Nonholonomic control based on approximate inversion

Abstract

A variety of simple mechanical systems are known to exploit nonholonomic effects to achieve their goals. Theories describing the operation of such systems have been developed and applied, especially in the study of robotics. Not surprisingly, the inclusion of dynamical effects adds complexity and changes some of the qualitative properties. In this paper we give a complete analysis of the optimal positioning problem for a natural class of dynamical systems whose inertial effects are linear but whose kinematics are those of the standard nonholonomic integrator. Based on these results we develop a suitable modification of the approximate inverse method for solving tracking and stabilization problems.