We study GCS-TSP, a variant of the Traveling Salesman Problem (TSP) defined over a Graph of Convex Sets (GCS) - a powerful representation for trajectory planning that decomposes the configuration space into convex regions connected by a sparse graph. In GCS-TSP, edge costs are not fixed but depend on the specific trajectory passing through each convex region, making classical TSP methods inapplicable. We introduce GHOST, a hierarchical framework that optimally solves GCS-TSP by combining combinatorial tour search with convex trajectory optimization. GHOST systematically explores tours on a complete graph induced by the GCS, using a novel abstract-path-unfolding algorithm to compute admissible lower bounds that guide best-first search at both the high level (over tours) and the low level (over feasible GCS paths realizing the tour). These bounds provide strong pruning power, reducing unnecessary optimization calls. We prove that GHOST guarantees optimality and present a bounded-suboptimal variant for time-critical settings. Experiments show that GHOST is orders-of-magnitude faster than unified mixed-integer convex programming baseline while uniquely handling complex problems involving high-order continuity constraints and incomplete GCSs.

We address the Multi-Robot Motion Planning (MRMP) problem of computing collision-free trajectories for multiple robots in shared continuous environments. While existing frameworks effectively decompose MRMP into singlerobot subproblems, spatiotemporal motion planning with dynamic obstacles remains challenging, particularly in cluttered or narrow-corridor settings. We propose Space-Time Graphs of Convex Sets (ST-GCS), a novel planner that systematically covers the collision-free space-time domain with convex sets instead of relying on random sampling. By extending Graphs of Convex Sets (GCS) into the time dimension, ST-GCS formulates time-optimal trajectories in a unified convex optimization that naturally accommodates velocity bounds and flexible arrival times. We also propose Exact Convex Decomposition (ECD) to "reserve" trajectories as spatiotemporal obstacles, maintaining a collision-free space-time graph of convex sets for subsequent planning. Integrated into two prioritized-planning frameworks, ST-GCS consistently achieves higher success rates and better solution quality than state-of-the-art sampling-based planners— often at orders-of-magnitude faster runtimes—underscoring its benefits for MRMP in challenging settings. Project page: https://sites.google.com/view/stgcs.

Multi-Agent Path Finding (MAPF) aims to arrange collision-free goal-reaching paths for a group of agents. Anytime MAPF solvers based on large neighborhood search (LNS) have gained prominence recently due to their flexibility and scalability, leading to a surge of methods, especially those leveraging machine learning, to enhance neighborhood selection. However, several pitfalls exist and hinder a comprehensive evaluation of these new methods, which mainly include: 1) Lower than actual or incorrect baseline performance; 2) Lack of a unified evaluation setting and criterion; 3) Lack of a codebase or executable model for supervised learning methods. To address these challenges, we introduce a unified evaluation framework, implement prior methods, and conduct an extensive comparison of prominent methods. Our evaluation reveals that rule-based heuristics serve as strong baselines, while current learning-based methods show no clear advantage on time efficiency or improvement capacity. Our extensive analysis also opens up new research opportunities for improving MAPF-LNS, such as targeting high-delayed agents, applying contextual algorithms, optimizing replan order and neighborhood size, where machine learning can potentially be integrated.

We study Multi-Robot Coverage Path Planning (MCPP) on a 4-neighbor 2D grid$G$, which aims to compute paths for multiple robots to cover all cells of$G$. Traditional approaches are limited as they first compute coverage trees on a quadrant coarsened grid$\mathcal {H}$and then employ the Spanning Tree Coverage (STC) paradigm to generate paths on$G$, making them inapplicable to grids with partially obstructed$2 \times 2$blocks. To address this limitation, we reformulate the problem directly on$G$, revolutionizing grid-based MCPP solving and establishing new NP-hardness results. We introduce Extended-STC (ESTC), a novel paradigm that extends STC to ensure complete coverage with bounded suboptimality, even when$\mathcal {H}$includes partially obstructed blocks. Furthermore, we present LS-MCPP, a new algorithmic framework that integrates ESTC with three novel types of neighborhood operators within a local search strategy to optimize coverage paths directly on$G$. Unlike prior grid-based MCPP work, our approach also incorporates a versatile post-processing procedure that applies Multi-Agent Path Finding (MAPF) techniques to MCPP for the first time, enabling a fusion of these two important fields in multi-robot coordination. This procedure effectively resolves inter-robot conflicts and accommodates turning costs by solving a MAPF variant, making our MCPP solutions more practical for real-world applications. Extensive experiments demonstrate that our approach significantly improves solution quality and efficiency, managing up to 100 robots on grids as large as$256 \times 256$within minutes of runtime. Validation with physical robots confirms the feasibility of our solutions under real-world conditions.

