Feedback Stabilization of Nonholonomic Drift-Free Systems Using Adaptive Integral Sliding Mode Control

This article presents a novel stabilizing control algorithm for nonholonomic drift-free systems. The control algorithm is based on adaptive integral sliding mode control technique. In order to utilize the benefit of integral sliding mode control, extended Lie bracket system is used as a nominal system which can easily be asymptotically stabilized. Firstly the original nonholonomic drift-free system is augmented by adding its missing Lie brackets and some unknown adaptive parameters. Secondly the controller and the adaptive laws are designed in such a way that the behaviour of the augmented system is similar to that of the nominal system on the sliding surface and the addition of missing Lie brackets in the original system can be compensated adaptively. The proposed method is applied on two nonholonomic drift-free systems including the Brockett’s system and the hopping robot in flight phase. The controllability Lie Algebra of the Brockett’s system has Lie brackets of depth one, whereas the hopping robot model in flight phase contains Lie brackets of depth one and two. The effectiveness of the proposed technique is verified through simulation studies.