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Optimal and Bounded Suboptimal Any-Angle Multi-agent Pathfinding

Konstantin Yakovlev, Anton Andreychuk, Roni Stern

TL;DR

The paper tackles optimal multi-agent pathfinding when agents may move freely between locations if line-of-sight to obstacles is clear (any-angle MAPF). It brands AA-CCBS, a framework that combines CCBS with TO-AA-SIPP to guarantee optimality, and tackles scalability with Disjoint Splitting (DS) and Multi-Constraints (MC) strategies, including several MC variants. It demonstrates that MC3 and DS-based variants solve substantially more instances within time limits and enable a bounded-suboptimal mode with near-constant overhead (often ≲2%) for realistic suboptimality factors. The results establish that allowing even limited suboptimality or stronger pruning drastically expands solvable problem sizes in any-angle MAPF, with practical implications for robotics and automation systems requiring conflict-free, efficient multi-robot planning. Overall, AA-CCBS provides a principled, scalable approach to optimal and bounded-suboptimal any-angle MAPF with concrete, transferable enhancements for high-level search efficiency.

Abstract

Multi-agent pathfinding (MAPF) is the problem of finding a set of conflict-free paths for a set of agents. Typically, the agents' moves are limited to a pre-defined graph of possible locations and allowed transitions between them, e.g. a 4-neighborhood grid. We explore how to solve MAPF problems when each agent can move between any pair of possible locations as long as traversing the line segment connecting them does not lead to a collision with the obstacles. This is known as any-angle pathfinding. We present the first optimal any-angle multi-agent pathfinding algorithm. Our planner is based on the Continuous Conflict-based Search (CCBS) algorithm and an optimal any-angle variant of the Safe Interval Path Planning (TO-AA-SIPP). The straightforward combination of those, however, scales poorly since any-angle path finding induces search trees with a very large branching factor. To mitigate this, we adapt two techniques from classical MAPF to the any-angle setting, namely Disjoint Splitting and Multi-Constraints. Experimental results on different combinations of these techniques show they enable solving over 30% more problems than the vanilla combination of CCBS and TO-AA-SIPP. In addition, we present a bounded-suboptimal variant of our algorithm, that enables trading runtime for solution cost in a controlled manner.

Optimal and Bounded Suboptimal Any-Angle Multi-agent Pathfinding

TL;DR

The paper tackles optimal multi-agent pathfinding when agents may move freely between locations if line-of-sight to obstacles is clear (any-angle MAPF). It brands AA-CCBS, a framework that combines CCBS with TO-AA-SIPP to guarantee optimality, and tackles scalability with Disjoint Splitting (DS) and Multi-Constraints (MC) strategies, including several MC variants. It demonstrates that MC3 and DS-based variants solve substantially more instances within time limits and enable a bounded-suboptimal mode with near-constant overhead (often ≲2%) for realistic suboptimality factors. The results establish that allowing even limited suboptimality or stronger pruning drastically expands solvable problem sizes in any-angle MAPF, with practical implications for robotics and automation systems requiring conflict-free, efficient multi-robot planning. Overall, AA-CCBS provides a principled, scalable approach to optimal and bounded-suboptimal any-angle MAPF with concrete, transferable enhancements for high-level search efficiency.

Abstract

Multi-agent pathfinding (MAPF) is the problem of finding a set of conflict-free paths for a set of agents. Typically, the agents' moves are limited to a pre-defined graph of possible locations and allowed transitions between them, e.g. a 4-neighborhood grid. We explore how to solve MAPF problems when each agent can move between any pair of possible locations as long as traversing the line segment connecting them does not lead to a collision with the obstacles. This is known as any-angle pathfinding. We present the first optimal any-angle multi-agent pathfinding algorithm. Our planner is based on the Continuous Conflict-based Search (CCBS) algorithm and an optimal any-angle variant of the Safe Interval Path Planning (TO-AA-SIPP). The straightforward combination of those, however, scales poorly since any-angle path finding induces search trees with a very large branching factor. To mitigate this, we adapt two techniques from classical MAPF to the any-angle setting, namely Disjoint Splitting and Multi-Constraints. Experimental results on different combinations of these techniques show they enable solving over 30% more problems than the vanilla combination of CCBS and TO-AA-SIPP. In addition, we present a bounded-suboptimal variant of our algorithm, that enables trading runtime for solution cost in a controlled manner.
Paper Structure (13 sections, 1 theorem, 6 figures, 1 table, 1 algorithm)

This paper contains 13 sections, 1 theorem, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORKS
  3. PROBLEM STATEMENT
  4. BACKGROUND
  5. CCBS
  6. TO-AA-SIPP
  7. AA-CCBS
  8. Multi-Constraints in Any-Angle MAPF
  9. Disjoint Splitting
  10. Experimental Results
  11. Bounded-Suboptimal AA-CCBS
  12. CONCLUSION AND FUTURE WORK
  13. Additional Experiments

Key Result

Theorem 1

AA-CCBS with any of the enhancements -- MC1, MC2, MC3, and DS -- is sound, solution-complete, and optimal, i.e., it is guaranteed to return a valid solution is such exists, and the solution it returns is cost-optimal.

Figures (6)

  • Figure 1: Two optimal solutions of the same MAPF instance: the one composed of the cardinal moves only (left) and the one with any-angle moves (right). The cost of the latter is $22\%$ lower.
  • Figure 2: An example of vanilla AA-CCBS multi-constraint.
  • Figure 3: Actions comprising different versions of multi-constraints. Please note that the time intervals of the actions in MC2 and MC3 are notably larger compared to MC1. Thus MC2 and MC3 are expected to exhibit more pruning power.
  • Figure 4: Evaluation of different variants of AA-CCBS. Left pane shows the amount of totally solved instances (within a 5 min. time cap) by each version of AA-CCBS. Middle pane shows the time taken to find a solution (Y-axis is in log-scale). Each data point tells how many instances (X-axis) the algorithm is capable to solve within a certain time (Y-axis). Right pane demonstrates how many high-level iterations are needed to solve different MAPF problem instances. X-axis shows instance id. Each data point tells how many high-level iterations were made by the algorithm (Y-axis) on a particular problem instance (X-axis).
  • Figure 5: The results of the evaluation of AA-CCBS and its modifications with different suboptimality factors.
  • ...and 1 more figures

Theorems & Definitions (1)

  • Theorem 1