We study graph-based Multi-Robot Coverage Path Planning (MCPP) that aims to compute coverage paths for multiple robots to cover all vertices of a given 2D grid terrain graph G. Existing graph-based MCPP algorithms first compute a tree cover on G---a forest of multiple trees that cover all vertices---and then employ the Spanning Tree Coverage (STC) paradigm to generate coverage paths on the decomposed graph D of the terrain graph G by circumnavigating the edges of the computed trees, aiming to optimize the makespan (i.e., the maximum coverage path cost among all robots). In this paper, we take a different approach by exploring how to systematically search for good coverage paths directly on D. We introduce a new algorithmic framework, called LS-MCPP, which leverages a local search to operate directly on D. We propose a novel standalone paradigm, Extended-STC (ESTC), that extends STC to achieve complete coverage for MCPP on any decomposed graph, even those resulting from incomplete terrain graphs. Furthermore, we demonstrate how to integrate ESTC with three novel types of neighborhood operators into our framework to effectively guide its search process. Our extensive experiments demonstrate the effectiveness of LS-MCPP, consistently improving the initial solution returned by two state-of-the-art baseline algorithms that compute suboptimal tree covers on G, with a notable reduction in makespan by up to 35.7% and 30.3%, respectively. Moreover, LS-MCPP consistently matches or surpasses the results of optimal tree cover computation, achieving these outcomes with orders of magnitude faster runtime, thereby showcasing its significant benefits for large-scale real-world coverage tasks.

We introduce Multi-Robot Connected Fermat Spiral (MCFS), a novel algorithmic framework for Multi-Robot Coverage Path Planning (MCPP) that adapts Coverage Fermat Spiral (CFS) from the computer graphics community to multi-robot coordination for the first time. MCFS uniquely enables the orchestration of multiple robots to generate coverage paths that contour around arbitrarily shaped obstacles, a feature notably lacking in traditional methods. Our framework not only enhances area coverage and optimizes task performance, particularly in terms of makespan, for workspaces rich in irregular obstacles but also addresses the challenges of path continuity and curvature critical for non-holonomic robots by generating smooth paths without decomposing the workspace. MCFS solves MCPP by constructing a graph of isolines and transforming MCPP into a combinatorial optimization problem, aiming to minimize the makespan while covering all vertices. Our contributions include developing a unified CFS version for scalable and adaptable MCPP, extending it to MCPP with novel optimization techniques for cost reduction and path continuity and smoothness, and demonstrating through extensive experiments that MCFS outperforms existing MCPP methods in makespan, path curvature, coverage ratio, and overlapping ratio. Our research marks a significant step in MCPP, showcasing the fusion of computer graphics and automated planning principles to advance the capabilities of multi-robot systems in complex environments. Our code is publicly available at https://github.com/reso1/MCFS.

We study a decentralized version of Moving Agents in Formation (MAiF), a variant of Multi-Agent Path Finding aiming to plan collision-free paths for multiple agents with the dual objectives of reaching their goals quickly while maintaining a desired formation. The agents must balance these objectives under conditions of partial observation and limited communication. The formation maintenance depends on the joint state of all agents, whose dimensionality increases exponentially with the number of agents, rendering the learning process intractable. Additionally, learning a single policy that can accommodate different linear preferences for these two objectives presents a significant challenge. In this paper, we propose Mean-Field Control with Envelop Q-learning (MFC-EQ), a scalable and adaptable learning framework for this bi-objective multi-agent problem. We approximate the dynamics of all agents using mean-field theory while learning a universal preference-agnostic policy through envelop Q-learning. Our empirical evaluation of MFC-EQ across numerous instances shows that it outperforms state-of-the-art centralized MAiF baselines. Furthermore, MFC-EQ effectively handles more complex scenarios where the desired formation changes dynamically—a challenge that existing MAiF planners cannot address.

