Counterexample guided abstraction refinement (CEGAR) represents a powerful symbolic technique for various tasks such as model checking and reachability analysis. Recently, CEGAR combined with Boolean satisfiability (SAT) has been applied for multi-agent path finding (MAPF), a problem where the task is to navigate agents from their start positions to given individual goal positions so that the agents do not collide with each other. The recent CEGAR approach used the initial abstraction of the MAPF problem where collisions between agents were omitted and were eliminated in subsequent abstraction refinements. We propose in this work a novel CEGAR-style solver for MAPF based on SAT in which some abstractions are deliberately left non-refined. This adds the necessity to post-process the answers obtained from the underlying SAT solver as these answers slightly differ from the correct MAPF solutions. Non-refining however yields order-of-magnitude smaller SAT encodings than those of the previous approach and speeds up the overall solving process making the SAT-based solver for MAPF competitive again in relevant benchmarks.
Conflict-Based Search is one of the most popular methods for multi-agent path finding. Though it is complete and optimal, it does not scale well. Recent works have been proposed to accelerate it by introducing various heuristics. However, whether these heuristics can apply to non-grid-based problem settings while maintaining their effectiveness remains an open question. In this work, we find that the answer is prone to be no. To this end, we propose a learning-based component, i.e., the Graph Transformer, as a heuristic function to accelerate the planning. The proposed method is provably complete and bounded-suboptimal with any desired factor. We conduct extensive experiments on two environments with dense graphs. Results show that the proposed Graph Transformer can be trained in problem instances with relatively few agents and generalizes well to a larger number of agents, while achieving better performance than state-of-the-art methods.
Multi-agent path finding (MAPF) is the problem of moving agents to the goal vertex without collision. In the online MAPF problem, new agents may be added to the environment at any time, and the current agents have no information about future agents. The inability of existing online methods to reuse previous planning contexts results in redundant computation and reduces algorithm efficiency. Hence, we propose a three-level approach to solve online MAPF utilizing sustainable information, which can decrease its redundant calculations. The high-level solver, the Sustainable Replan algorithm (SR), manages the planning context and simulates the environment. The middle-level solver, the Sustainable Conflict-Based Search algorithm (SCBS), builds a conflict tree and maintains the planning context. The low-level solver, the Sustainable Reverse Safe Interval Path Planning algorithm (SRSIPP), is an efficient single-agent solver that uses previous planning context to reduce duplicate calculations. Experiments show that our proposed method has significant improvement in terms of computational efficiency. In one of the test scenarios, our algorithm can be 1.48 times faster than SOTA on average under different agent number settings.
Multi-agent path finding (MAPF) is a task of finding non-conflicting paths connecting agents' specified initial and goal positions in a shared environment. We focus on compilation-based solvers in which the MAPF problem is expressed in a different well established formalism such as mixed-integer linear programming (MILP), Boolean satisfiability (SAT), or constraint programming (CP). As the target solvers for these formalisms act as black-boxes it is challenging to integrate MAPF specific heuristics in the MAPF compilation-based solvers. We show in this work how the build a MAPF encoding for the target SAT solver in which domain specific heuristic knowledge is reflected. The heuristic knowledge is transferred to the SAT solver by selecting candidate paths for each agent and by constructing the encoding only for these candidate paths instead of constructing the encoding for all possible paths for an agent. The conducted experiments show that heuristically guided compilation outperforms the vanilla variants of the SAT-based MAPF solver.
In this paper, we consider the problem of path finding for a set of homogeneous and autonomous agents navigating a previously unknown stochastic environment. In our problem setting, each agent attempts to maximize a given utility function while respecting safety properties. Our solution is based on ideas from evolutionary game theory, namely replicating policies that perform well and diminishing ones that do not. We do a comprehensive comparison with related multiagent planning methods, and show that our technique beats state of the art RL algorithms in minimizing path length by nearly 30% in large spaces. We show that our algorithm is computationally faster than deep RL methods by at least an order of magnitude. We also show that it scales better with an increase in the number of agents as compared to other methods, path planning methods in particular. Lastly, we empirically prove that the policies that we learn are evolutionarily stable and thus impervious to invasion by any other policy.
