Nondimensionalized Univariate Equation Characterizing Optimal State Feedback Control for Collision Avoidance

In this paper, integration of steering and braking are studied for collision avoidance from the standpoint of optimal control theory. First, the collision avoidance by braking, steering, and steering with braking maneuvers are theoretically investigated. By some assumptions, such as, the point mass vehicle model and constant resultant vehicle force in all directions, the selection of the best maneuver for collision avoidance is represented by the regions on a 2-D diagram. The nondimensionalized axes of this diagram stand for all required vehicle state and geometrical conditions, more specifically, the remaining distance, longitudinal vehicle velocity, lane width, and friction coefficient. Second, a two-point boundary value problem derived for the integrated control is reduced to a single equation with an unknown via algebraic simplifications, and the bisection method turns out to be the most appropriate among the algorithms that have been tested. It turned out that the efficient and precise solution of the optimal control problem is guaranteed, including the cases in which the intervention has been initiated. Consequently, this paper realizes the efficient identification of the theoretically reliable reference maneuver of single lane change with the minimum collision avoidance distance in the framework of feedback control.