Controllability and motion planning of multibody systems with nonholonomic constraints

We consider the dynamics and control of a multibody spherical robot. Internal rotors and sliders are considered as the mechanism for control. Our model is based on equations developed for certain systems with nonholonomic constraints (in particular, systems based on Chaplygin's sphere and Chaplygin's top) and the multibody framework for unconstrained systems developed. The methods for determining controllability and path planning for multibody systems with symmetry that are developed, are extended to treat systems with constraints. Several results on the controllability and path planning of our spherical robot model are presented.

[1]  Francesco Bullo,et al.  A series describing the evolution of mechanical control systems , 1999 .

[2]  P. Krishnaprasad,et al.  Nonholonomic mechanical systems with symmetry , 1996 .

[3]  Anthony M. Bloch,et al.  Local equilibrium controllability of multibody systems controlled via shape change , 2004, IEEE Transactions on Automatic Control.

[4]  A. Bloch,et al.  ON THE DYNAMICS AND CONTROL OF NONHOLONOMIC SYSTEMS ON RIEMANNIAN MANIFOLDS , 1992 .

[5]  Richard M. Murray,et al.  Controllability of simple mechanical control systems , 1997 .

[6]  A. D. Lewis,et al.  Configuration Controllability of Simple Mechanical Control Systems , 1997 .

[7]  Ranjan Mukherjee,et al.  Design considerations in the development of a spherical mobile robot , 2001, SPIE Defense + Commercial Sensing.

[8]  Edward John Routh,et al.  The elementary part of A treatise on the dynamics of a system of rigid bodies , 2009 .

[9]  Andrew D. Lewis,et al.  Simple mechanical control systems with constraints , 2000, IEEE Trans. Autom. Control..

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

[11]  David Schneider.  Non-holonomic Euler-Poincare´ equations and stability in Chaplygin's sphere , 2002 .

[12]  Jinglai Shen,et al.  NONLINEAR CONTROL OF MULTIBODY SYSTEMS WITH SYMMETRIES VIA SHAPE CHANGE , 2002 .

[13]  Richard Cushman.  Routh's sphere , 1997 .

[14]  A. Bloch,et al.  Nonholonomic Mechanics and Control , 2004, IEEE Transactions on Automatic Control.

[15]  R. Mukherjee,et al.  Motion Planning for a Spherical Mobile Robot: Revisiting the Classical Ball-Plate Problem , 2002 .

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