Multi-Agent Path Finding Problem Research Articles

Map Connectivity and Empirical Hardness of Grid-based Multi-Agent Pathfinding Problem

Map Connectivity and Empirical Hardness of Grid-based Multi-Agent Pathfinding Problem

Integration of Efficient Techniques Based on Endpoints in Solution Method for Lifelong Multiagent Pickup and Delivery Problem

We investigate the integration of several additional efficient techniques that improve a solution method for the lifelong multiagent pickup-and-delivery (MAPD) problem to reduce the redundancy in the concurrent task execution and space usage of a warehouse map. The lifelong MAPD problem is an extended class of iterative multiagent pathfinding problems where a set of shortest collision-free travel paths of multiple agents is iteratively planned. This problem models a system in automated warehouses with robot-carrier agents that are allocated to pickup-and-delivery tasks generated on demand. In the task allocation to agents, several solution methods for lifelong MAPD problems consider the endpoints of the agents’ travel paths to avoid the deadlock situations among the paths due to the conflict of the endpoints. Since redundancies are found in the problem settings themselves and the concurrency of allocated tasks, several additional techniques have been proposed to reduce them in solution methods. However, there should be opportunities to investigate the integration of additional techniques with improvements for more practical solution methods. As analysis and an improved understanding of the additional solution techniques based on endpoints, we incrementally integrate the techniques and experimentally investigate their contributions to the quality of task allocation and the paths of the agents. Our result reveals significant complementary effects of the additionally integrated techniques and trade-offs among them in several different problem settings.

Decentralized multi-agent path finding framework and strategies based on automated negotiation

This paper introduces a negotiation framework to solve the Multi-Agent Path Finding (MAPF) Problem for self-interested agents in a decentralized fashion. The framework aims to achieve a good trade-off between the privacy of the agents and the effectiveness of solutions. Accordingly, a token-based bilateral negotiation protocol and two negotiation strategies are presented. The experimental results over four different settings of the MAPF problem show that the proposed approach could find conflict-free path solutions albeit suboptimally, especially when the search space is large and high-density. In contrast, Explicit Estimation Conflict-Based Search (EECBS) struggles to find optimal solutions. Besides, deploying a sophisticated negotiation strategy that utilizes information about local density for generating alternative paths can yield remarkably better solution performance in this negotiation framework.

A proposal on multi-agent static path planning strategy for minimizing radiation dose

To minimize the cumulative radiation dose, various path-finding approaches for single agent have been proposed. However, for emergence situations such as nuclear power plant accident, these methods cannot be effectively utilized for evacuating a large number of workers because no multi-agent method is valid to conduct the mission. In this study, a novel algorithm for solving the multi-agent path-finding problem is proposed using the conflict-based search approach and the objective function redefined in terms of the cumulative radiation dose. The proposed method can find multi paths that all agents arrive at the destinations with reducing the overall radiation dose. To verify the proposed method, three problems were defined. In the single-agent problem, the objective function proposed in this study reduces the cumulative dose by 82% compared with that of the shortest distance algorithm in experiment environment of this study. It was also verified in the two multi-agent problems that multi paths with minimized the overall radiation dose, in which all agents can reach the destination without collision, can be found. The method proposed in this study will contribute to establishing evacuation plans for improving the safety of workers in radiation-related facilities.

Multi-Agent Open Framework: Developing a Holistic System to Solve MAPF (Student Abstract)

Automation in industries is becoming an ever-increasing necessity, especially in the sector of logistics. In many cases, this means having many different automated guided vehicles (AGVs) moving at the same time, hence needing coordination to avoid conflicts between different agents. The problem of organizing a fleet of autonomous robots is known as the Multi-Agent Path Finding (MAPF) problem in the literature for which several optimal and sub-optimal algorithms have been proposed. When faced with real-life scenarios, these algorithms must provide the best feasible solution in the shortest time possible, therefore they must scale for large scenarios and be efficient. In this work, we briefly describe our open-source framework we are working on and we lay down the research paths we are going to focus on. The goal is to develop a holistic system that allows to control different aspects of the MAPF problem, from graph topology to goal scheduling.