We investigate time-optimal Multi-Robot Coverage Path Planning (MCPP) for both unweighted and weighted terrains, which aims to minimize the coverage time, defined as the maximum travel time of all robots. Specifically, we focus on a reduction from MCPP to Min-Max Rooted Tree Cover (MMRTC). For the first time, we propose a Mixed Integer Programming (MIP) model to optimally solve MMRTC, resulting in an MCPP solution with a coverage time that is provably at most four times the optimal. Moreover, we propose two suboptimal yet effective heuristics that reduce the number of variables in the MIP model, thus improving its efficiency for large-scale MCPP instances. We show that both heuristics result in reduced-size MIP models that remain complete (i.e., guaranteed to find a solution if one exists) for all MMRTC instances. We validate the effectiveness of our MIP-based MCPP planner through experiments that compare it with two state-of-the-art MCPP planners on various instances, demonstrating a reduction in the coverage time by an average of 27.65% and 23.24% over them, respectively.

We study graph-based Multi-Robot Coverage Path Planning (MCPP) that aims to compute paths for multiple robots to cover all vertices of a given 2D grid terrain graph G. Existing graph-based MCPP algorithms rely on computing a tree cover on G and then employ the Spanning Tree Coverage (STC) paradigm to generate coverage paths on the decomposed graph D of G. In this paper, we take a different approach by exploring how to systematically search for good coverage paths directly on D. We introduce a new algorithmic framework, called LS-MCPP, which leverages a local search to operate directly on D. We propose ESTC, that extends STC to achieve complete coverage for MCPP on any decomposed graphs, even those resulting from incomplete terrain graphs. Furthermore, we demonstrate how to integrate ESTC with three novel types of neighborhood operators into our framework to effectively guide its search process. Remarkably, LS-MCPP scales efficiently to handle MCPP instances with 32 robots on terrain graphs with 11,892 vertices with just minutes of runtime, thereby showcasing its significant benefits for large-scale real-world coverage tasks.

We formalize and study the multi-goal task assignment and path finding (MG-TAPF) problem from theoretical and algorithmic perspectives. The MG-TAPF problem is to compute an assignment of tasks to agents, where each task consists of a sequence of goal locations, and collision-free paths for the agents that visit all goal locations of their assigned tasks in sequence. Theoretically, we prove that the MG-TAPF problem is NP-hard to solve optimally. We present algorithms that build upon algorithmic techniques for the multi-agent path finding problem and solve the MG-TAPF problem optimally and bounded-suboptimally. We experimentally compare these algorithms on a variety of different benchmark domains.

In this work, we consider the Multi-Agent Pickup-and-Delivery (MAPD) problem, where agents constantly engage with new tasks and need to plan collision-free paths to execute them. To execute a task, an agent needs to visit a pair of goal locations, consisting of a pickup location and a delivery location. We propose two variants of an algorithm that assigns a sequence of tasks to each agent using the anytime algorithm Large Neighborhood Search (LNS) and plans paths using the Multi-Agent Path Finding (MAPF) algorithm Priority-Based Search (PBS). LNS-PBS is complete for well-formed MAPD instances, a realistic subclass of MAPD instances, and empirically more effective than the existing complete MAPD algorithm CENTRAL. LNS-wPBS provides no completeness guarantee but is empirically more efficient and stable than LNS-PBS. It scales to thousands of agents and thousands of tasks in a large warehouse and is empirically more effective than the existing scalable MAPD algorithm HBH+MLA*. LNS-PBS and LNS-wPBS also apply to a more general variant of MAPD, namely the Multi-Goal MAPD (MG-MAPD) problem, where tasks can have different numbers of goal locations.

Multi-Agent Path Finding (MAPF) is essential to large-scale robotic systems. Recent methods have applied reinforcement learning (RL) to learn decentralized polices in partially observable environments. A fundamental challenge of obtaining collision-free policy is that agents need to learn co-operation to handle congested situations. This paper combines communication with deep Q-learning to provide a novel learning based method for MAPF, where agents achieve cooperation via graph convolution. To guide RL algorithm on long-horizon goal-oriented tasks, we embed the potential choices of shortest paths from single source as heuristic guidance instead of using a specific path as in most existing works. Our method treats each agent independently and trains the model from a single agent’s perspective. The final trained policy is applied to each agent for decentralized execution. The whole system is distributed during training and is trained under a curriculum learning strategy. Empirical evaluation in obstacle-rich environment indicates the high success rate with low average step of our method.

