Motion/force tracking control of nonholonomic mechanical systems via combining cascaded design and backstepping

This paper considers motion/force tracking control of a class of Lagrange mechanical systems with classical nonholonomic constraints. A tracking control method is proposed by combining cascaded methods and backstepping techniques. The main results of this paper include three parts: (1) error dynamics between the kinematic system and the desired paths are transformed into a cascaded system consisting of two subsystems and an interconnection function; (2) under the framework of cascaded methods, virtual controllers for the subsystems are designed to stabilize the error dynamics; (3) the tracking controller is designed for the overall mechanical systems using backstepping techniques.