A Single-Query Bi-Directional Probabilistic Roadmap Planner with Lazy Collision Checking

This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: (1) singlequery –i.e., it does not pre-compute a roadmap, but uses the two input query configurations to explore as little space as possible; (2) bi-directional i.e., it searches the robot’s free space by concurrently building a roadmap made of two trees rooted at the query configurations – and (3) applies a systematic lazy collision-checking strategy –i.e., it postpones collision tests along connections in the roadmap until they are absolutely needed. Several observations motivated this collision-checking strategy: (1) PRM planners spend more than 90% of their time checking collision; (2) most connections in a PRM are not on the final path; (3) the collision test for a connection is the most expensive when there is no collision; and (4) the probability that a short connection is collision-free is large. The strengths of single-query and bidirectional sampling techniques, and those of lazy collision checking reinforce each other. This combination reduces planning time by large factors, making it possible to handle more difficult planning problems, including multi-robot problems in geometrically complex environments.