面向NMPC运动规划系统的数值优化加速技术  

Accelerating Technologies of Numerical Optimization for Motion Planning Designed by Nonlinear Model Predictive Control

作　　者：高锋[1] 冯德福 胡秋霞 Gao Feng;Feng Defu;Hu Qiuxia(College of Mechanical and Vehicle Engineering,Chongqing University,Chongqing 400044)

机构地区：[1]重庆大学机械与运载工程学院,重庆400044

出　　处：《汽车工程》2023年第8期1438-1447,1497,共11页Automotive Engineering

基　　金：汽车安全与节能国家重点实验室开放基金(KFY2209);汽车协同创新中心揭榜挂帅项目(2022CDJDX-004);重庆市技术创新与应用发展专项(CSTB2022TIAD-KPX0139)资助。

摘　　要：非线性模型预测控制(nonlinear model predictive control,NMPC)是一种有效的自动驾驶运动规划方法,但数值优化对计算资源的巨大需求限制其实际应用。本文通过降低优化变量维度,简化非凸避障约束,提高NMPC运动规划系统数值优化的求解速度。针对车辆动力学的强非线性,采用拉格朗日插值逼近动力学方程和目标函数,在保证精度的前提下有效较少离散点。并在数值分析离散化误差分布特征基础上,设计拉格朗日多项式阶次自适应策略,进一步减少了优化变量维度。通过提出综合椭圆和线性时变约束的混合避障约束策略,在保证安全性的同时实现了数值优化难度与优化结果保守性之间的良好平衡。在多障碍物场景下,通过仿真和实验验证了所提方法的加速效果和性能。结果表明,与传统方法相比离散化精度和求解效率分别提高了74%和60%。Nonlinear Model Predictive Control(NMPC)is an effective method for the motion planning of automated vehicles,but its high demand of computation resources for numerical optimization limits its practical ap⁃plication.This paper improves the solving speed of the numerical optimization of NMPC motion planning system by reducing the dimension of optimization variables and simplifying the non-convex constraints for obstacle avoidance.Given the high nonlinearity of vehicle dynamics,Lagrange interpolation is adopted to discretize the state function of vehicle dynamics and the objective function to ensure the accuracy with less discretization points.Furthermore,an adaptive strategy is designed to adjust the order of Lagrange polynomials based on the numerical analysis of the dis⁃tribution characteristics of the discretization error to further reduce the dimension of optimization variables.More⁃over,a hybrid strategy is presented to construct the constraints for obstacle avoidance by combing the elliptic and linear time-varying ones together to realize good balance between the difficulty of numerical optimization and the conservatism of optimized results while ensuring the driving safety.The acceleration effect and performance of the proposed method are validated by simulation and experimental tests under various scenarios with multi-obstacles.The results show that compared with traditional methods the accuracy and efficiency of discretization of the proposed method is improved by 74%and 60%,respectively.

关 键 词：自动驾驶 运动规划 模型预测控制 拉格朗日插值 避障约束 

分 类 号：U463.6[机械工程—车辆工程] TP18[交通运输工程—载运工具运用工程] TP273[交通运输工程—道路与铁道工程]