2015 Volume 8 Issue 2 Pages 122-130
A locally semiconcave control Lyapunov function exists for every globally asymptotically controllable system; however for nonholonomic systems, the issue of a locally semiconcave generalized homogeneous control Lyapunov function is not investigated. In this paper, the authors propose a locally semiconcave generalized homogeneous control Lyapunov function for Brockett integrator as a canonical form of nonholonomic systems. Moreover, the authors propose an exponentially stabilizing controller for a two-wheeled mobile robot with the function. The effectiveness of the proposed method are confirmed by computer simulation and an experiment, and advantages over previously proposed controllers are confirmed by experiments.