Exact Optimization of Four-Wheel Steering and Four-Wheel Independent Driving/Braking Force Distribution with Minimax Criterion of Tire Workload

Abstract

The direct yaw-moment control (DYC) poses an optimization problem of determining the traction/braking forces distribution that is to be solved online to minimize the risk of tire force saturation to avoid instable vehicle behaviors. One of the authors has derived an algebraic solution to a similar minimax optimization problem of minimizing the maximum value of the tire workload where the direct yaw moment is explicitly specified. In this study, this algebraic solution is applied to the solution procedure for the extended minimax optimization problem where the total value of the traction/braking forces, that of the lateral force by the steering of the front and rear wheels, that of the yaw moment by the direct yaw moment and by the lateral forces of the front and rear wheels are specified. The proposed numerical approach that uses the golden section method rapidly converges to the exact solution of the essential decision variables as the traction/braking forces of the four wheels. The effects of problem relaxation are demonstrated through numerical examples.