Star-shaped Roadmaps - A Deterministic Sampling Approach for Complete Motion Planning

Abstract

We present a simple algorithm for complete motion planning using deterministic sampling. Our approach relies on computing a star-shaped roadmap of the free space. We partition the free space into star-shaped regions such that a single point called the guard can see every point in the starshaped region. The resulting set of guards capture the intraregion connectivity. We capture the inter-region connectivity by computing connectors that link guards of adjacent regions. We use the guards and connectors to construct a star-shaped roadmap of the free space. We present an efficient algorithm to compute the roadmap in a deterministic manner without computing an explicit representation of the free space. We show that the star-shaped roadmap captures the connectivity of the free space while providing sufficient information to perform complete motion planning. Our approach is relatively simple to implement for robots with translational and rotational degrees of freedom (dof). We highlight the performance of our algorithm on challenging scenarios with narrow passages or when there is no collision-free path for low-dof robots.