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The paper deals with the time optimal control of automatically driven electric cars in a test path under state and input constraints. The problem can be formulated as a dynamic nonlinear optimal control problem (DNOCP). The resulting DNOCP is solved by reformulating it to a static nonlinear program (NLP) using time discretization and direct multiple shooting methods. A novel method is presented to convert the optimal solution obtained using the single-track model to the optimal control of four-in-wheels-motors driven (4WD) cars. The conversion assures similar motion of the COG of both models and optimal distribution of the longitudinal wheel forces. A discrete model predictive control (MPC) is proposed for the linearized 4WD vehicle model under perturbations which uses the distributed wheel forces and optimizes the perturbations with analytically solvable end constraints. The elaborated method can form the basis to generate an offline database of a general collision avoidance system (CAS).

Time Optimal Control of Four-in-Wheel-Motors Driven Electric Cars