Path Following of a Wheeled Mobile Robot Combining Piecewise-Affine Synthesis and Backstepping Approaches

This paper presents a novel controller synthesis method for the path following problem of a wheeled mobile robot (WMR). The controller synthesis consists of a three- step procedure mixing piecewise-afflne (PWA) techniques with backstepping ideas. In the first step, a PWA controller is designed for the steering torque while assuming the forward velocity is constant. In the second step, a backstepping-type approach is used to include the forward velocity dynamics and design the forward input force. Finally, in the third step, the actuator dynamics are included using backstepping and the input voltage laws are designed. There are three primary advantages to the synthesis method proposed here. First, it includes both the actuator dynamics and a general, non-singular path parameterization. Second, it is a first step toward including hard nonlinearities in the actuator dynamics, which are PWA characteristics. Third, this technique does not require higher-order derivatives of the states as previously suggested techniques that rely solely on backstepping do. This is of fundamental importance given that those derivatives are typically not measured. The proposed method is demonstrated through a numerical example for the case of a circular path.