Evaluation of vehicle maneuverability based on controllability region analysis (An algorithm for controllability region computation and effects of tire force characteristics on the controllability region)

Abstract

This paper proposes an analytical method to evaluate vehicle maneuverability based on the comparison of null-controllability regions that are defined as the set of all initial states which can be transferred to the origin of the state space by means of admissible controls. Assuming that the multidimensional null-controllability region can be analyzed by a number of two dimensional cross sections, an optimization-based algorithm combined with a trajectory reversing approach and a ray gridding method to compute the projection of multi-dimensional controllability region onto a two-dimensional cross section is proposed. In this algorithm, the problem to determine the boundary of the controllability region is formulated as an optimal control problem to find the control inputs that maximize the norm of the terminal state of a time-reversal system starting from the origin. The null-controllability region and a reachability region of two simple examples are computed and compared with the results of previous research to demonstrate the validity of the proposed algorithm. Then the effect of tire nonlinear property on vehicle maneuverability is evaluated by comparing the size and shape of the null-controllability regions for two vehicle configurations. The results clarify the effect of tire property on the null-controllability region.