An Adaptive Backstepping Trajectory Tracking Control of a Tractor Trailer Wheeled Mobile Robot

The considered Tractor Trailer Wheeled Mobile Robot (TTWMR) is type of Mobile Robot including a master robot – Tractor and slave robots – Trailers which moves along Tractor to track a given desired trajectory. The main difficulties of the stabilization and the tracking control of TTWMR are due to nonlinear and underactuated systems subjected to nonholonomic constraints. In order to overcome these problems, firstly, we develop the model of TTWMR and transform the tracking error model to the triangular form to propose a control law and an adaptive law. Secondly, the varying time state feedback controllers are designed to generate actuator torques by using Backstepping technique and Lyapunov direct’s method, in that these are able to guarantee the stability of the whole system including kinematics and dynamics. In addition, the Babarlat’s lemma is used to prove that the proposed tracking errors converge to the origin and the proposed adaptive law is carried on to tackle unknown parameter problem. The simulations are implemented to demonstrate the effective performances of the proposed adaptive law and the proposed control law.