Motion Planning: with Probabilistic Roadmaps

Over the last few years, Probabilistic Roadmaps(PRMs) have emerged as a powerful approach forsolving complex motion planning problems in robotics. Even beyond robotics, PRMs can be used to predictmotions of biological macro-molecules such asproteins and synthesize motions for digital actors. Current PRM-based research focuses on challenges thatarise as PRMs are being applied to motion planningproblems in various scenarios. In response to some ofthose challenges, the following four contributionsare being made in this thesis: (1) a dynamic checkerfor PRMs that exactly determines whether a path liesin free space, (2) a sampling strategy, called"small-step retraction" (SSR), that allows a PRMplanner to efficiently construct roadmaps in freespaces with narrow passages, (3) an efficientmulti-goal PRM planner, and (4) a PRM planner thatcan compute the motions and (re-) grasp operations ofa two-arm system in order to tie self-knots ofdeformable linear objects (DLOs), as well as knotsaround simple static objects.