Minimum Resultant Vehicle Force Optimal State Feedback Control for Obstacle Avoidance

An optimal feedback control with the minimum resultant vehicle force for obstacle avoidance is investigated. In the authors' previous report, four equations were derived for the two-point boundary value problem that determines the optimal feedback control for the minimum longitudinal avoidance distance problem in which the maximum vehicle force is given. In this paper, these equations are fully nondimensionalized, and the dimensionless equations are simplified by successive algebraic manipulations; until the control parameters are identified as functions of one unknown that is readily determined by an equation defined in an implicit form. The stable solution of this equation is expectable by the application of the bisection method. The two dimensionless inputs to this equation are: the ratio of the lateral to longitudinal velocity and the ratio of the remaining lateral to longitudinal distance. The optimal control is, therefore, described in the form of a state feedback controller. In the numerical simulations, the longitudinal and lateral vehicle forces required to realize the optimal control are distributed to the tires using a minimax optimization scheme that assumes a four-wheel steering vehicle. In each case, the maximum tire workload is minimized, and the vehicle center of gravity closely traced the paths expected by the point-mass model assumed in the controller design. Additional examples are provided to demonstrate the effectiveness of online optimization in accommodating the lateral movement of the obstacle or the appearance of another object, after the initiation of the avoidance maneuver.