Lattice piecewise affine approximation of explicit nonlinear model predictive control with application to trajectory tracking of mobile robot

To promote the widespread use of mobile robots in diverse fields, the performance of trajectory tracking must be ensured. To address the constraints and nonlinear features associated with mobile robot systems, nonlinear model predictive control (MPC) is applied to realize trajectory tracking of mobile robots. Specifically, to alleviate the online computational complexity of nonlinear MPC, this paper devises a lattice piecewise affine (PWA) approximation method that can approximate both the nonlinear system and control law of explicit nonlinear MPC. The kinematic model of the mobile robot is successively linearized along the trajectory to obtain a linear time-varying description of the system, which is then expressed using a lattice PWA model. Subsequently, the nonlinear MPC problem can be transformed into a series of linear MPC problems. Furthermore, to reduce the complexity of online calculation of multiple linear MPC problems, the optimal solution of the linear MPCs is approximated by using the lattice PWA models. That is, for different sampling states, the optimal control inputs are obtained offline, and lattice PWA approximations are constructed for the state control pairs. Simulations are performed to evaluate the performance of the method in comparison with the state-of-the-art methods, and the results show that the method has a higher online computing speed and can decrease the offline computing time without significantly increasing the tracking error. This paper proposes a lattice PWA approximation method based on explicit linear MPC to effectively track the trajectories of fast nonlinear robots. The lattice PWA model is used both in approximating the nonlinear dynamics of the mobile robot and the optimal control laws of explicit linear MPCs. The results show that compared with the explicit linear MPC, our method has a higher online computing speed and can decrease the offline computing time without significantly increasing the tracking error.image