The Multi-Objective Multi-Agent Path Finding (MO-MAPF) problem is the problem of finding the Pareto-optimal frontier of collision-free paths for a team of agents while minimizing multiple cost metrics. Examples of such cost metrics include arrival times, travel distances, and energy consumption.In this paper, we focus on the Multi-Objective Conflict-Based Search (MO-CBS) algorithm, a state-of-the-art MO-MAPF algorithm. We show that the standard splitting strategy used by MO-CBS can lead to duplicate search nodes and hence can duplicate the search effort that MO-CBS needs to make. To address this issue, we propose two new splitting strategies for MO-CBS, namely cost splitting and disjoint cost splitting. Our theoretical results show that, when combined with either of these two new splitting strategies, MO-CBS maintains its completeness and optimality guarantees. Our experimental results show that disjoint cost splitting, our best splitting strategy, speeds up MO-CBS by up to two orders of magnitude and substantially improves its success rates in various settings.
In recent years, Multi-Agent Path Finding (MAPF) has attracted attention from the fields of both Operations Research (OR) and Reinforcement Learning (RL). However, in the 2021 Flatland3 Challenge, a competition on MAPF, the best RL method scored only 27.9, far less than the best OR method. This paper proposes a new RL solution to Flatland3 Challenge, which scores 125.3, several times higher than the best RL solution before. We creatively apply a novel network architecture, TreeLSTM, to MAPF in our solution. Together with several other RL techniques, including reward shaping, multiple-phase training, and centralized control, our solution is comparable to the top 2-3 OR methods.
We propose an extension to the MAPF formulation, called SocialMAPF, to account for private incentives of agents in constrained environments such as doorways, narrow hallways, and corridor intersections. SocialMAPF is able to, for instance, accurately reason about the urgent incentive of an agent rushing to the hospital over another agent's less urgent incentive of going to a grocery store; MAPF ignores such agent-specific incentives. Our proposed formulation addresses the open problem of optimal and efficient path planning for agents with private incentives. To solve SocialMAPF, we propose a new class of algorithms that use mechanism design during conflict resolution to simultaneously optimize agents' private local utilities and the global system objective. We perform an extensive array of experiments that show that optimal search-based MAPF techniques lead to collisions and increased time-to-goal in SocialMAPF compared to our proposed method using mechanism design. Furthermore, we empirically demonstrate that mechanism design results in models that maximizes agent utility and minimizes the overall time-to-goal of the entire system. We further showcase the capabilities of mechanism design-based planning by successfully deploying it in environments with static obstacles. To conclude, we briefly list several research directions using the SocialMAPF formulation, such as exploring motion planning in the continuous domain for agents with private incentives.
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.
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.
We study the planning and acting phase for the problem of multi-agent path finding (MAPF) in this paper. MAPF is a problem of navigating agents from their start positions to specified individual goal positions so that agents do not collide with each other. Specifically we focus on executing MAPF plans with a group of Crazyflies, small indoor quadcopters . We show how to modify the existing continuous time conflict-based search algorithm (CCBS) to produce plans that are suitable for execution with the quadcopters. The acting phase uses the the Loco positioning system to check if the plan is executed correctly. Our finding is that the CCBS algorithm allows for extensions that can produce safe plans for quadcopters, namely cylindrical protection zone around each quadcopter can be introduced at the planning level.
The multiple-target self-organizing pursuit (SOP) problem has wide applications and has been considered a challenging self-organization game for distributed systems, in which intelligent agents cooperatively pursue multiple dynamic targets with partial observations. This work proposes a framework for decentralized multi-agent systems to improve the implicit coordination capabilities in search and pursuit. We model a self-organizing system as a partially observable Markov game (POMG) featured by large-scale, decentralization, partial observation, and noncommunication. The proposed distributed algorithm: fuzzy self-organizing cooperative coevolution (FSC2) is then leveraged to resolve the three challenges in multi-target SOP: distributed self-organizing search (SOS), distributed task allocation, and distributed single-target pursuit. FSC2 includes a coordinated multi-agent deep reinforcement learning (MARL) method that enables homogeneous agents to learn natural SOS patterns. Additionally, we propose a fuzzy-based distributed task allocation method, which locally decomposes multi-target SOP into several single-target pursuit problems. The cooperative coevolution principle is employed to coordinate distributed pursuers for each single-target pursuit problem. Therefore, the uncertainties of inherent partial observation and distributed decision-making in the POMG can be alleviated. The experimental results demonstrate that by decomposing the SOP task, FSC2 achieves superior performance compared with other implicit coordination policies fully trained by general MARL algorithms. The scalability of FSC2 is proved that up to 2048 FSC2 agents perform efficient multi-target SOP with almost 100 percent capture rates. Empirical analyses and ablation studies verify the interpretability, rationality, and effectiveness of component algorithms in FSC2.
