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This paper introduces a generalized framework for Global Tensor Motion Planning (GTMP) that utilizes batched tensor operations over a multipartite graph, allowing for the integration of various black-box local planners. The authors present two anytime policies鈥擜nytime GTMP and AO-GTMP鈥攖hat ensure comprehensive coverage of homotopy classes and optimal cost convergence, respectively. Empirical results demonstrate that the proposed methods achieve state-of-the-art performance on manipulation benchmarks and provide diverse solutions in 2D navigation tasks, outperforming informed baselines that focus on limited classes.
Anytime GTMP guarantees coverage of all homotopy classes while achieving state-of-the-art performance on manipulation tasks.
Global Tensor Motion Planning (GTMP) solves motion planning with batched tensor operations over a layered multipartite graph. We generalize GTMP so that adjacent-layer edges are realized by any black-box local planner (e.g., linear interpolation, splines, sampling-based planning, trajectory optimization, or generative sampling). We provide two anytime policies on top of this generalization: Anytime GTMP with random restarts at a fixed budget, which covers every homotopy class almost surely, and AO-GTMP with informed expansion with growing budgets, which converges to the optimal cost. We prove that a single sampled graph covers every endpoint-fixed homotopy class admitting a \(\delta\)-clear representative of bounded length. We also prove that additional samples per layer reduce the per-layer miss probability exponentially, whereas stronger local planners reduce the required layer count only sublinearly. On manipulation benchmarks the method matches state-of-the-art performance, and on 2D navigation it returns batches of topologically diverse solutions, while the informed baselines concentrate on one or two classes.
