Vehicle Optimal Velocity Curves for Minimum-Time Maneuver

A problem in vehicle minimum-time maneuver is the assumption that a vehicle passes through a given path in a minimal amount of time without deviating from the boundary of the given path. Vehicle handling inverse dynamics provides a new perspective to solve such problem. Based on inverse dynamics, this paper transformed the problem of optimal vehicle velocity for minimum-time maneuver into that of optimal control with the objective function of minimum time. The path for minimum vehicle travel time and the optimal control model were established. The optimal velocity curves for three types of paths, namely, monotonically increasing path, monotonically decreasing path, and constant radius path, were analyzed. On this basis, the optimal velocity curves were solved for two kinds of concrete paths: a path of decreasing curvature radius followed by a path of increasing curvature radius and another path of increasing curvature radius followed by a path of decreasing curvature radius. Nine cases of possible optimal velocity curves were acquired. The optimal velocity curve of the given path, that is, a parabola followed by a semicircle, was obtained. Optimal velocity curves can be used as reference for vehicle minimum-time maneuver, which is an important issue for driver safety in fast-moving vehicles.