Adaptive robust stabilization of dynamic nonholonomic chained systems

Abstract

In this article, the stabilization problem is investigated for dynamic nonholonomic systems with unknown inertia parameters and disturbances. First, to facilitate control system design, the nonholonomic kinematic subsystem is transformed into a skew-symmetric form and the properties of the overall systems are discussed. Then, a robust adaptive controller is presented in which adaptive control techniques are used to compensate for the parametric uncertainties and sliding mode control is used to suppress the bounded disturbances. The controller guarantees the outputs of the dynamic subsystem (the inputs to the kinematic subsystem) to track some bounded auxiliary signals which subsequently drive the kinematic subsystem to the origin. In addition, it can also be shown all the signals in the closed loop are bounded. Simulation studies on the control of a unicycle wheeled mobile robot are used to show the effectiveness of the proposed scheme.