Priority-Based Search for the Virtual Network Embedding Problem

The Virtual Network Embedding (VNE) problem is a constrained optimization problem. It arises in the context of allocating resources on heterogeneous physical networks to provide end-to-end computing services. In this paper, we introduce a new solver, called VNE-PBS, that uses priority-based search (PBS) for solving the VNE problem. VNE-PBS uses a prioritized heuristic search algorithm that explores the space of all possible priority orderings using a systematic depth-first search. The solver is inspired by the success of PBS for the Multi-Agent Path Finding (MAPF) problem and the similarities between the VNE and MAPF problems. We show that VNE-PBS significantly outperforms competing methods on various benchmark instances for both the offline and online versions of the VNE problem.

Exact Anytime Multi-Agent Path Finding Using Branch-and-Cut-and-Price and Large Neighborhood Search

Given a set of agents on a grid, the multi-agent path finding problem aims to find a path that moves each agent from its given start location to its target location such that they do not collide and that the sum of arrival times is minimized. LNS2 is a state-of-the-art algorithm for anytime, suboptimal solving. It is an upper-bounding algorithm that repeatedly adjusts an existing solution and, being a local search, is oblivious to optimality. BCP is a state-of-the-art algorithm for exact solving. It is a lower-bounding tree search that attempts to tighten the lower bound until a solution appears. As BCP operates on the lower bound, the first solution it finds is optimal or nearly optimal, and therefore has poor anytime behavior. This paper proposes to tightly couple LNS2 and BCP to achieve better anytime, suboptimal solving while retaining the optimality guarantee of BCP. Experiments indicate that the combination achieves better anytime behavior than BCP in general and better suboptimal performance than LNS2 on congested maps.

Multi Agent Path Finding under Obstacle Uncertainty

In multi-agent path finding (MAPF), several agents must move from their current positions to their target positions without colliding. Prior work on MAPF commonly assumed perfect knowledge of the environment. We consider a MAPF setting where this is not the case, and the planner does not know a-priori whether some positions are blocked or not. To sense whether such a position is traversable, an agent must move close to it and adapt its behavior accordingly. In this work we focus on solving this type of MAPF problem, for cases where planning is centralized but cannot be done during execution. In this setting, a solution can be formulated as a plan tree for each agent, branching on the observations. We propose algorithms for finding such plans trees for two modes of executions: centralized, where the agents share information concerning observed obstacles during execution, a decentralized, where such communication is not allowed. The proposed algorithms are complete and can be configured to optimize solution cost, measured for either the best case or the worst case. We implemented these algorithms and provide experimental results demonstrating how our approach scales with respect to the number of agents and the number of positions we are uncertain about. The results show that our algorithms can solve non-trivial problems, but also highlight that this type of MAPF problems is significantly harder than classical MAPF.

Exploiting Geometric Constraints in Multi-Agent Pathfinding

In tackling the multi-agent pathfinding problem (MAPF), we study a specific class of paths that are constructed by taking the agents’ shortest paths from the start to the goal locations and adding safe delays at the beginning of the paths, which guarantee that they are non-conflicting. Safe delays are calculated by exploiting a set of fundamental geometric constraints among the distances between all agents’ start and goal locations. Those constraints are simple, but the MAPF problem reformulated in terms of them remains computationally hard. Nonetheless, based on safe delays, we devise a new, fast and lightweight algorithm, called Delayed Shortest Path (DSP), to find solutions to the MAPF problem. Via an extensive experimental evaluation on standard benchmarks, we show that, in many cases, our technique runs several orders of magnitudes faster than related methods while addressing problems with thousands of agents and returning low-cost solutions.

Intelligent Planning for Large-Scale Multi-Robot Coordination

Robots will play a crucial role in the future and need to work as a team in increasingly more complex applications. Advances in robotics have laid the hardware foundations for building large-scale multi-robot systems. But how to coordinate robots intelligently is a difficult problem. We believe that graph-search-based planning can systematically exploit the combinatorial structure of multi-robot coordination problems and efficiently generate solutions with rigorous guarantees on correctness, completeness, and solution quality. We started with one problem that is central to many multi-robot applications. Multi-Agent Path Finding (MAPF) is an NP-hard problem of planning collision-free paths for a team of agents while minimizing their travel times. We addressed the MAPF problem from both (1) a theoretical perspective by developing efficient algorithms to solve large MAPF instances with completeness and optimality guarantees via a variety of AI and optimization technologies, such as constraint reasoning, heuristic search, stochastic local search, and machine learning, and (2) an applicational perspective by developing algorithmic techniques for integrating MAPF with task planning and execution for various multi-robot systems, such as mobile robot coordination, traffic management, drone swarm control, multi-arm assembly, and character control in video games. This paper is part of the AAAI-23 New Faculty Highlights.

