A Theoretical Framework for Parallel Lifelong MAPF Using Group Decentralized Planning
GD-RHCR framework, grounded in LI-MDP theory, guarantees near-optimality with significantly reduced computational cost for large-scale lifelong MAPF.
Key Findings
Methodology
This paper models the Lifelong Multi-Agent Path Finding (L-MAPF) as a discounted multi-agent MDP, leveraging LI-MDP theory to establish exponential near-optimal guarantees for RHCR. Building on this, the authors propose the Group Decentralized RHCR (GD-RHCR), which partitions agents into connected components based on transitive communication, enabling parallel planning for each group. The framework integrates soft constraints and heterogeneous solvers to optimize computational efficiency. Theoretically, the authors demonstrate a duality between spatial partitioning and temporal planning restrictions, ensuring performance close to the optimal. Empirical results across various maps show that GD-RHCR reduces average planning time by 24.9x and improves throughput by up to 57.7%, validating its scalability and effectiveness.
Key Results
- Experimental results demonstrate that GD-RHCR achieves a 24.9-fold reduction in average planning time compared to traditional RHCR, while maintaining high throughput in large-scale environments, outperforming PIBT and original RHCR. Theoretical analysis confirms the space-time duality, bounding the performance error by a function involving the maximum spatial distance V and planning horizon H, with an error bound of 6γmin(⌊V/2⌋+1, H)/(1−γ)^2 + ϵ.
- By combining soft constraints and heterogeneous solvers, GD-RHCR exhibits robust performance in complex environments, especially in high-density, multi-goal, multi-obstacle scenarios, achieving high efficiency and low computational overhead.
- The framework's ability to dynamically adjust groupings and leverage parallel computation significantly enhances scalability, making it suitable for real-world applications such as warehouse automation, drone traffic management, and autonomous vehicle coordination.
Significance
This work provides a significant theoretical advancement by extending the performance guarantees of RHCR within the LI-MDP framework, enabling scalable, near-optimal path planning for large multi-agent systems. It addresses the longstanding challenge of computational bottlenecks in high-density environments, offering a practical solution that balances path quality and efficiency. The proposed group decentralization paradigm bridges the gap between centralized optimality and fully decentralized scalability, opening new avenues for research in multi-agent coordination, reinforcement learning, and distributed control. Its implications span industrial automation, logistics, urban mobility, and beyond, promising more intelligent, autonomous multi-agent systems capable of operating efficiently in complex, dynamic environments.
Technical Contribution
The primary technical contributions include: 1) Theoretical proof of RHCR’s exponential near-optimality in the LI-MDP setting, providing a rigorous performance guarantee; 2) Development of a group decentralization scheme based on transitive connectivity, enabling parallel planning without significant performance loss; 3) Integration of soft constraints and heterogeneous solvers, allowing flexible adaptation to environment complexity; 4) Formal analysis establishing the duality between spatial partitioning and temporal planning horizons, underpinning the algorithm’s near-optimality. These innovations collectively advance the theoretical understanding of scalable multi-agent path planning and open pathways for practical implementations in large-scale systems.
Novelty
This research is pioneering in applying LI-MDP theory to analyze and guarantee the near-optimality of RHCR, a widely used heuristic in lifelong MAPF. It introduces a novel group decentralization approach based on transitive connectivity, which is theoretically justified and empirically validated. The combination of soft constraints, heterogeneous solvers, and lazy evaluation mechanisms further distinguishes this work from prior methods that rely solely on either centralized optimal algorithms or greedy heuristics. The duality established between space-based partitioning and time-based planning restrictions provides a new conceptual framework, bridging theoretical guarantees with practical scalability.
Limitations
- The performance guarantees depend on the assumption that the solver outputs are ϵ-optimal; in practice, solver performance variability can affect the guarantees. Moreover, the theoretical bounds are derived under simplified settings that may not fully capture real-world complexities.
- The group partitioning relies on static distance thresholds, which may not adapt well to dynamic environments with moving obstacles or changing topology, necessitating further research into adaptive partitioning strategies.
- Soft constraint parameters require manual tuning, and their optimal settings are environment-dependent, limiting the method’s plug-and-play applicability. Automating this process remains an open challenge.
- The current framework primarily addresses static maps; extending it to dynamic, unpredictable environments with real-time updates is a future direction. Additionally, scalability to extremely dense or highly dynamic scenarios still faces computational challenges.
Future Work
Future research will focus on developing adaptive, environment-aware group partitioning strategies that dynamically adjust based on real-time observations. Integrating deep reinforcement learning to tune soft constraint parameters automatically could further enhance robustness. Exploring multi-agent communication protocols to improve coordination efficiency and resilience in dynamic environments is another promising avenue. Extending the theoretical analysis to non-discounted, long-horizon settings will broaden applicability. Finally, real-world deployment in autonomous warehouses, drone swarms, and urban traffic systems will be pursued to validate and refine the framework’s practical utility.
AI Executive Summary
Multi-agent pathfinding (MAPF) is a fundamental problem in robotics and autonomous systems, involving the coordination of multiple agents navigating in shared environments while avoiding collisions. Traditional algorithms like Conflict-Based Search (CBS) and Priority-Based Search (PBS) have achieved success in small-scale scenarios, but their computational complexity grows exponentially with the number of agents, limiting scalability. Greedy approaches such as PIBT offer faster solutions but often sacrifice path optimality and can lead to deadlocks, especially in dense environments. As the demand for large-scale, real-time multi-agent coordination increases—such as in automated warehouses, drone swarms, and urban traffic management—new scalable, theoretically grounded solutions are urgently needed.
