Controllability and motion planning of a multibody Chaplygin's sphere and Chaplygin's top

Abstract

Abstract This paper studies local configuration controllability of multibody systems with nonholonomic constraints. As a nontrivial example of the theory, we consider the dynamics and control of a multibody spherical robot. Internal rotors and sliders are used as the mechanisms for control. Our model is based on equations developed by the second author for certain mechanical systems with nonholonomic constraints, e.g. Chaplygin's sphere and Chaplygin's top in particular, and the multibody framework for unconstrained mechanical systems developed by the first and third authors. Recent methods for determining controllability and path planning for multibody systems with symmetry are extended to treat a class of mechanical systems with nonholonomic constraints. Specific results on the controllability and path planning of the spherical robot model are presented. Copyright © 2007 John Wiley & Sons, Ltd.