anytime 全局张量运动规划
Anytime Global Tensor Motion Planning
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中文总结 AI 辅助
该研究泛化全局张量运动规划（GTMP），提出两种 anytime 策略，证明其同伦类覆盖与概率特性，在操作任务和二维导航基准上表现良好。
中文摘要 AI 辅助
全局张量运动规划（GTMP）通过分层二部图上的批量张量运算求解运动规划问题。我们对GTMP进行泛化，使相邻层边可由任意黑盒局部规划器实现（例如线性插值、样条曲线、基于采样的规划、轨迹优化或生成式采样）。我们在此泛化基础上提供两种 anytime 策略：固定预算下带随机重启的 anytime GTMP，几乎必然覆盖所有同伦类；以及预算递增下带启发式扩展的 AO-GTMP，收敛至最优代价。我们证明，单个采样图覆盖所有端点固定且存在长度有界的δ-清晰代表的同伦类；每一层增加额外样本可指数级降低该层未命中概率，而更强的局部规划器仅能亚线性减少所需层数。在操作任务基准上，该方法达到与现有最优方法相当的性能；在二维导航任务中，它返回一批拓扑多样的解，而启发式基准仅聚焦于一或两个类。
英文摘要
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 \(δ\)-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.
发表机构
- Purdue University（普渡大学）
- VinUniversity（范安大学）
- TU Darmstadt（达姆施塔特工业大学）
机构由 AI 辅助整理，请以论文原文为准。
