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.

翻译：为促进移动机器人在不同领域的广泛应用，必须保证其轨迹跟踪性能。针对移动机器人系统中的约束和非线性特征，本文采用非线性模型预测控制（MPC）实现移动机器人轨迹跟踪。具体而言，为降低非线性MPC的在线计算复杂度，本文提出一种格点分段仿射（PWA）逼近方法，该方法可同时逼近显式非线性MPC的非线性系统和控制律。沿轨迹对移动机器人运动学模型进行逐次线性化，获得系统的线性时变描述，进而利用格点PWA模型表示。随后，非线性MPC问题可转化为一系列线性MPC问题。此外，为降低多个线性MPC问题的在线计算复杂度，我们利用格点PWA模型逼近线性MPC的最优解。即针对不同采样状态，获取最优控制输入，并基于状态-控制对构建格点PWA逼近。通过仿真将本文方法与线性MPC和显式线性MPC框架进行性能对比。结果表明，与显式线性MPC相比，本文方法具有更高的在线计算速度，且能在不显著增加跟踪误差的前提下降低离线计算时间。