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.