Volumetric Tree*: Adaptive Sparse Graph for Effective Exploration of Homotopy Classes

Abstract

We present volumetric tree*, a hybridization of sampling-based and optimization-based motion planning. Volumetric tree* constructs an adaptive sparse graph with volumetric vertices, hyper-spheres encoding free configurations, using a sampling-based motion planner for a homotopy exploration. The coarse-grained paths computed on the sparse graph are refined by optimization-based planning during the execution, while exploiting the probabilistic completeness of the sampling- based planning for the initial path generation. We also suggest a dropout technique probabilistically ensuring that the sampling- based planner is capable of identifying all possible homotopies of solution paths. We compare the proposed algorithm against the state-of-the-art planners in both synthetic and practical benchmarks with varying dimensions, and experimentally show the benefit of the proposed algorithm.