Inevitable collision states — a step towards safer robots?

An inevitable collision state for a robotic system can be defined as a state for which, no matter what the future trajectory followed by the system is, a collision with an obstacle eventually occurs. An inevitable collision state takes into account the dynamics of both the system and the obstacles, fixed or moving. The main contribution of this paper is to lay down and explore this novel concept (and the companion concept of inevitable collision obstacle). Formal definitions of the inevitable collision states and obstacles are given. Properties fundamental for their characterization are established. This concept is very general, and can be useful both for navigation and motion planning purposes (for its own safety, a robotic system should never find itself in an inevitable collision state). To illustrate the interest of this concept, it is applied to a problem of safe motion planning for a robotic system subject to sensing constraints in a partially known environment (i.e. that may contain unexpected obstacles). In safe motion planning, the issue is to compute motions for which it is guaranteed that, no matter what happens at execution time, the robotic system never finds itself in a situation where there is no way for it to avoid collision with an unexpected obstacle.