Online Motion Planning Over Multiple Homotopy Classes with Gaussian Process Inference Efficient planning in dynamic and uncertain environments is a fundamental challenge in robotics. In the context of trajectory optimization, the feasibility of paths can change as the environment evolves. Therefore, it can be beneficial to reason about multiple possible paths simultaneously. We build on prior work that considers graphbased trajectories to find solutions in multiple homotopy classes concurrently. Specifically, we extend this previous work to an online setting where the unreachable (in time) part of the graph is pruned and the remaining graph is reoptimized at every time step. As the robot moves within the graph on the path that is most promising, the pruning and reoptimization allows us to retain candidate paths that may become more viable in the future (a) as the environment changes, essentially enabling the robot to dynamically switch between numerous homotopy classes. We compare our approach against prior work without the homotopy switching capability and show improved performance across several metrics in simulation with a 2D robot in multiple dynamic environments under noisy measurements and execution.

Volumetric Tree * : Adaptive Sparse Graph for Effective Exploration of Homotopy Classes We present volumetric tree*, a hybridization of samplingbased and optimizationbased motion planning. Volumetric tree* constructs an adaptive sparse graph with volumetric vertices, hyperspheres encoding free configurations, using a samplingbased motion planner for a homotopy exploration. The coarsegrained paths computed on the sparse graph are refined by optimizationbased 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 stateoftheart planners in both synthetic and practical benchmarks with varying dimensions, and experimentally show the benefit of the proposed algorithm.