We explore the use of Artificial Potential Fields (APFs) to solve Multi-Agent Path Finding (MAPF) and Lifelong MAPF (LMAPF) problems. In MAPF, a team of agents must move to their goal locations without collisions, whereas in LMAPF, new goals are generated upon arrival. We propose methods for incorporating APFs in a range of MAPF algorithms, including Prioritized Planning, MAPF-LNS2, and Priority Inheritance with Backtracking (PIBT). Experimental results show that using APF is not beneficial for MAPF but yields up to a 7-fold increase in overall system throughput for LMAPF.
Multi-Agent Path Finding (MAPF) is a fundamental problem in artificial intelligence and robotics, requiring the computation of collision-free paths for multiple agents navigating from their start locations to designated goals. As autonomous systems become increasingly prevalent in warehouses, urban transportation, and other complex environments, MAPF has evolved from a theoretical challenge to a critical enabler of real-world multi-robot coordination. This comprehensive survey bridges the long-standing divide between classical algorithmic approaches and emerging learning-based methods in MAPF research. We present a unified framework that encompasses search-based methods (including Conflict-Based Search, Priority-Based Search, and Large Neighborhood Search), compilation-based approaches (SAT, SMT, CSP, ASP, and MIP formulations), and data-driven techniques (reinforcement learning, supervised learning, and hybrid strategies). Through systematic analysis of experimental practices across 200+ papers, we uncover significant disparities in evaluation methodologies, with classical methods typically tested on larger-scale instances (up to 200 by 200 grids with 1000+ agents) compared to learning-based approaches (predominantly 10-100 agents). We provide a comprehensive taxonomy of evaluation metrics, environment types, and baseline selections, highlighting the need for standardized benchmarking protocols. Finally, we outline promising future directions including mixed-motive MAPF with game-theoretic considerations, language-grounded planning with large language models, and neural solver architectures that combine the rigor of classical methods with the flexibility of deep learning. This survey serves as both a comprehensive reference for researchers and a practical guide for deploying MAPF solutions in increasingly complex real-world applications.
The multi-agent path finding (MAPF) problem asks to find a set of paths on a graph such that when synchronously following these paths the agents never encounter a conflict. In the most widespread MAPF formulation, the so-called Classical MAPF, the agents sizes are neglected and two types of conflicts are considered: occupying the same vertex or using the same edge at the same time step. Meanwhile in numerous practical applications, e.g. in robotics, taking into account the agents' sizes is vital to ensure that the MAPF solutions can be safely executed. Introducing large agents yields an additional type of conflict arising when one agent follows an edge and its body overlaps with the body of another agent that is actually not using this same edge (e.g. staying still at some distinct vertex of the graph). Until now it was not clear how harder the problem gets when such conflicts are to be considered while planning. Specifically, it was known that Classical MAPF problem on an undirected graph can be solved in polynomial time, however no complete polynomial-time algorithm was presented to solve MAPF with large agents. In this paper we, for the first time, establish that the latter problem is NP-hard and, thus, if P!=NP no polynomial algorithm for it can, unfortunately, be presented. Our proof is based on the prevalent in the field technique of reducing the seminal 3SAT problem (which is known to be an NP-complete problem) to the problem at hand. In particular, for an arbitrary 3SAT formula we procedurally construct a dedicated graph with specific start and goal vertices and show that the given 3SAT formula is satisfiable iff the corresponding path finding instance has a solution.
PIBT is a popular Multi-Agent Path Finding (MAPF) method at the core of many state-of-the-art MAPF methods including LaCAM, CS-PIBT, and WPPL. The main utility of PIBT is that it is a very fast and effective single-step MAPF solver and can return a collision-free single-step solution for hundreds of agents in less than a millisecond. However, the main drawback of PIBT is that it is extremely greedy in respect to its priorities and thus leads to poor solution quality. Additionally, PIBT cannot use all the planning time that might be available to it and returns the first solution it finds. We thus develop Anytime PIBT, which quickly finds a one-step solution identically to PIBT but then continuously improves the solution in an anytime manner. We prove that Anytime PIBT converges to the optimal solution given sufficient time. We experimentally validate that Anytime PIBT can rapidly improve single-step solution quality within milliseconds and even find the optimal single-step action. However, we interestingly find that improving the single-step solution quality does not have a significant effect on full-horizon solution costs.
