Piecewise-affine parameter-varying control of wheeled mobile robots

This paper defines a new class of systems and presents a novel controller synthesis method. This new methodology is motivated by and applied to the problem of path following of a wheeled mobile robot (WMR). The new class of systems proposed in this paper is called piecewise-afflne parameter- varying (PWAPV), which is a combination of piecewise-afflne (PWA) and linear parameter-varying (LPV) systems. The synthesis of PWAPV controllers for uncertain PWAPV systems can be cast as a parameterized set of matrix inequalities, which can be approximated by a finite set of LMIs and solved efficiently using available software. As an application, actuator input voltage laws are designed to guarantee that a WMR follows a desired path that is parameterized by a time-varying curvature. Simulation results show the effectiveness of the new control law.