Perceiving guaranteed continuously collision-free robot trajectories in an unknown and unpredictable environment

This paper addresses continuous collision-checking of a high-DOF robot trajectory in a completely unknown and unpredictable environment (i.e., obstacles are unknown and their motions are also unknown). In, the authors introduced how to discover, if a robot at configuration q at a future time t is guaranteed collision-free or not using the novel concept of the dynamic envelope and atomic obstacles based on sensing in such an unknown and unpredictable environment. In this paper, we further show that if a point (q, t) in the robot's configuration-time space (CT-space) is discovered collision-free, a neighborhood (CT-region) of (q, t) is also guaranteed collision-free. Based on that, given a continuous robot trajectory, we present a method to compute a set of discrete CT-points such that, if these points are discovered to be guaranteed collision-free, their associated collision-free neighborhood CT-regions contains the continuous trajectory, i.e., the trajectory is guaranteed continuously collision-free.