Abstract
This report summarizes the authors´ recent research toward optimizing tire workload. From the viewpoint of active safety, there is a strong need for further progress in vehicle dynamics control. In order to maintain direct yaw-moment control, traction/braking forces must be effectively distributed over the four wheels. Increasingly precise online optimization algorithms are being studied to replace the former empirical methods. According to the tire friction circle model, the tire force will not exceed the product of the vertical load on the tire with the road friction coefficient. If the tire workload is optimized in minimax criterion, the optimal distribution of traction/braking force can be determined for all tires, under the natural condition that the tires have identical friction coefficients; the actual friction coefficient is not required.
This report evaluates the optimization of tire workload using the minimax criterion for a range of vehicles, including conventional front-wheel steering vehicles, four-wheel steering vehicles, front-wheel independent steering vehicles and four-wheel independent steering vehicles. In optimizing the conventional steering system precisely using minimax criterion, algebraic solutions can be found for the literally optimized distribution using estimated values for vertical load and lateral forces and the reference values for total traction/breaking force and direct yaw moment. Since this basic solution works at the lower level, i.e., in the distribution of traction/breaking force, this is applicable to any isometric steering system including frontwheel active steering and four-wheel active steering vehicles.
Front-wheel independent steering means vehicles whose front wheels´ steering actions are independently controlled. In optimization of the tire workload, the distribution of tire forces is optimized between the left and right front wheels using control conditions of the front axle lateral forces. In addition to the traction/braking forces on all wheels, the steering angles of the front two wheels are variables. A combination of the binary search method and the above algebraic solutions realizes efficient optimization and results in considerable drivability improvements. In the case of four-wheel independent steering, additional variables of rear wheel steering angles are included, and the equality constraint of lateral force acting on the rear axle is imposed to the problem, but the robust golden section search method can be used as an exterior loop for the binary search. The convergence of these algorithms is guaranteed by the convexity of each objective function that defines the distribution problem, and most of them can be implemented for practical real time optimizations.
Keywords - Active Steering, Independent Steering, Direct Yaw-moment Control, Tire Workload, Minimax Optimization