This is an extended abstract of a paper to be published at ICAPS 2021. We study online Multi-Agent Path Finding (MAPF), where new agents are constantly revealed over time and all agents must find collision-free paths to their given goal locations. We generalize existing complexity results of (offline) MAPF to online MAPF. We classify online MAPF algorithms into different categories. We present several complexity and competitiveness results for online MAPF and its algorithms, which provides theoretical insights into the effectiveness of using MAPF algorithms in an online setting for the first time.

Multi-Agent Path Finding (MAPF) is the combinatorial problem of finding collision-free paths for multiple agents on a graph. This paper describes MAPF-based software for solving train planning and replanning problems on large-scale railway networks under uncertainty. The software recently won the 2020 Flatland Challenge, a NeurIPS competition trying to determine how to efficiently manage dense traffic on rail networks. The software incorporates many state-of-the-art MAPF, or in general, optimization technologies, such as prioritized planning, large neighborhood search, safe interval path planning, minimum communication policies, parallel computing, and simulated annealing. It can plan collision-free paths for thousands of trains within a few minutes and deliver deadlock-free actions in real-time during execution.

In this paper, we study the one-shot and lifelong versions of the Target Assignment and Path Finding problem in automated sortation centers, where each agent needs to constantly assign itself a sorting station, move to its assigned station without colliding with obstacles or other agents, wait in the queue of that station to obtain a parcel for delivery, and then deliver the parcel to a sorting bin. The throughput of such centers is largely determined by the total idle time of all stations since their queues can frequently become empty. To address this problem, we first formalize and study the one-shot version that assigns stations to a set of agents and finds collision-free paths for the agents to their assigned stations. We present efficient algorithms for this task based on a novel min-cost max-flow formulation that minimizes the total idle time of all stations in a fixed time window. We then demonstrate how our algorithms for solving the one-shot problem can be applied to solving the lifelong problem as well. Experimentally, we believe to be the first researchers to consider real-world automated sortation centers using an industrial simulator with realistic data and a kinodynamic model of real robots. On this simulator, we showcase the benefits of our algorithms by demonstrating their efficiency and effectiveness for up to 350 agents.

In this paper, we formalize and study the Moving Agents in Formation (MAiF) problem, that combines the tasks of finding short collision-free paths for multiple agents and keeping them in close adherence to a desired formation. Previous work includes controller-based algorithms, swarm-based algorithms, and potential-field-based algorithms. They usually focus on only one or the other of these tasks, solve the problem greedily without systematic search, and thus generate costly solutions or even fail to find solutions in congested environment. In this paper, we develop a two-phase search algorithm, called SWARM-MAPF, whose first phase is inspired by swarm-based algorithms (in open regions) and whose second phase is inspired by multi-agent path-finding (MAPF) algorithms (in congested regions). In the first phase, SWARM-MAPF selects a leader among the agents and finds a path for it that is sufficiently far away from the obstacles so that the other agents can preserve the desired formation around it. It also identifies the critical segments of the leader's path where the other agents cannot preserve the desired formation and the refinement of which has thus to be delegated to the second phase. In the second phase, SWARM-MAPF refines these segments. Theoretically, we prove that SWARM-MAPF is complete. Empirically, we show that SWARM-MAPF scales well and is able to find close-to-optimal solutions.

We consider two new types of pairwise path symmetries which appear in the context of Multi-Agent Path Finding (MAPF). The first of them, corridor symmetry, arises when two agents attempt to pass through the same narrow passage but in opposite directions. The second, target symmetry, arises when the shortest path of one agent requires the target location of a second agent after the second agent has already arrived. These symmetries can produce an exponential blowup in the space of possible collision resolutions, leading to timeout failure even for state-of-the-art algorithms such as Conflict-Based Search. We propose to break symmetries using new reasoning techniques that: (1) detect each type of situation and, (2) resolve them by introducing specialized constraints. We implement our ideas in the context of Conflict-Based Search where, in a range of experiments, we report up to an order-of-magnitude improvement in runtime performance and, in some cases, more than a doubling in success rate.

The Multi-Agent Pickup and Delivery (MAPD) problem models applications where a large number of agents attend to a stream of incoming pickup-and-delivery tasks. Token Passing (TP) is a recent MAPD algorithm that is efficient and effective. We make TP even more efficient and effective by using a novel combinatorial search algorithm, called Safe Interval Path Planning with Reservation Table (SIPPwRT), for single-agent path planning. SIPPwRT uses an advanced data structure that allows for fast updates and lookups of the current paths of all agents in an online setting. The resulting MAPD algorithm TP-SIPPwRT takes kinematic constraints of real robots into account directly during planning, computes continuous agent movements with given velocities that work on non-holonomic robots rather than discrete agent movements with uniform velocity, and is complete for wellformed MAPD instances. We demonstrate its benefits for automated warehouses using both an agent simulator and a standard robot simulator. For example, we demonstrate that it can compute paths for hundreds of agents and thousands of tasks in seconds and is more efficient and effective than existing MAPD algorithms that use a post-processing step to adapt their paths to continuous agent movements with given velocities.

