An Inevitable Collision State-Checker for a Car-Like Vehicle

An inevitable collision state (ICS) for a robotic system is a state for which, no matter what the future trajectory followed by the system is, a collision with an obstacle eventually occurs. The ICS concept takes into account both the dynamics of the robotic system and the future motion of the moving objects of the environment. For obvious safety reasons, a robotic system should never ever end up in an ICS hence the interest of the ICS concept when it comes to safely drive robotic systems in dynamic environments. In theory, determining whether a given state is an ICS requires to check for collision all possible future trajectories of infinite duration that the robotic system can follow from this particular state! In practise, it is fortunately possible to build a conservative approximation of the ICS set by considering only a finite subset of the whole set of possible future trajectories. The primary contribution of the paper is a general principle to select the subset of trajectories based upon the concept of imitating maneuvres, i.e., trajectories leading the robotic system to duplicate the behaviour of the environment objects (fixed or moving), it is shown how a good approximation of the ICS set can be obtained. The second contribution of the paper is an ICS-Checker for a car-like vehicle moving in a dynamic environment. This ICS-Checker integrates the above-mentioned selection principle. It is efficient and could be used in practise to compute truly safe motions for a car-like vehicle amidst moving objects.