A Unified Pseudospectral Computational Framework for Optimal Control of Road Vehicles
A Unified Pseudospectral Computational Framework for Optimal Control of Road Vehicles
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DOI：
10.1109/tmech.2014.2360613
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发表时间：
2015-08
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影响因子：
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通讯作者：
Shaobing Xu;S. Li;Kun Deng;Sisi Li;B. Cheng
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文献类型：
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作者：
Shaobing Xu;S. Li;Kun Deng;Sisi Li;B. Cheng
本文提出了一个统一的伪谱计算框架，用于准确有效地解决道路车辆的最优控制问题（OCP）。在此框架下，任何连续时间 OCP 都通过伪谱变换转换为非线性规划（NLP）问题，其中状态和控制均通过 Legendre-Gauss-Lobatto（LGL）配置点处的全局拉格朗日插值多项式来近似。推导了OCP的助数与NLP的KKT乘数之间的映射关系，以检验解的最优性。着眼于工程实践，集成拟牛顿迭代算法来精确计算LGL点，并提出了处理非光滑问题的多阶段预处理策略。在 MATLAB 环境中开发了一种称为伪谱 OCP 求解器 (POPS) 的通用求解器来实现计算框架。最后，提出了两个经典的车辆自动化问题并通过 POPS 进行数值求解：1）丘陵路况下生态驾驶策略的优化； 2）超车场景下的最优路径规划。与等间距直接方法的比较显示了该统一框架的有效性。
This paper presents a unified pseudospectral computational framework for accurately and efficiently solving optimal control problems (OCPs) of road vehicles. Under this framework, any continuous-time OCP is converted into a nonlinear programming (NLP) problem via pseudospectral transformation, in which both states and controls are approximated by global Lagrange interpolating polynomials at Legendre-Gauss-Lobatto (LGL) collocation points. The mapping relationship between the costates of OCP and the KKT multipliers of NLP is derived for checking the optimality of solutions. For the sake of engineering practice, a quasi-Newton iterative algorithm is integrated to accurately calculate the LGL points, and a multiphase preprocessing strategy is proposed to handle nonsmooth problems. A general solver called pseudospectral OCP solver (POPS) is developed in MATLAB environment to implement the computational framework. Finally, two classic vehicle automation problems are formulated and numerically solved by POPS: 1) optimization of ecodriving strategy in hilly road conditions; and 2) optimal path planning in an overtaking scenario. The comparison with an equally spaced direct method is presented to show the effectiveness of this unified framework.