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-driven combinatorial search framework. In a variety of empirical comparisons, we demonstrate state-of-the-art solution qualities and success rates, often with similar runtimes to existing algorithms. We also develop new theoretical results that explore the limitations of prioritized planning, in terms of completeness and optimality, for the first time.

We describe a new way of reasoning about symmetric collisions for Multi-Agent Path Finding (MAPF) on 4-neighbor grids. We also introduce a symmetry-breaking constraint to resolve these conflicts. This specialized technique allows us to identify and eliminate, in a single step, all permutations of two currently assigned but incompatible paths. Each such permutation has exactly the same cost as a current path, and each one results in a new collision between the same two agents. We show that the addition of symmetry-breaking techniques can lead to an exponential reduction in the size of the search space of CBS, a popular framework for MAPF, and report significant improvements in both runtime and success rate versus CBSH and EPEA* – two recent and state-of-the-art MAPF algorithms.

Multi-Agent Path Finding (MAPF) has been widely studied in the AI community. For example, Conflict-Based Search (CBS) is a state-of-the-art MAPF algorithm based on a twolevel tree-search. However, previous MAPF algorithms assume that an agent occupies only a single location at any given time, e.g., a single cell in a grid. This limits their applicability in many real-world domains that have geometric agents in lieu of point agents. Geometric agents are referred to as “large” agents because they can occupy multiple points at the same time. In this paper, we formalize and study LAMAPF, i.e., MAPF for large agents. We first show how CBS can be adapted to solve LA-MAPF. We then present a generalized version of CBS, called Multi-Constraint CBS (MCCBS), that adds multiple constraints (instead of one constraint) for an agent when it generates a high-level search node. We introduce three different approaches to choose such constraints as well as an approach to compute admissible heuristics for the high-level search. Experimental results show that all MC-CBS variants outperform CBS by up to three orders of magnitude in terms of runtime. The best variant also outperforms EPEA* (a state-of-the-art A*-based MAPF solver) in all cases and MDD-SAT (a state-of-the-art reduction-based MAPF solver) in some cases.

Conflict-Based Search (CBS) and its enhancements are among the strongest algorithms for Multi-Agent Path Finding. Recent work introduced an admissible heuristic to guide the high-level search of CBS. In this work, we prove the limitation of this heuristic, as it is based on cardinal conflicts only. We then introduce two new admissible heuristics by reasoning about the pairwise dependencies between agents. Empirically, CBS with either new heuristic significantly improves the success rate over CBS with the recent heuristic and reduces the number of expanded nodes and runtime by up to a factor of 50.

The Multi-Agent Pickup and Delivery (MAPD) problem models applications where a large number of agents attend to a stream of incoming pickup-and-delivery tasks. Token Passing (TP) is a recent MAPD algorithm that is efficient and effective. We make TP even more efficient and effective by using a novel combinatorial search algorithm, called Safe Interval Path Planning with Reservation Table (SIPPwRT), for single-agent path planning. SIPPwRT uses an advanced data structure that allows for fast updates and lookups of the current paths of all agents in an online setting. The resulting MAPD algorithm TP-SIPPwRT takes kinematic constraints of real robots into account directly during planning, computes continuous agent movements with given velocities that work on non-holonomic robots rather than discrete agent movements with uniform velocity, and is complete for well-formed MAPD instances. We demonstrate its benefits for automated warehouses using both an agent simulator and a standard robot simulator. For example, we demonstrate that it can compute paths for hundreds of agents and thousands of tasks in seconds and is more efficient and effective than existing MAPD algorithms that use a post-processing step to adapt their paths to continuous agent movements with given velocities. This paper was published at AAAI 2019.

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-driven combinatorial search framework. In a variety of empirical comparisons, we demonstrate state-of-the-art solution qualities and success rates, often with similar runtimes to existing algorithms. We also develop new theoretical results that explore the limitations of prioritized planning, in terms of completeness and optimality, for the first time. This paper was published at AAAI 2019.

