Path tracking control for backing-up tractor-trailer system via model predictive control

In order to implement the accurate path tracking control for the backing-up tractor-trailer system with off-axle hitching, a new control framework relying on mixed logical dynamics (MLD) hybrid modeling and model predictive control (MPC) method is presented in this paper. At first, a MLD hybrid model is proposed to describe the open-loop kinematic of the tractor-trailer system. For the resulting MLD model, an extended cost function defined as a quadratic form is addressed, in which the steering angle of the tractor, as well as two errors combining the position and the orientation of the trailer are considered. To minimize the tracking error of the trailer, and smooth the steering angle behavior of the tractor, an equivalent linear quadratic tracking problem is presented. Then, a receding horizon finite-time optimal controller is designed, by employing multi-parametric mixed-integer quadratic programming (mp-MIQP) technique. Finally, the controller performance is evaluated through simulation, and achieves closed-loop system asymptotical stability, accurate tracking performance and constraint fulfillment properties, even under the case of non-smooth tracking reference path.