  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, we apply nonlinear
model predictive control (MPC) to realize the 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, we approximate the optimal
solution of the linear MPC by using the lattice PWA model. That is, for
different sampling states, the optimal control inputs are obtained, and lattice
PWA approximations are constructed for the state control pairs. Simulations are
performed to evaluate the performance of our method in comparison with the
linear MPC and explicit linear MPC frameworks. 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.
