Feedback control of nonholonomic systems with multi-generators

This paper is concerned with feedback control algorithm for a class of nonholonomic symmetric affine systems with multigenerators. The controllability Lie algebra of multigenerator systems have essentially different nature from single-generator systems (such as chained form systems), in terms of their controllability structure. This difference prevents us to apply conventional time-varying/discontinuous feedback control methods and a new clue is now required. In this paper., we make a notice that a multigenerator dynamics is partially considered a single-generator system, and each subsystem can be stabilized by any existing controller proposed for chained systems. What we propose here is a switching control algorithm, in that each generator is chosen in sequence and corresponding sub-controllers are applied, where each sub-controller is designed by existing methods for chained systems. The efficiency of the proposed strategy is evaluated via numerical simulations.