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.

翻译：状态空间投影与分解已成为解决高维多机器人运动规划中维度灾难问题的有力工具。然而，现有方法缺乏能够无缝处理投影（优先级化或任务空间）与分解（并行或解耦子空间）组合的统一框架。为填补这一空白，我们引入纤维丛树——以状态空间为节点、纤维化为边的树结构，其中纤维化描述了从高维空间到低维（或简化）空间的投影。通过将投影建模为纤维化，我们将顺序优先级化、并行分解及任务空间投影统一于单一且自洽的形式体系中。在此基础上，我们开发了快速探索随机纤维丛树（Fibration-RRT）规划器——一种基于采样的运动规划方法，它泛化了商空间RRT（用于顺序优先级化）与离散RRT（用于并行分解）的策略，同时允许纳入任务空间投影。Fibration-RRT在用户定义的纤维丛树上运行，并具有概率完备性。为验证Fibration-RRT的通用性与效率，我们提供开源实现，并在32个场景中针对自由度高达96的多机器人团队进行实验。结果表明，Fibration-RRT通过利用用户定义的纤维丛树高效求解高维问题，从而确立了纤维丛树作为多机器人运动规划的强有力统一框架。