Abstract
Vehicles acquire longitudinal force, lateral force, and yaw moment to achieve desired movements by generating tire force, which is the friction force between the four wheels and the road. In this study, we formulate an optimization problem of seeking the magnitude and direction of tire force that minimizes the maximum μ rate (=tire force/friction circle) of each tire under restricted conditions to obtain the desired force and yaw moment of the vehicle. Subsequently, we propose two calculation methods to solve the optimization problem: one is based on sequential quadratic programming (SQP) and the other is based on the penalty function method. By numerical calculations, we show that each method can be used under certain conditions. Moreover, we obtain the number of calculations for each method and compare it with that for yaw moment optimization by the golden section method, which is another method for generating tire force efficiently. We show that of the three methods, the golden section method requires the least number of calculations under the conditions tested.
