For robotics navigation, artificial potential functions are commonly utilized. Among these functions, control Lyapunov functions (CLFs) guarantee stability of nonlinear autonomous systems. Particularly, a vehicle such as a two-wheeled mobile robot is a major application for a navigation problem. However, it is difficult to stabilize due to the its nonholonomic constraint. This paper presents a controller design procedure based on a non-smooth CLF. The controller achieves asymptotic stability of the origin of the two-wheeled mobile robot in a complex workspace. For the complex workspace, the multilayer minimum projection method can generate a CLF. The method requires a CLF for an unconstrained system and a smooth mapping. This paper proposes a composite mapping constructed by smooth mappings. The composite mapping is adopted to be combined with a non-smooth CLF. The non-smooth CLF manages theoretical difficulty from the nonholonomic constraint of the two-wheeled mobile robot. The approach is validated in computer simulation. The result demonstrates the effectiveness of the presented method.
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