Conflict-Based Search (CBS) and its enhancements are among the strongest algorithms for Multi-Agent Pathfinding. Recent work introduced an admissible heuristic to guide the high-level search of CBS. In this work, we prove the limitation of this heuristic, as it is based on cardinal conflicts only. We then introduce two new admissible heuristics by reasoning about the pairwise dependency between agents. Empirically, CBS with both new heuristics significantly improves the success rate over CBS with the recent heuristic and reduces the number of expanded nodes and runtime by up to a factor of 50, yielding a new state-of-the-art CBS-based algorithm.

We describe a new way of reasoning about symmetric collisions for Multi-Agent Path Finding (MAPF) on 4-neighbor grids. We also introduce a symmetry-breaking constraint to resolve these conflicts. This specialized technique allows us to identify and eliminate, in a single step, all permutations of two currently assigned but incompatible paths. Each such permutation has exactly the same cost as a current path, and each one results in a new collision between the same two agents. We show that the addition of symmetry-breaking techniques can lead to an exponential reduction in the size of the search space of CBS, a popular framework for MAPF, and report significant improvements in both runtime and success rate versus CBSH and EPEA* – two recent and state-of-the-art MAPF algorithms.

Multi-Agent Path Finding (MAPF) has been widely studied in the AI community. For example, Conflict-Based Search (CBS) is a state-of-the-art MAPF algorithm based on a two-level tree-search. However, previous MAPF algorithms assume that an agent occupies only a single location at any given time, e.g., a single cell in a grid. This limits their applicability in many real-world domains that have geometric agents in lieu of point agents. Geometric agents are referred to as “large” agents because they can occupy multiple points at the same time. In this paper, we formalize and study LAMAPF, i.e., MAPF for large agents. We first show how CBS can be adapted to solve LA-MAPF. We then present a generalized version of CBS, called Multi-Constraint CBS (MC-CBS), that adds multiple constraints (instead of one constraint) for an agent when it generates a high-level search node. We introduce three different approaches to choose such constraints as well as an approach to compute admissible heuristics for the high-level search. Experimental results show that all MC-CBS variants outperform CBS by up to three orders of magnitude in terms of runtime. The best variant also outperforms EPEA* (a state-of-the-art A*-based MAPF solver) in all cases and MDD-SAT (a state-of-the-art reduction-based MAPF solver) in some cases.

The multi-agent pathfinding problem (MAPF) is the fundamental problem of planning paths for multiple agents, where the key constraint is that the agents will be able to follow these paths concurrently without colliding with each other. Applications of MAPF include automated warehouses, autonomous vehicles, and robotics. Research on MAPF has been flourishing in the past couple of years. Different MAPF research papers assume different sets of assumptions, e.g., whether agents can traverse the same road at the same time, and have different objective functions, e.g., minimize makespan or sum of agents' actions costs. These assumptions and objectives are sometimes implicitly assumed or described informally. This makes it difficult for establishing appropriate baselines for comparison in research papers, as well as making it difficult for practitioners to find the papers relevant to their concrete application. This paper aims to fill this gap and facilitate future research and practitioners by providing a unifying terminology for describing the common MAPF assumptions and objectives. In addition, we also provide pointers to two MAPF benchmarks. In particular, we introduce a new grid-based benchmark for MAPF, and demonstrate experimentally that it poses a challenge to contemporary MAPF algorithms.

We formalize Multi-Agent Path Finding with Deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within the deadline, without colliding with each other. We first show that MAPF-DL is NP-hard to solve optimally. We then present two classes of optimal algorithms, one based on a reduction of MAPF-DL to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network and the other one based on novel combinatorial search algorithms. Our empirical results demonstrate that these MAPF-DL solvers scale well and each one dominates the other ones in different scenarios.

Focal search (FS) is a bounded-suboptimal search (BSS) variant of A*. Like A*, it uses an open list whose states are sorted in increasing order of their f-values. Unlike A*, it also uses a focal list containing all states from the open list whose f-values are no larger than a suboptimality factor times the smallest f-value in the open list. In this paper, we develop an anytime version of FS, called anytime FS (AFS), that is useful when deliberation time is limited. AFS finds a "good" solution quickly and refines it to better and better solutions if time allows. It does this refinement efficiently by reusing previous search efforts. On the theoretical side, we show that AFS is bounded suboptimal and that anytime potential search (ATPS/ANA*), a state-of-the-art anytime bounded-cost search (BCS) variant of A*, is a special case of AFS. In doing so, we bridge the gap between anytime search algorithms based on BSS and BCS. We also identify different properties of priority functions, used to sort the focal list, that may allow for efficient reuse of previous search efforts. On the experimental side, we demonstrate the usefulness of AFS for solving hard combinatorial problems, such as the generalized covering traveling salesman problem and the multi-agent pathfinding problem.

