Computing unions of Inevitable Collision States and increasing safety to unexpected obstacles

For reasoning about the safety of a robot system, it is sufficient to pretend the robot to reach an Inevitable Collision Sate (ICS). Otherwise, there exists no future trajectory which can avoid a collision. The usage of ICS is limited due to its computational complexity. One reason for this is, that the ICS computation cannot be done separately for each obstacle. Hence, ICS needs to be recomputed from scratch if another object appears in the scene. The main contribution of this paper is a modified ICS calculation which allows to compute the union of ICS sets in a sequential manner, thus reducing the computational requirements in case of new obstacles. Therefore, two novel ICS-Checker algorithms are presented reducing the computational effort. Furthermore, this novel calculation is used to reduce the probability of being in an ICS regarding an unforeseen obstacle.