A Unified Pseudospectral Computational Framework for Optimal Control of Road Vehicles

Abstract

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.