Time-varying Control Lyapunov Function Design for Nonlinear Systems Defined on Manifolds

This study deals with a design method of a time-varying control Lyapunov function for nonlinear systems defined on manifolds. We introduce herein a definition of a time-varying control Lyapunov function (time-varying CLF) defined on manifolds, which is a natural extension of the CLF defined on Euclidean space. We also propose a time-varying CLF design method by extending a conventional CLF design method, called the minimum projection method. We demonstrate the effectiveness of the proposed method by an application, namely the dynamical obstacle avoidance control problem. As a result, we can design an analytic global controller for dynamical obstacle avoidance of a mobile robot.