Trajectory tracking of a tractor-trailer robot using model predictive control

The tractor-trailer system is a wheeled mobile robot (WMR), including one wheeled unit named tractor that is equipped with actuators and one or some wheeled units named trailer that are connected to each other with a passive joint. As a special case, in this paper, the system locomotion is by tractor, and trailer is completely passive. In this paper, we develop the kinematic model of tractor-trailer; so the inputs of system are supposed to be tractor angular velocity and trailer linear velocity. Because of pure rolling condition between wheel and ground surface, we encounter a nonholonomic system. In this paper Model Predictive Control (MPC) is used in control designing of Tractor-Trailer for the first time and the goal is trajectory tracking of trailer position. First, the kinematic equations of tractor-trailer are developed. Then a feasible reference geometrical path is considered. After linearizing the system equations around reference path and using MPC that is an optimal control based method, a tracking controller is designed that minimizes a predefined cost function. Considering actuator saturation in system inputs, we solve a constrained optimization problem using numerical methods. The controller designed in this paper, will be compared against classic controller PID and its better performance is presented. Finally, the effectiveness and robustness of controller against disturbances and parameter uncertainties is proved using MATLAB results.