Collision avoidance as a differential game: real-time approximation of optimal strategies using higher derivatives of the value function

Contemporary developments of on-board systems for automatic or semi-automatic driving include car collision avoidance. For this purpose a worst case approach based on pursuit-evasion differential games is investigated. On a freeway a correct driver (evader) is faced with a wrong driver (pursuer) ahead. The correct driver tries to avoid a collision against all possible wrong driver's maneuvers and additionally tries to stay on the freeway. The representation of an optimal collision avoidance strategy along a lot of optimal paths is used to synthesize a collision avoidance strategy globally by means of Taylor series expansions of the value function's gradient. Examples of simulations which proved satisfactory performance of the on-board collision avoidance system against various typical maneuvers of wrong drivers are presented.