Reachable volume RRT

Reachable volumes are a new technique that allows one to efficiently restrict sampling to feasible/reachable regions of the planning space even for high degree of freedom and highly constrained problems. However, they have so far only been applied to graph-based sampling-based planners. In this paper we develop the methodology to apply reachable volumes to tree-based planners such as Rapidly-Exploring Random Trees (RRTs). In particular, we propose a reachable volume RRT called RVRRT that can solve high degree of freedom problems and problems with constraints. To do so, we develop a reachable volume stepping function, a reachable volume expand function, and a distance metric based on these operations. We also present a reachable volume local planner to ensure that local paths satisfy constraints for methods such as PRMs. We show experimentally that RVRRTs can solve constrained problems with as many as 64 degrees of freedom and unconstrained problems with as many as 134 degrees of freedom. RVRRTs can solve problems more efficiently than existing methods, requiring fewer nodes and collision detection calls. We also show that it is capable of solving difficult problems that existing methods cannot.