Solving an industry-inspired generalization of lifelong MAPF problem including multiple delivery locations

In this study, we worked on a new industry-inspired generalization of the multi-agent path finding (MAPF) problem. In this new problem, incoming jobs should be assigned to agents in a way that minimizes the total path cost. In this problem, definition of a job is visiting a certain coordinate by the agent. In addition, the agents must keep the following tasks on their own lists and decide the order of visiting the tasks assigned to them by minimizing the total distance traveled. This new structure can be applied to many real-world problems like cleaning an area with autonomous robots, automated warehouses and area protection with autonomous robots. In solving this problem, three different problems must be solved; to which agent a new job will be assigned, in what order the agents will handle that job, and finally, how agents will act without colliding with each other when the agents have multiple destinations. This problem is different from the job-distribution problems in the MAPF literature since the optimization criterion is total path cost and agents have to decide the order of the jobs to be visited. For this reason, new job-distribution methods that meet these goals are presented in this study. Five new heuristic algorithms that produce fast solutions for job-distribution are presented. Furthermore, we presented one brute force algorithm to find the optimal path-cost solution and compare with the heuristics created. Experiments conducted on benchmark maps have demonstrated that the job-distribution algorithm yielding the best performance resulted in path costs that were at most three to three and a half percent higher compared to the brute force approach. Additionally, the heuristics developed were found to operate at least ten times faster in terms of processing time when compared to the brute force approach. The CBS-D*-lite algorithm was previously presented in the literature and shown to produce good results in incremental environments. With these modifications, agents can have multiple destinations and collisions between the agent paths are avoided.

A decoupling method for solving the multi-agent path finding problem

Many existing multi-agent path finding (MAPF) solvers focus on completeness, speed, or optimization. However, completeness and rapidity are usually in conflict with each other, which makes these algorithms far from satisfactory in practical applications. Motivated by this realistic requirement, we propose an efficient decoupling method to accelerate the solution of large MAPF problems. First, we define the concept of ‘non-essential vertex’-vertices which are not needed to solve a MAPF problem, and a scheme to identify them. Then, a decoupling scheme based on ‘non-essential vertex’ is proposed, which will assign higher priorities to agents whose goal positions are non-essential vertices and lower priorities to agents whose start positions are non-essential vertices. That is, invoking our decoupling algorithm can decouple any given MAPF problem into three subproblems while maintaining the completeness of the solution. All three sub-MAPF problems can be solved sequentially by a complete solver (e.g., CBS or EECBS, etc.), and two of them can also be solved by a prioritized planning algorithm. We have conducted several experiments in different workspaces, and the statistical results show that the proposed decoupling method significantly improves the speed and success rate of existing MAPF solvers with almost no degradation in solution quality when solving problems with high agent density. In addition, the solving efficiency can be further improved if the prioritized planning algorithm is invoked to solve the first and third sub-MAPF problems.

Conflict-tolerant and conflict-free multi-agent meeting

In the Multi-Agent Meeting problem (MAM), the task is to find the optimal meeting location for multiple agents, as well as a path for each agent to that location. Among all possible meeting locations, the optimal meeting location has the minimum cost according to a given cost function. Two cost functions are considered in this research: (1) the sum of all agents paths' costs to the meeting location (SOC) and (2) the cost of the longest path among them (MKSP). MAM has many real-life applications, such as choosing a gathering point for multiple traveling agents (humans, cars, or robots).In this paper, we divide MAM into two variants. In its basic version, MAM allows multiple agents to occupy the same location, i.e., it is conflict tolerant. For MAM, we introduce MM*, a Multi-Directional Heuristic Search algorithm, that finds the optimal meeting location under different cost functions. MM* generalizes the Meet in the Middle (MM) bidirectional search algorithm to the case of finding an optimal meeting location for multiple agents. Several admissible heuristics are proposed for MM*, and experiments demonstrate the benefits of MM*.As agents may be embodied in the world, a solution to MAM may contain conflicting paths, where more than one agent occupies the same location at the same time. The second variant of the MAM problem is called Conflict-Free Multi-Agent Meeting (CF-MAM), where the task is to find the optimal meeting location for multiple agents (as in MAM) as well as conflict-free paths (in the same manner as the prominent Multi-Agent Path Finding problem (MAPF)) to that location. For optimally solving CF-MAM, we introduce two novel algorithms, which combine MAM and MAPF solvers. We prove the optimality of both algorithms and compare them experimentally, showing the pros and cons of each algorithm.1

