Planning motions of rolling surfaces

Rolling between rigid surfaces in space is a well-known nonholonomic system, whose mathematical model has some interesting features that make it a paradigm for the study of some very general systems. It also turns out that the nonholonomic features of this system can be exploited in practical devices with some appeal for engineers. However, in order to achieve all potential benefits, a greater understanding of these rather complex systems and more practical algorithms for planning and controlling their motions are necessary. In this paper, we will consider some geometric and control aspects of the problem of arbitrarily displacing and reorienting a body which rolls without slipping among other bodies.

[1]  Roger W. Brockett.  On the rectification of vibratory motion , 1989 .

[2]  C. Samson.  Control of chained systems application to path following and time-varying point-stabilization of mobile robots , 1995, IEEE Trans. Autom. Control..

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

[4]  Henry Hermes,et al.  Distributions and the Lie algebras their bases can generate , 1989 .

[5]  Y. Nakamura,et al.  Space multibody structure connected with free joints and its shape control , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[6]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[7]  Richard M. Murray,et al.  Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems , 1994, Math. Control. Signals Syst..

[8]  D. Normand-Cyrot,et al.  An introduction to motion planning under multirate digital control , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[9]  Gerardo Lafferriere,et al.  Motion planning for controllable systems without drift , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[10]  G. Jacob.  MOTION PLANNING BY PIECEWISE CONSTANT OR POLYNOMIAL INPUTS , 1992 .

[11]  Joel W. Burdick,et al.  Nonholonomic mechanics and locomotion: the snakeboard example , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[12]  M. Fliess,et al.  Flatness, motion planning and trailer systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[13]  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.

[14]  Velimir Jurdjevic.  The geometry of the plate-ball problem , 1993 .

[15]  Ole Jakob Sørdalen,et al.  Conversion of the kinematics of a car with n trailers into a chained form , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[16]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

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

[18]  L. Dai,et al.  Non-holonomic Kinematics and the Role of Elliptic Functions in Constructive Controllability , 1993 .

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

[20]  David J. Montana,et al.  The Kinematics of Contact and Grasp , 1988, Int. J. Robotics Res..

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

[22]  Woojin Chung,et al.  Design of a nonholonomic manipulator , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[23]  O. J. Sørdalen,et al.  Exponential stabilization of nonholonomic chained systems , 1995, IEEE Trans. Autom. Control..

[24]  Antonio Bicchi,et al.  Dexterous manipulation through rolling , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[25]  Zexiang Li,et al.  Motion of two rigid bodies with rolling constraint , 1990, IEEE Trans. Robotics Autom..