res..

[23]  Naomi Ehrich Leonard,et al.  Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups , 2000, IEEE Trans. Autom. Control..

[24]  Jean-Claude Latombe,et al.  Randomized Kinodynamic Motion Planning with Moving Obstacles , 2002, Int. J. Robotics Res..