提出统一框架，让多机器人规划更高效。
Fibration Trees: A Unified Approach to Multi-Robot Motion Planning
- 用纤维树建模状态空间投影与分解，统一处理多种规划策略。
- 在96自由度场景下，算法成功规划并验证了高维多机器人路径。
- 适合需要高效多机协同规划的科研与工程人员使用。
状态空间投影与分解已成为应对高维多机器人运动规划中维度灾难的强大工具。然而，现有方法缺乏一个统一框架，难以无缝整合投影（如优先级或任务空间）与分解（如并行或解耦子空间）的组合。为此，本文提出纤维树，即以状态空间为节点、纤维映射为边的树结构，其中纤维映射将高维空间投影到低维或简化空间。通过将投影建模为纤维，本工作统一了顺序优先、并行分解与任务空间投影三种范式。在此基础上，提出快速探索随机纤维树（Fibration-RRT）规划器，该算法基于采样，泛化了商空间RRT（用于顺序优先）和离散RRT（用于并行分解）的策略，并支持任务空间投影。Fibration-RRT在用户定义的纤维树上运行，且被证明具有概率完备性。我们提供开源实现，在包含32个场景的实验中测试其性能，涉及最多96自由度的多机器人团队。结果表明，通过利用用户定义的纤维树，Fibration-RRT能高效求解高维问题，确立了纤维树作为多机器人运动规划的统一强大框架。
原文摘要 · Abstract (English)
State space projections and decompositions have emerged as powerful tools to tackle the curse of dimensionality in high-dimensional, multi-robot motion planning problems. However, existing methods lack a unified framework which seamlessly handles combinations of projections (prioritization or task-space) and decompositions (parallel or decoupled subspaces). To fill this gap, we introduce fibration trees, which are trees consisting of state spaces as nodes and fibrations as edges, whereby a fibration models a projection from a higher-dimensional space to a lower-dimensional (or simplified) space. By modeling projections as fibrations, we unify sequential prioritization, parallel decomposition, and task-space projections under a single, coherent formalism. Building on this, we develop the rapidly-exploring random fibration trees (Fibration-RRT) planner, a sampling-based motion planner that generalizes strategies from quotient-space RRT (for sequential prioritizations) and discrete RRT (for parallel decompositions), while allowing the inclusion of task-space projections. Fibration-RRT operates on user-defined fibration trees and is proven to be probabilistically complete. To test the generality and efficiency of Fibration-RRT, we provide an open-source implementation and conduct experiments on 32 scenarios using multi robot teams with up to 96 degrees of freedom. Our results indicate that Fibration-RRT efficiently solves high-dimensional problems by exploiting user-defined fibration trees, thereby establishing fibration trees as a powerful, unified framework for multi-robot motion planning.
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