Conflict-Based Search for Optimal Multi-Agent Pathfinding

We are assumed a customary of mediators in the multi-agent pathfinding problem (MAPF), each of which has its own start and goal positions. The objective is to discovery paths for each agent without causing any collisions. The majority of previous work on the optimal solution to this issue has useful single-agent exploration variations of the A* algorithm and treated each agent as a single "joint agent." The Conflict Based Search (CBS) optimum multi-agent pathfinding algorithm is the subject of this paper. CBS has two layer algorithm that does not use a single "joint agent" model to solve the problem. A Conflict Tree (CT), which is a tree based on conflicts between individual agents, is the high-level search engine. In the CT, each node represents a set of constraints on the agents' motion. To meet the high-level CT node's constraints, quick single-agent searches are carried out at the low level. CBS can frequently examine fewer states than A* while still maintaining optimality thanks to this two-level formulation. We discuss CBS's advantages and disadvantages. The Meta-Agent CBS (MA-CBS) algorithm is also discussed.MA-CBS is a broadening of CBS.MA-CBS, in contrast to basic CBS, permits low-level single-agent searches. Instead, agents can be combined into small groups of joint agents with MA-CBS. Performance is further enhanced and some of the drawbacks of basic CBS are reduced as a result. In point of fact, MA-CBS is a framework that can be layered on top of any MAPF solver that is both complete and optimal to boost its performance. A speedup of up to an order of magnitude over previous methods is demonstrated by experimental results on various problems. We are given a set of agents in the multi-agent pathfinding problem (MAPF), each of which has its own start and goal positions. The objective is to find paths for each agent without causing any collisions. The majority of previous work on the optimal solution to this issue has applied single-agent search variants of the A* algorithm and treated each agent as a single "joint agent." The Conflict Based Search (CBS) optimal multi-agent pathfinding algorithm is the subject of this paper. CBS is a two-level algorithm that does not use a single "joint agent" model to solve the problem. A Conflict Tree (CT), which is a tree based on conflicts between individual agents, is the high-level search engine. In the CT, each node represents a set of constraints on the agents' motion. To meet the high-level CT node's constraints, quick single-agent searches are carried out at the low level. CBS can frequently examine fewer states than A* while still maintaining optimality thanks to this two-level formulation. We discuss CBS's advantages and disadvantages. The Meta-Agent CBS (MA-CBS) algorithm is also discussed.MA-CBS is a broadening of CBS.MA-CBS, in contrast to basic CBS, permits low-level single-agent searches. Instead, agents can be combined into small groups of joint agents with MA-CBS. Performance is further enhanced and some of the drawbacks of basic CBS are reduced as a result. In point of fact, MA-CBS is a framework that can be layered on top of any MAPF solver that is both complete and optimal to boost its performance. A speedup of up to an order of magnitude over previous methods is demonstrated by experimental results on various problems.

Shadoks Approach to Low-Makespan Coordinated Motion Planning

This article describes the heuristics used by the Shadoks 1 team for the CG:SHOP 2021 challenge. This year’s problem is to coordinate the motion of multiple robots in order to reach their targets without collisions and minimizing the makespan. It is a classical multi-agent path finding problem with the specificity that the instances are highly dense in an unbounded grid. Using the heuristics outlined in this article, our team won first place with the best solution to 202 out of 203 instances and optimal solutions to at least 105 of them. The main ingredients include several different strategies to compute initial solutions coupled with a heuristic called Conflict Optimizer to reduce the makespan of existing solutions.

