Point stabilization control of a car-like mobil robot in hierarchical skew symmetry chained form

Abstract

Nonholonomic properties most commonly arise in mechanical systems where the non-integrable constraints are imposed on the motions, i.e. the constraints cannot be written as the time derivatives of some function of the generalized coordinates. Classical examples of nonholonomic control systems include sledges or knife-edge systems that slide on the plane, simple wheels rolling without slipping on a plane and spheres rolling without slipping on a plane. In this paper, we consider a hierarchical controller to point stabilization problem for the so-called skew symmetry chained form nonholonomic car-like mobile robot. Based on the diffeomorphic input-state transformations, we introduce a set of sufficient conditions for determining if a nonlinear kinematic model can be converted to a skew symmetry chained form. Next, a hierarchal controller is developed to incorporate the kinematic skew symmetric form into the dynamic simplified model to achieve global asymptotically stability. In hierarchical controller, we use the adaptive control features to overcome the uncertain dynamic parameters and use the sliding mode techniques to attenuate the effect of external disturbances. Finally, the efficacy of the proposed point stabilization algorithm is illustrated with car-like mobile robots. Simulation results are utilized to illustrate the effectiveness of the proposed control algorithm.