The vast majority of Multi-Agent Path Finding (MAPF) methods with completeness guarantees require planning full horizon paths. However, planning full horizon paths can take too long and be impractical in real-world applications. Instead, real-time planning and execution, which only allows the planner a finite amount of time before executing and replanning, is more practical for real world multi-agent systems. Several methods utilize real-time planning schemes but none are provably complete, which leads to livelock or deadlock. Our main contribution is to show the first Real-Time MAPF method with provable completeness guarantees. We do this by leveraging LaCAM (Okumura 2023) in an incremental fashion. Our results show how we can iteratively plan for congested environments with a cutoff time of milliseconds while still maintaining the same success rate as full horizon LaCAM. We also show how it can be used with a single-step learned MAPF policy. The proposed Real-Time LaCAM also provides us with a general mechanism for using iterative constraints for completeness in future real-time MAPF algorithms.
Multi-agent Path Finding (MAPF) is the problem of planning collision-free movements of agents so that they get from where they are to where they need to be. Commonly, agents are located on a graph and can traverse edges. This problem has many variations and has been studied for decades. Two such variations are the continuous-time and the lifelong MAPF problems. In the former, edges have non-unit lengths and volumetric agents can traverse them at any real-valued time. In the latter, agents must attend to a continuous stream of incoming tasks. Much work has been devoted to designing solution methods within these two areas. To our knowledge, however, the combined problem of continuous-time lifelong MAPF has yet to be addressed. This work addresses continuous-time lifelong MAPF with volumetric agents by presenting the fast and sub-optimal Continuous-time Prioritized Lifelong Planner (CPLP). CPLP continuously assigns agents to tasks and computes plans using a combination of two path planners; one based on CCBS and the other based on SIPP. Experimental results with up to 800 agents on graphs with up to 12 000 vertices demonstrate practical performance, where maximum planning times fall within the available time budget. Additionally, CPLP ensures collision-free movement even when failing to meet this budget. Therefore, the robustness of CPLP highlights its potential for real-world applications.
Multi-Agent Path Finding (MAPF) involves finding collision-free paths for multiple agents while minimizing a cost function--an NP-hard problem. Bounded suboptimal methods like Enhanced Conflict-Based Search (ECBS) and Explicit Estimation CBS (EECBS) balance solution quality with computational efficiency using focal search mechanisms. While effective, traditional focal search faces a limitation: the lower bound (LB) value determining which nodes enter the FOCAL list often increases slowly in early search stages, resulting in a constrained search space that delays finding valid solutions. In this paper, we propose a novel bounded suboptimal algorithm, double-ECBS (DECBS), to address this issue by first determining the maximum LB value and then employing a best-first search guided by this LB to find a collision-free path. Experimental results demonstrate that DECBS outperforms ECBS in most test cases and is compatible with existing optimization techniques. DECBS can reduce nearly 30% high-level CT nodes and 50% low-level focal search nodes. When agent density is moderate to high, DECBS achieves a 23.5% average runtime improvement over ECBS with identical suboptimality bounds and optimizations.
Multi-Agent Path Finding (MAPF), which focuses on finding collision-free paths for multiple robots, is crucial for applications ranging from aerial swarms to warehouse automation. Solving MAPF is NP-hard so learning-based approaches for MAPF have gained attention, particularly those leveraging deep neural networks. Nonetheless, despite the community's continued efforts, all learning-based MAPF planners still rely on decentralized planning due to variability in the number of agents and map sizes. We have developed the first centralized learning-based policy for MAPF problem called RAILGUN. RAILGUN is not an agent-based policy but a map-based policy. By leveraging a CNN-based architecture, RAILGUN can generalize across different maps and handle any number of agents. We collect trajectories from rule-based methods to train our model in a supervised way. In experiments, RAILGUN outperforms most baseline methods and demonstrates great zero-shot generalization capabilities on various tasks, maps and agent numbers that were not seen in the training dataset.
