Lyapunov-Certified Trajectory Tracking for Mobile Robot With a Tail Wheel: Differential-Flatness and Adaptive Backstepping Design

Abstract

This paper proposes a trajectory tracking control law for a mobile robot with two front differential wheels and a tail wheel. The dynamics is given by mimicking Ackerman steering model for the dynamics of position and orientation, associated with the actuator dynamics of the tail wheel's angle modeled by a first-order response with respect to the robot's angular velocity. First we develop a nominal trajectory tracking control law to track a given desired trajectory by applying differential-flatness property of the unicycle model and backstepping approach to handle the actuator dynamics. The effectiveness of the trajectory tracking is demonstrated by conducting hardware robot experiment after performing system identification, which illustrates the superior performance over a benchmark method. The design is also extended to an adaptive tracking control under parameter uncertainty in the tail wheel dynamics through introducing the adaptation law of the parameters, and the performance is demonstrated in numerical simulation.