Determining the Nonexistence of Evasive Trajectories for Collision Avoidance Systems

It is of utmost importance for automatic collision avoidance systems to correctly evaluate the risk of a current situation and constantly decide, if and what kind of evasive maneuver must be initiated. Most motion planning algorithms find such maneuver by searching a deterministic or random subset of the state space or input space. These approaches can be designed to be complete in the sense that they converge to a feasible solution as sampling is made denser. However, they are not suitable to determine whether a solution exists. In this paper, we present an approach which overapproximates the reachable set of the host vehicle considering workspace obstacles. Thus, it provides an upper bound of the solution set and it can report if no solution exists. Furthermore, the calculated set can be used for guiding the search of an underlying planning algorithm to find a solution as each trajectory of the host vehicle is ensured to be contained within this set.