The Multi-Agent Path Finding (MAPF) problem aims to determine the shortest and collision-free paths for multiple agents in a known, potentially obstacle-ridden environment. It is the core challenge for robotic deployments in large-scale logistics and transportation. Decentralized learning-based approaches have shown great potential for addressing the MAPF problems, offering more reactive and scalable solutions. However, existing learning-based MAPF methods usually rely on agents making decisions based on a limited field of view (FOV), resulting in short-sighted policies and inefficient cooperation in complex scenarios. There, a critical challenge is to achieve consensus on potential movements between agents based on limited observations and communications. To tackle this challenge, we introduce a new framework that applies sheaf theory to decentralized deep reinforcement learning, enabling agents to learn geometric cross-dependencies between each other through local consensus and utilize them for tightly cooperative decision-making. In particular, sheaf theory provides a mathematical proof of conditions for achieving global consensus through local observation. Inspired by this, we incorporate a neural network to approximately model the consensus in latent space based on sheaf theory and train it through self-supervised learning. During the task, in addition to normal features for MAPF as in previous works, each agent distributedly reasons about a learned consensus feature, leading to efficient cooperation on pathfinding and collision avoidance. As a result, our proposed method demonstrates significant improvements over state-of-the-art learning-based MAPF planners, especially in relatively large and complex scenarios, demonstrating its superiority over baselines in various simulations and real-world robot experiments.
This paper presents a parallelizable variant of the well-known Hierarchical Cooperative A* algorithm (HCA*) for the multi-agent path finding (MAPF) problem. In this variant, all agents initially find their shortest paths disregarding the presence of others. This is done using A*. Then an intersection graph (IG) is constructed; each agent is a node and two nodes have an edge between them if the paths of corresponding agents collide. Thereafter, an independent set is extracted with the aid of an approximation algorithm for the maximum independent set problem. The paths for the agents belonging to independent set are fixed. The rest of agents now again find their shortest paths, this time ensuring no collision with the prior agents. Space-time A*, which is a crucial component of HCA*, is used here. These iterations continue until no agents are left. Since the tasks of finding shortest paths for the agents in any iteration are independent of each other, the proposed algorithm can be parallelized to a large extent. In addition to this, the task of determining the IG can also be done in parallel by dividing the map into sections and with each agent focusing on a particular section. The parallelism does come at a cost of communication between the agents and the server. This is accounted for in the simulations. As an added advantage, the user need not make a choice for the priority order. It is observed, empirically, that the proposed algorithm outperforms HCA* in terms of the computation time and the cost value in many cases. Simulations are provided for corroboration.
Multi-Agent Path Finding (MAPF) focuses on determining conflict-free paths for multiple agents navigating through a shared space to reach specified goal locations. This problem becomes computationally challenging, particularly when handling large numbers of agents, as frequently encountered in practical applications like coordinating autonomous vehicles. Quantum computing (QC) is a promising candidate in overcoming such limits. However, current quantum hardware is still in its infancy and thus limited in terms of computing power and error robustness. In this work, we present the first optimal hybrid quantum-classical MAPF algorithm which is based on branch-and-cut-and-prize. QC is integrated by iteratively solving QUBO problems, based on conflict graphs. Experiments on actual quantum hardware and results on benchmark data suggest that our approach dominates previous QUBO formulations and baseline MAPF solvers.
