Path following control of wheeled mobile robots combining piecewise-affine, linear parameter-varying, and backstepping theories

This thesis presents a novel controller synthesis method for path following of a wheeled mobile robot (WMR). The proposed control method consists of a three-step procedure mixing piecewise-affine (PWA) and linear parameter-varying (LPV) techniques with backstepping. In the first step, two curvature limits and a curvature rate of change limit are defined for the desired path and the nonlinear WMR parameterized path kinematics are approximated by an uncertain piecewise-affine parameter-varying (PWAPV) system, while assuming that the WMR forward velocity is constant. A numerical method is proposed for determining PWA bounds on the uncertainty terms such that the original nonlinear parameter-dependent system is contained in the uncertain PWAPV system. Then, a PWAPV steering control law is designed using a parameter-dependent quadratic Lyapunov function. In the second step, a backstepping-type approach is used to include the vehicle dynamics and design the wheel control torques that guarantee convergence of the WMR forward and rotational velocities to the desired values. Finally, in the third step, the actuator dynamics are included and the input voltages are designed using backstepping. There are four primary advantages to the path following controller synthesis method proposed in this thesis. First, the PWAPV controller synthesis method can be formulated as a convex optimization program subject to a parameterized set of Linear Matrix Inequalities (LMIs), which will be approximated by a finite set of LMIs using LPV theory and then solved efficiently using available software. Second, it includes both a general, non-singular path parameterization and the actuator dynamics. Third, the PWAPV control law can also stabilize the type of nonlinear parameter-dependent system considered here. And fourth, it is a first step toward including hard nonlinearities in the actuator dynamics, which are important PWA characteristics. The effectiveness of the proposed path following control method is demonstrated through numerical simulations.