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This report focuses on developing a control algorithm for obstacle avoidance in automobile maneuvering. For the derivation, an optimal control problem is formulated as minimizing the longitudinal movement to avoid the collision. The optimal inputs are then obtained by referring a simple map constructed in a 3-dimensional space expressing a functional relationship between the vehicle velocities in the longitudinal and lateral directions, the distance to avoid, and the maximal allowable force acting to the vehicle, and the optimal solution. The optimal force input is then shown to be expressed as the distributed forces to the four tires.

An Optimum Vehicle Trajectory Control for Obstacle Avoidance with the Shortest Longitudinal Traveling Distance