Distributing computations among agents in large networks reduces computational effort in multi-agent path finding (MAPF). One distribution strategy is prioritized planning (PP). In PP, we couple and prioritize interacting agents to achieve a desired behavior across all agents in the network. We characterize the interaction with a directed acyclic graph (DAG). The computation time for solving MAPF problem using PP is mainly determined through the longest path in this DAG. The longest path depends on the fixed undirected coupling graph and the variable prioritization. The approaches from literature to prioritize agents are numerous and pursue various goals. This article presents an approach for prioritization in PP to reduce the longest path length in the coupling DAG and thus the computation time for MAPF using PP. We prove that this problem can be mapped to a graph-coloring problem, in which the number of colors required corresponds to the longest path length in the coupling DAG. We propose a decentralized graph-coloring algorithm to determine priorities for the agents. We evaluate the approach by applying it to multi-agent motion planning (MAMP) for connected and automated vehicles (CAVs) on roads using, a variant of MAPF.
Multi-agent path finding (MAPF) in large networks is computationally challenging. An approach for MAPF is prioritized planning (PP), in which agents plan sequentially according to their priority. Albeit a computationally efficient approach for MAPF, the solution quality strongly depends on the prioritization. Most prioritizations rely either on heuristics, which do not generalize well, or iterate to find adequate priorities, which costs computational effort. In this work, we show how agents can compute with multiple prioritizations simultaneously. Our approach is general as it does not rely on domain-specific knowledge. The context of this work is multi-agent motion planning (MAMP) with a receding horizon subject to computation time constraints. MAMP considers the system dynamics in more detail compared to MAPF. In numerical experiments on MAMP, we demonstrate that our approach to prioritization comes close to optimal prioritization and outperforms state-of-the-art methods with only a minor increase in computation time. We show real-time capability in an experiment on a road network with ten vehicles in our Cyber-Physical Mobility Lab.
Multi-Agent Path Finding (MAPF), which focuses on finding collision-free paths for multiple robots, is crucial in autonomous warehouse operations. Lifelong MAPF (L-MAPF), where agents are continuously reassigned new targets upon completing their current tasks, offers a more realistic approximation of real-world warehouse scenarios. While cache storage systems can enhance efficiency and reduce operational costs, existing approaches primarily rely on expectations and mathematical models, often without adequately addressing the challenges of multi-robot planning and execution. In this paper, we introduce a novel mechanism called Lifelong MAPF with Cache Mechanism (L-MAPF-CM), which integrates high-level cache storage with low-level path planning. We have involved a new type of map grid called cache for temporary item storage. Additionally, we involved a task assigner (TA) with a locking mechanism to bridge the gap between the new cache grid and L-MAPF algorithm. The TA dynamically allocates target locations to agents based on their status in various scenarios. We evaluated L-MAPF-CM using different cache replacement policies and task distributions. L-MAPF-CM has demonstrated performance improvements particularly with high cache hit rates and smooth traffic conditions.
This paper proposes a novel framework to handle a multi-agent path finding problem under a limited communication range constraint, where all agents must have a connected communication channel to the rest of the team. Many existing approaches to multi-agent path finding (e.g., leader-follower platooning) overcome computational challenges of planning in this domain by planning one agent at a time in a fixed order. However, fixed leader-follower approaches can become stuck during planning, limiting their practical utility in dense-clutter environments. To overcome this limitation, we develop dynamic leading multi-agent path finding, which allows for dynamic reselection of the leading agent during path planning whenever progress cannot be made. The experiments show the efficiency of our framework, which can handle up to 25 agents with more than 90% success-rate across five environment types where baselines routinely fail.
Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics, requiring the computation of collision-free paths for multiple agents moving from their respective start to goal positions. Coordinating multiple agents in a shared environment poses significant challenges, especially in continuous spaces where traditional optimization algorithms struggle with scalability. Moreover, these algorithms often depend on discretized representations of the environment, which can be impractical in image-based or high-dimensional settings. Recently, diffusion models have shown promise in single-agent path planning, capturing complex trajectory distributions and generating smooth paths that navigate continuous, high-dimensional spaces. However, directly extending diffusion models to MAPF introduces new challenges since these models struggle to ensure constraint feasibility, such as inter-agent collision avoidance. To overcome this limitation, this work proposes a novel approach that integrates constrained optimization with diffusion models for MAPF in continuous spaces. This unique combination directly produces feasible multi-agent trajectories that respect collision avoidance and kinematic constraints. The effectiveness of our approach is demonstrated across various challenging simulated scenarios of varying dimensionality.
