Problem
Research questions and friction points this paper is trying to address.
multi-robot motion planning
state space projection
state space decomposition
curse of dimensionality
unified framework
Fibration Trees: A Unified Approach to Multi-Robot Motion Planning
🤖 AI Summary
This work addresses the lack of a unified framework for simultaneously handling projection and decomposition in high-dimensional multi-robot motion planning. It introduces fibration trees—a novel structure where nodes represent state spaces and edges encode fibration mappings—to formally unify priority-based planning, parallel decomposition, and task-space projection within a single theoretical framework. Building on this foundation, the authors develop Fibration-RRT, a sampling-based planner that flexibly combines multiple dimensionality reduction strategies while preserving theoretical guarantees. The approach demonstrates effectiveness on multi-robot systems with up to 96 degrees of freedom and is validated across 32 diverse scenarios in an open-source implementation. The method achieves both probabilistic completeness and computational efficiency, offering a principled and scalable solution to complex coordination problems.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
fibration trees
multi-robot motion planning
state space decomposition
sampling-based planning
probabilistic completeness
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