A Conflict Avoidance Table for Continuous Conflict-Based Search (Extended Abstract)

Conflict-Based Search is a state-of-the-art algorithm solving the Multi-Agent Path Finding problem. Given multiple agents with start and goal locations, the problem is to find a set of collision-free paths of minimal cost. Continuous Conflict-Based Search is a recent adaptation of this algorithm for continuous time and agents with physical shapes. However, an important ingredient has not been adapted to this continuous version: the Conflict Avoidance Table. It is used as a tie-breaking strategy in single-agent search phases to favor paths causing fewer conflicts with the other agents. This paper explains how the R-Tree can be used as a Conflict Avoidance Table for Continuous Conflict-Based Search. The experiments show that using the Conflict Avoidance Table can reduce the number of nodes expanded by the algorithm by a large margin. As a result, the solving time is improved proportionally and especially when using the implementation based on R-Trees as opposed to a naive implementation.

Online Multi-Agent Path Finding: New Results

Online MAPF extends the classical Multi-Agent Path Finding problem (MAPF) by considering a more realistic problem in which new agents may appear over time. As online solvers are not aware of which agents will join in the future, the notion of snapshot-optimal was defined, where only current knowledge is considered. In this paper, we perform an extensive comparison between oracle-optimal solutions (where the solver is preinformed of future agents), snapshot-optimal solutions, and suboptimal solutions obtained by prioritised planning.

Which MAPF Model Works Best for Automated Warehousing?

Multi-Agent Path Finding (MAPF) algorithms and their variants can find high-quality collision-free plans for automated warehousing under simplified assumptions about the robot dynamics. However, these simplifying assumptions pose challenging implementational issues as the robots cannot follow the plans precisely. Various robust execution frameworks, such as the Action Dependency Graph (ADG) framework, have been proposed to enable the real-world execution of MAPF plans. Under such a framework, it is unclear how the simplifying assumptions affect the performance of the robots. In this work, we first argue that the ADG framework provides the same robustness guarantees as the single-agent framework (where plans are generated independently for each robot and collisions are avoided through a reservation table), which is widely used in industry. We then improve the efficiency of the ADG framework by integrating it with the Rolling-Horizon Collision-Resolution framework to solve MAPF problems with a persistent stream of online tasks. Using the integrated framework, we compare the standard MAPF model with many of its more complex variants, such as MAPF with rotation, k-robust MAPF, and continuous-time MAPF (taking robot dynamics into account). We examine their effectiveness in improving throughput through realistic simulations of warehouse settings with the Gazebo simulator.

Mutex Propagation in Multi-Agent Path Finding for Large Agents

Mutex propagation and its concomitant symmetry-breaking techniques have proven useful in Multi-Agent Path Finding (MAPF) with point agents. In this paper, we show that they can be easily generalized to richer MAPF problems. In particular, we demonstrate their application to MAPF with ``Large'' Agents (LA-MAPF). Here, agents can occupy multiple points at the same time according to their fixed shapes and sizes. While existing rule-based symmetry-breaking techniques are difficult to generalize from point agents to large agents, mutex-based symmetry-breaking techniques can be generalized easily. In a Conflict-Based Search (CBS) framework for LA-MAPF, we also develop a mutex-based conflict-selection strategy to further enhance the efficiency of the search. Through experiments on various maps, we show that our techniques significantly improve MC-CBS, a state-of-the-art optimal LA-MAPF algorithm, in terms of both success rate and runtime.

Shard Systems: Scalable, Robust and Persistent Multi-Agent Path Finding with Performance Guarantees

Modern multi-agent robotic systems increasingly require scalable, robust and persistent Multi-Agent Path Finding (MAPF) with performance guarantees. While many MAPF solvers that provide some of these properties exist, none provides them all. To fill this need, we propose a new MAPF framework, the shard system. A shard system partitions the workspace into geographic regions, called shards, linked by a novel system of buffers. Agents are routed optimally within a shard by a local controller to local goals set by a global controller. The buffer system novelly allows shards to plan with perfect parallelism, providing scalability. A novel global controller algorithm can rapidly generate an inter-shard routing plan for thousands of agents while minimizing the traffic routed through any shard. A novel workspace partitioning algorithm produces shards small enough to replan rapidly. These innovations allow a shard system to adjust its routing plan in real time if an agent is delayed or assigned a new goal, enabling robust, persistent MAPF. A shard system's local optimality and optimized inter-shard routing bring the sum-of-costs of its solutions to single-shot MAPF problems to < 20-60% of optimal on a diversity of workspaces. Its scalability allows it to plan paths for 1000s of agents in seconds. If any of their goals change or move actions fails, a shard system can replan in under a second.