Path Planning with Loop Closure Constraints Using an Atlas-Based RRT

In many relevant path planning problems, loop closure constraints reduce the configuration space to a manifold embedded in the higher-dimensional joint ambient space. Whereas many progresses have been done to solve path planning problems in the presence of obstacles, only few work consider loop closure constraints. In this paper, we present the AtlasRRT algorithm, a planner specially tailored for such constrained systems that builds on recently developed tools for higher-dimensional continuation. These tools provide procedures to define charts that locally parametrize manifolds and to coordinate them forming an atlas. AtlasRRT simultaneously builds an atlas and a Rapidly-Exploring Random Tree (RRT), using the atlas to sample relevant configurations for the RRT, and the RRT to devise directions of expansion for the atlas. The advantage of the new planner comes from that samples obtained from the atlas allow a more efficient extension of the RRT as compared to state of the art approaches where samples are generated in the joint ambient space.