Several recently developed Multi-Agent Path Finding (MAPF) solvers scale to large MAPF instances by searching for MAPF plans on 2 levels: The high-level search resolves collisions between agents, and the low-level search plans paths for single agents under the constraints imposed by the high-level search. We make the following contributions to solve the MAPF problem with imperfect plan execution with small average makespans: First, we formalize the MAPF Problem with Delay Probabilities (MAPF-DP), define valid MAPF-DP plans and propose the use of robust plan-execution policies for valid MAPF-DP plans to control how each agent proceeds along its path. Second, we discuss 2 classes of decentralized robust plan-execution policies (called Fully Synchronized Policies and Minimal Communication Policies) that prevent collisions during plan execution for valid MAPF-DP plans. Third, we present a 2-level MAPF-DP solver (called Approximate Minimization in Expectation) that generates valid MAPF-DP plans.

Multi-Agent Path Finding (MAPF) is well studied in both AI and robotics. Given a discretized environment and agents with assigned start and goal locations, MAPF solvers from AI find collision-free paths for hundreds of agents with user-provided sub-optimality guarantees. However, they ignore that actual robots are subject to kinematic constraints (such as velocity limits) and suffer from imperfect plan-execution capabilities. We therefore introduce MAPF-POST to postprocess the output of a MAPF solver in polynomial time to create a plan-execution schedule that can be executed on robots. This schedule works on non-holonomic robots, considers kinematic constraints, provides a guaranteed safety distance between robots, and exploits slack to avoid time-intensive replanning in many cases. We evaluate MAPF-POST in simulation and on differential-drive robots, showcasing the practicality of our approach.

We study transportation problems where robots have to deliver packages and can transfer the packages among each other. Specifically, we study the package-exchange robot-routing problem (PERR), where each robot carries one package, any two robots in adjacent locations can exchange their packages, and each package needs to be delivered to a given destination. We prove that exchange operations make all PERR instances solvable. Yet, we also show that PERR is NP-hard to approximate within any factor less than 4/3 for makespan minimization and is NP-hard to solve for flowtime minimization, even when there are only two types of packages. Our proof techniques also generate new insights into other transportation problems, for example, into the hardness of approximating optimal solutions to the standard multi-agent path-finding problem (MAPF). Finally, we present optimal and suboptimal PERR solvers that are inspired by MAPF solvers, namely a flow-based ILP formulation and an adaptation of conflict-based search. Our empirical results demonstrate that these solvers scale well and that PERR instances often have smaller makespans and flowtimes than the corresponding MAPF instances.

We study formation change for robot groups in known environments. We are given a team of robots partitioned into groups, where robots in the same group are interchangeable with each other. A formation specifies the locations occupied by each group. The objective is to find collision-free paths that move all robots from a given start formation to a given goal formation. Our algorithm TAPF* has the following features: (a) it incorporates kinematic constraints of robots in form of velocity limits; (b) it maintains a user-specified safety distance between robots; (c) it attempts to minimize the makespan; and (d) it runs efficiently for hundreds of robots and dozens of groups even in dense 3D environments with narrow corridors and other occlusions. We demonstrate the efficiency and effectiveness of TAPF* in simulation and on robots.

Planning in large partially observable Markov decision processes (POMDPs) is challenging especially when a long planning horizon is required. A few recent algorithms successfully tackle this case but at the expense of a weaker information-gathering capacity. In this paper, we propose Information Gathering and Reward Exploitation of Subgoals (IGRES), a randomized POMDP planning algorithm that leverages information in the state space to automatically generate "macro-actions" to tackle tasks with long planning horizons, while locally exploring the belief space to allow effective information gathering. Experimental results show that IGRES is an effective multi-purpose POMDP solver, providing state-of-the-art performance for both long horizon planning tasks and information-gathering tasks on benchmark domains. Additional experiments with an ecological adaptive management problem indicate that IGRES is a promising tool for POMDP planning in real-world settings.