Bhat, S., Davari, M., and Nybacka, M., "Study on Energy Loss due to Cornering Resistance in Over-Actuated Vehicles using Optimal Control," SAE Int. J. Veh. Dyn., Stab., and NVH 1(2):263-269, 2017, doi:10.4271/2017-01-1568.
As vehicles become electrified and more intelligent in terms of sensing, actuation and processing; a number of interesting possibilities arise in controlling vehicle dynamics and driving behavior. Over-actuation with in- wheel motors, all wheel steering and active camber is one such possibility, which facilitate the control strategies that push boundaries in energy consumption and safety. Optimal control can be used to investigate the best combinations of control inputs to an over-actuated system. This paper shows how an optimal control problem can be formulated and solved for an over-actuated vehicle case, and highlights the translation of this optimal solution to a real-world scenario, enabling intelligent means to improve vehicle efficiency.This paper gives an insight into Dynamic Programming (DP) as an offline optimal control method that guarantees the global optimum. Therefore the optimal control allocation to minimize an objective function and simultaneously fulfill the defined constraints can be achieved. As a case study the effects of over-actuation on the cornering resistance were investigated in two different maneuvers i.e. step steer and sine with dwell, where in both cases the vehicle assumes to be in steady state situation. In this work the cornering resistance is the main objective function and maintaining the reference trajectory is the constraint which should be fulfilled. A parameter study is conducted on the benefits of over-actuation, and depending on the type of over-actuation about 15% to 50% reduction in cornering resistance were observed during step steer and sine with dwell maneuver respectively. From a second parameter study that focused on COG position from a safety perspective, it is more beneficial for the vehicle to be designed to under-steer than over-steer. Finally, a method is described to translate the offline optimal results to vehicle implementable controllers in the form of both feed-through lookup-tables and rule-based feed-forward control.