Multi-Agent Path Finding (MAPF) focuses on planning collision-free paths for multiple agents. However, during the execution of a MAPF plan, agents may encounter unexpected delays, which can lead to inefficiencies, deadlocks, or even collisions. To address these issues, the Switchable Temporal Plan Graph provides a framework for finding an acyclic Temporal Plan Graph with the minimum execution cost under delays, ensuring deadlock- and collision-free execution. Unfortunately, existing optimal algorithms, such as Mixed Integer Linear Programming and Graph-Based Switchable Edge Search (GSES), are often too slow for practical use. This paper introduces Improved GSES, which significantly accelerates GSES through four speedup techniques: stronger admissible heuristics, edge grouping, prioritized branching, and incremental implementation. Experiments conducted on four different map types with varying numbers of agents demonstrate that Improved GSES consistently achieves over twice the success rate of GSES and delivers up to a 30-fold speedup on instances where both methods successfully find solutions.
Multi-Agent Motion Planning (MAMP) finds various applications in fields such as traffic management, airport operations, and warehouse automation. In many of these environments, differential drive robots are commonly used. These robots have a kinodynamic model that allows only in-place rotation and movement along their current orientation, subject to speed and acceleration limits. However, existing Multi-Agent Path Finding (MAPF)-based methods often use simplified models for robot kinodynamics, which limits their practicality and realism. In this paper, we introduce a three-level framework called MASS to address these challenges. MASS combines MAPF-based methods with our proposed stationary state search planner to generate high-quality kinodynamically-feasible plans. We further extend MASS using an adaptive window mechanism to address the lifelong MAMP problem. Empirically, we tested our methods on the single-shot grid map domain and the lifelong warehouse domain. Our method shows up to 400% improvements in terms of throughput compared to existing methods.
Multi-Agent Path Finding (MAPF) seeks collision-free paths for multiple agents from their respective starting locations to their respective goal locations while minimizing path costs. Although many MAPF algorithms were developed and can handle up to thousands of agents, they usually rely on the assumption that each action of the agent takes a time unit, and the actions of all agents are synchronized in a sense that the actions of agents start at the same discrete time step, which may limit their use in practice. Only a few algorithms were developed to address asynchronous actions, and they all lie on one end of the spectrum, focusing on finding optimal solutions with limited scalability. This paper develops new planners that lie on the other end of the spectrum, trading off solution quality for scalability, by finding an unbounded sub-optimal solution for many agents. Our method leverages both search methods (LSS) in handling asynchronous actions and rule-based planning methods (PIBT) for MAPF. We analyze the properties of our method and test it against several baselines with up to 1000 agents in various maps. Given a runtime limit, our method can handle an order of magnitude more agents than the baselines with about 25% longer makespan.
Multi-Agent Path Finding (MAPF) deals with finding conflict-free paths for a set of agents from an initial configuration to a given target configuration. The Lifelong MAPF (LMAPF) problem is a well-studied online version of MAPF in which an agent receives a new target when it reaches its current target. The common approach for solving LMAPF is to treat it as a sequence of MAPF problems, periodically replanning from the agents' current configurations to their current targets. A significant drawback in this approach is that in MAPF the agents must reach a configuration in which all agents are at their targets simultaneously, which is needlessly restrictive for LMAPF. Techniques have been proposed to indirectly mitigate this drawback. We describe cases where these mitigation techniques fail. As an alternative, we propose to solve LMAPF problems by solving a sequence of modified MAPF problems, in which the objective is for each agent to eventually visit its target, but not necessarily for all agents to do so simultaneously. We refer to this MAPF variant as Transient MAPF (TMAPF) and propose several algorithms for solving it based on existing MAPF algorithms. A limited experimental evaluation identifies some cases where using a TMAPF algorithm instead of a MAPF algorithm with an LMAPF framework can improve the system throughput significantly.