This paper introduces a novel framework called GD-RHCR (Group Decentralized Rolling-Horizon Collision Resolution), grounded in the recent theoretical development of LI-MDP (Locally Interdependent Multi-Agent Markov Decision Process). The authors first rigorously analyze the classical RHCR framework within the LI-MDP setting, proving that its performance converges exponentially close to the optimal as the planning horizon increases. This theoretical insight provides a solid foundation for the proposed extension.
Building on this, the authors propose a group decentralization strategy that partitions agents into connected components based on a transitive communication graph. Each group plans independently, leveraging soft constraints to handle inter-group conflicts, and employs heterogeneous solvers—such as PBS for small groups and PIBT for large groups—to optimize computational resources. The core innovation lies in establishing a duality between spatial partitioning (via the maximum distance V) and temporal planning horizon H, ensuring that the performance degradation remains bounded and close to optimal.
Empirical evaluations across various complex maps demonstrate that GD-RHCR significantly outperforms traditional RHCR and PIBT in large-scale scenarios. The results show a 24.9-fold reduction in average planning time and a 57.7% increase in throughput, confirming the framework’s scalability and efficiency. The method maintains high path quality while drastically reducing computational overhead, making it suitable for real-time applications in logistics, autonomous vehicles, and drone coordination.
Overall, this work bridges the gap between theoretical guarantees and practical scalability in lifelong multi-agent pathfinding. It provides a robust, flexible, and efficient solution that can be extended to dynamic, uncertain environments. Future research will explore adaptive partitioning, learning-based parameter tuning, and real-world deployments, pushing the boundaries of autonomous multi-agent systems toward greater autonomy, safety, and efficiency.
Deep Dive
Abstract
In the Lifelong Multi-Agent Path Finding (L-MAPF) problem, agents must repeatedly move from one destination to another while avoiding obstacles and inter-agent collisions. Widely regarded as one of the highest-performing solutions to this problem is the Rolling-Horizon Collision Resolution (RHCR) framework. However, commensurate with its quality solutions, it incurs a computational cost that limits its applicability to even modest agent counts. In this paper, leveraging theoretical methods from the Locally Interdependent Multi-Agent MDP literature, we first theoretically prove the near-optimality of RHCR in a discounted MDP formulation of the L-MAPF problem. Then, we leverage these results to naturally motivate an extended framework called Group Decentralized RHCR (GD-RHCR) which incorporates a group decentralized structure that partitions agents based on a transitive communication scheme and plans for each partition of agents in parallel. We show that both RHCR and GD-RHCR achieve similar exponentially close to optimal guarantees, establishing a theoretical duality between the time based restrictions performed by vanilla RHCR and the additional space based partitioning performed by GD-RHCR. Lastly, we show that across varying maps, GD-RHCR is able to attain high throughput that scales into higher agent counts while maintaining a significantly lower per plan cost.
References (20)
On multiple moving objects
M. Erdmann, Tomas Lozano-Perez
Dynamic Agent Grouping ECBS: Scaling Windowed Multi-Agent Path Finding with Completeness Guarantees
Tiannan Zhang, Rishi Veerapaneni, Shao-Hung Chan et al.
Searching with Consistent Prioritization for Multi-Agent Path Finding
Hang Ma, Daniel Damir Harabor, Peter James Stuckey et al.
Improving LaCAM for Scalable Eventually Optimal Multi-Agent Pathfinding
Keisuke Okumura
Lifelong Multi-Agent Path Finding in Large-Scale Warehouses
Jiaoyang Li, Andrew Tinka, Scott Kiesel et al.
Locally Interdependent Multi-Agent MDP: Theoretical Framework for Decentralized Agents with Dynamic Dependencies
Alex DeWeese, Guannan Qu
Shard Systems: Scalable, Robust and Persistent Multi-Agent Path Finding with Performance Guarantees
C. Leet, Jiaoyang Li, Sven Koenig
winPIBT: Extended Prioritized Algorithm for Iterative Multi-agent Path Finding
Keisuke Okumura, Yasumasa Tamura, X. Défago
Suboptimal Variants of the Conflict-Based Search Algorithm for the Multi-Agent Pathfinding Problem
Max Barer, Guni Sharon, Roni Stern et al.
Departure Scheduling and Taxiway Path Planning under Uncertainty
Jiaoyang Li, Mimi Gong, Zi Liang et al.
Structure and Intractability of Optimal Multi-Robot Path Planning on Graphs
Jingjin Yu, S. LaValle
Conflict-based search for optimal multi-agent pathfinding
Guni Sharon, Roni Stern, Ariel Felner et al.
PRIMAL$_2$: Pathfinding Via Reinforcement and Imitation Multi-Agent Learning - Lifelong
Mehul Damani, Zhiyao Luo, Emerson Wenzel et al.
Lifelong Multi-Agent Path Finding for Online Pickup and Delivery Tasks
Hang Ma, Jiaoyang Li, T. K. S. Kumar et al.
LaCAM: Search-Based Algorithm for Quick Multi-Agent Pathfinding
Keisuke Okumura
Multi-Agent Path Finding with Priority for Cooperative Automated Valet Parking
Ayano Okoso, Keisuke Otaki, Tomoki Nishi
PRIMAL: Pathfinding via Reinforcement and Imitation Multi-Agent Learning
Guillaume Sartoretti, J. Kerr, Yunfei Shi et al.
Moving Agents in Formation in Congested Environments
Jiaoyang Li, Kexuan Sun, Hang Ma et al.
EECBS: A Bounded-Suboptimal Search for Multi-Agent Path Finding
Jiaoyang Li, Wheeler Ruml, Sven Koenig
Thinking Beyond Visibility: A Near-Optimal Policy Framework for Locally Interdependent Multi-Agent MDPs
Alex DeWeese, Guannan Qu