A hybrid backstepping-like nonlinear control of a robot-trailer system

Abstract

The authors present a nonlinear controller to stabilize an autonomous wheeled robot and trailer system. A dynamic model based on robot-trailer kinematics is chosen for the ease of design. An iterative approach similar to backstepping is used to obtain the control input. In a manner reminiscent of feedback linearization, nonlinearities are cancelled at each step to obtain an equivalent linear system. The proposed method is significantly different from the usual integrator backstepping method because no signal differentiation is required. However, it is also different from conventional feedback linearization because no coordinate transformation is required. This hybrid method is essentially a selective amalgamation of the two methods. Whenever linear control gains are used in the design, they are tuned by the LQR method. In contrast to known state-of-the-art approaches, the proposed method stabilizes the system in both the forward and reverse motion directions, without modeling modifications. The proposed controller yields good tracking performance over a wide variety of initial conditions, both in simulation and experiments.