A direct multiple shooting method to improve vehicle handling and stability for four hub-wheel-drive electric vehicle during regenerative braking

Regenerative braking is an important technology to improve fuel economy for electric vehicles. Apart from improving energy recovery efficiency and vehicle stability, the arithmetic speed of the algorithm is also essential for an automotive-qualified micro control units. This paper presents a direct multiple shooting method-based algorithm to achieve multiple objectives for four hub-wheel-drive electric vehicle during mild braking situations. Mathematical models of the system are generated for numerical simulations in MATLAB, including a vehicle dynamics model, a modified tire model, a single-point preview driver model, and a regenerative braking motor efficiency map. With the limitation of hard constraint and minimization of adjustment rate in cost function, optimization tends to be accomplished by distribution of braking torque in front and rear wheels. Furthermore, the control strategy has been realized using a direct multiple shooting method to convert the nonlinear optimal control problem to a nonlinear programming problem, which will be settled by adopting a sequential quadratic programming method in each subintervals. The effectiveness and adaptation of the control strategy for four hub-wheel-drive electric vehicle has been evaluated by conducting many simulations during mild braking situations, and the simulation results also demonstrated that the direct multiple shooting-based strategy exhibits a better performance than that of proportional-integral-based or nonlinear model predictive control-based controller.