Min-Max Model Predictive Controller for Trajectory Tracking of a Wheeled Mobile Robot with Slipping Effects
A min-max model predictive controller is developed in this paper for tracking control of wheeled mobile robots (WMRs) subject to the violation of nonholonomic constraints in an environment without obstacles. The problem is simplified by neglecting the vehicle dynamics and considering only the steering system. The linearized tracking-error kinematic model with the presence of uncertain disturbances is formed in the frame of the robot. And then, the control policy is derived from the worst-case optimization of a quadratic cost function, which penalizes the tracking error and control variables in each sampling time over a finite horizon. As a result, the input sequence must be feasible for all possible disturbance realizations. The performance of the control algorithm is verified via the computer simulations with a predefined trajectory and is compared to a common discrete-time sliding mode control law. The result shows that the proposed method has a better tracking performance and convergence.
min-max model predictive control trajectory tracking wheeled mobile robot disturbances