Obstacle Avoidance by Steering and Braking with Minimum Total Vehicle Force

In this study of automatic obstacle avoidance maneuver, a fast and precise algorithm for solving a two-point boundary value problem (TPBVP) is developed. This algorithm realizes optimal control by minimizing the total vehicle force using integrated steering and braking control. Such optimal control is characterized by three nonlinear equations that result from the application of the necessary conditions for optimality. These highly nonlinear simultaneous equations are nondimensionalized, and algebraic manipulations are performed for simplification. As a result, they are reduced to a single nondimensionalized equation with the dimensionless final time as an unknown and aspect ratio as an input that describes the relative position between the obstacle and vehicle. For a fast and robust solution process, a search interval for a numerical root solving method is set using approximating polynomials. Based on the solution of the dimensionless final time, the dimensionless total vehicle force and dimensionless jerk, both of which are essential aspects of collision avoidance maneuver, can be easily computed.