Nonlinear Model Predictive Control (NMPC) is effective for local planning of automated vehicles, especially when there exist dynamical objects and multipe requirements. But it requires many computation resources for numerical optimization, which limits its practical application becase of the limited power of onboard unit. To extend the application range of the NMPC based local planner, the coupled nonlinear vehicle dynamics model is adopted based on the numerical analysis, which conversely requires much more discretization poits for acceptable accuracy. For better computation efficiency, Lagrange polynomials are used to discretize the vehicle dynamics model and objective function with less points and fine numerical accuracy. Furthermore, an adaptive strategy is designed to determine the order of Lagrange polynomials according to running state by numerical analysis of discretization error. Both acceleration effect and performance of the local planner designed by NMPC are validated by experimental tests under scenarios with multiple dynamical obstacles. The test results show that compared with the original one the accuracy and efficiency are improved by 74% and 60%, respectively.

非线性模型预测控制（NMPC）对于自动驾驶车辆的局部规划非常有效，特别是当存在动态对象和多种需求时。但数值优化需要大量计算资源，由于机载单元功率有限，限制了其实际应用。为了扩展基于NMPC的局部规划器的应用范围，采用基于数值分析的耦合非线性车辆动力学模型，这反过来需要更多的离散点才能达到可接受的精度。为了提高计算效率，采用拉格朗日多项式对车辆动力学模型和目标函数进行离散化，点数少，数值精度高。此外，通过离散化误差的数值分析，设计了一种自适应策略，根据运行状态确定拉格朗日多项式的阶数。NMPC设计的局部规划器的加速效果和性能均通过多动态障碍场景下的实验测试得到验证。测试结果表明，与原来相比，准确率和效率分别提高了74%和60%。