Constrained model predictive control for backing-up tractor-trailer system

In this paper, Lyapunov theory is used firstly to analyze the motion characteristics of the tractor-trailer system. Then, a novel mixed logical dynamics (MLD) model is proposed to describe the kinematic of the tractor-trailer system. For the resulting MLD model, an extended cost function with 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. In view of this problem, an explicit model predictive control (MPC) controller is designed, by employing the multi-parametric mixed-integer quadratic programming (mp-MIQP) technique. Finally, the controller performance is evaluated through simulation, and achieves the asymptotical stability, accurate tracking feature and the constraint fulfillment properties, even in the case of the nonsmooth tracking reference path.