任意时间全局张量运动规划，可生成拓扑多样解。
Anytime Global Tensor Motion Planning
- 用黑盒局部规划器构建分层图，支持多种插值与优化方法。
- 固定预算下随机重启覆盖所有同伦类，增量预算下收敛最优解。
- 2D导航中生成多样拓扑路径，适合需多解的机器人任务。
全局张量运动规划（GTMP）通过分层多部分图上的批量张量运算解决运动规划问题。我们将其泛化，使相邻层间边由任意黑盒局部规划器（如线性插值、样条、采样规划、轨迹优化或生成采样）实现。在此基础上提出两种任意时间策略：在固定预算下随机重启的任意时间GTMP，几乎必然覆盖每个端点固定的同伦类；以及具有启发式扩展和不断增长预算的AO-GTMP，收敛至最优代价。我们证明，单次采样图即可覆盖所有存在δ-清晰且长度有界的代表元的同伦类。此外，每层增加样本数使层内漏检概率呈指数下降，而更强的局部规划器仅能亚线性减少所需层数。在操作基准测试中性能达到当前最优水平，在二维导航中返回一批拓扑多样解，而启发式基线则集中于一两个类别。
原文摘要 · Abstract (English)
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.
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