Function Approximation Technique Based Control for a Class of Nonholonomic Systems

A generic control method is proposed for a class of nonholonomic systems. A nonholonomic system to be controlled is first restructured in form of the combination of a linear system and the variation from the original system. This variation term is treated as a time-varying uncertainty and the stabilization problem for a nonholonomic system is reformulated as an adaptive control problem for linear system with time-varying uncertainty. This adaptive control problem is addressed by applying the function approximation technique. Specifically, the variation is parameterized with a chosen basis function weighted by unknown constant parameters. An update law is defined such that the parameters of the weighted basis function can be automatically determined and the variation between the auxiliary linear system and the original nonholonomic system can then be eliminated. The stability is established for the closed loop system formulated by the nonholonomic system and the constructed controller. The feasibility of the proposed control method is verified under simulations for two typical nonholonomic systems: the unicycle system and the rolling ball system.