Minimum-time optimal control for vehicles with active rear-axle steering, transfer case and variable parameters

When aiming to improve the performance of industrial sports cars at the limits of driving dynamics, the passive vehicle setup should be tuned under consideration of the actuator configuration and the control system capabilities. To objectively quantify the performance of given vehicle settings, minimum lap times can be determined using optimal control methods. The computed trajectories can be used to assess the benefits of certain actuators as well as to identify optimal vehicle setups and control strategies. This paper analyses the effect of rear-axle steering, longitudinal torque allocation via transfer case and selected vehicle parameters on lap time. The optimal roll moment distribution and longitudinal position of the centre of gravity are identified via concurrent optimisation. The optimal lap trajectories are generated by numerically solving a minimum-time optimal control problem using direct Hermite-Simpson collocation. To eliminate the problem of an unknown initial solution, the authors present an initialisation routine for vehicular optimal control problems. Moreover, a novel approach for the generation of smooth track curvature data is introduced.