Purpose of Review Planning collision-free paths for multiple robots is important for real-world multi-robot systems and has been studied as an optimization problem on graphs, called Multi-Agent Path Finding (MAPF). This review surveys different categories of classic and state-of-the-art MAPF algorithms and different research attempts to tackle the challenges of generalizing MAPF techniques to real-world scenarios. Recent Findings Solving MAPF problems optimally is computationally challenging. Recent advances have resulted in MAPF algorithms that can compute collision-free paths for hundreds of robots and thousands of navigation tasks in seconds of runtime. Many variants of MAPF have been formalized to adapt MAPF techniques to different real-world requirements, such as considerations of robot kinematics, online optimization for real-time systems, and the integration of task assignment and path planning. Summary Algorithmic techniques for MAPF problems have addressed important aspects of several multi-robot applications, including automated warehouse fulfillment and sortation, automated train scheduling, and navigation of non-holonomic robots and quadcopters. This showcases their potential for real-world applications of large-scale multi-robot systems.
Conflict-Based Search (CBS) is a popular multi-agent path finding (MAPF) solver that employs a low-level single agent planner and a high-level constraint tree to resolve conflicts. The vast majority of modern MAPF solvers focus on improving CBS by reducing the size of this tree through various strategies with few methods modifying the low level planner. Typically low level planners in existing CBS methods use an unweighted cost-to-go heuristic, with suboptimal CBS methods also using a conflict heuristic to help the high level search. In this paper, we show that, contrary to prevailing CBS beliefs, a weighted cost-to-go heuristic can be used effectively alongside the conflict heuristic in two possible variants. In particular, one of these variants can obtain large speedups, 2-100x, across several scenarios and suboptimal CBS methods. Importantly, we discover that performance is related not to the weighted cost-to-go heuristic but rather to the relative conflict heuristic weight's ability to effectively balance low-level and high-level work. Additionally, to the best of our knowledge, we show the first theoretical relation of prioritized planning and bounded suboptimal CBS and demonstrate that our methods are their natural generalization. Update March 2024: We found that the relative speedup decreases to around 1.2-10x depending on how the conflict heuristic is computed (see appendix for more details).
Multi-agent pathfinding (MAPF) is concerned with planning collision-free paths for a team of agents from their start to goal locations in an environment cluttered with obstacles. Typical approaches for MAPF consider the locations of obstacles as being fixed, which limits their effectiveness in automated warehouses, where obstacles (representing pods or shelves) can be moved out of the way by agents (representing robots) to relieve bottlenecks and introduce shorter routes. In this work we initiate the study of MAPF with movable obstacles. In particular, we introduce a new extension of MAPF, which we call Terraforming MAPF (tMAPF), where some agents are responsible for moving obstacles to clear the way for other agents. Solving tMAPF is extremely challenging as it requires reasoning not only about collisions between agents, but also where and when obstacles should be moved. We present extensions of two state-of-the-art algorithms, CBS and PBS, in order to tackle tMAPF, and demonstrate that they can consistently outperform the best solution possible under a static-obstacle setting.
We study two state-of-the-art solutions to the multi-agent pickup and delivery (MAPD) problem based on different principles -- multi-agent path-finding (MAPF) and multi-agent reinforcement learning (MARL). Specifically, a recent MAPF algorithm called conflict-based search (CBS) and a current MARL algorithm called shared experience actor-critic (SEAC) are studied. While the performance of these algorithms is measured using quite different metrics in their separate lines of work, we aim to benchmark these two methods comprehensively in a simulated warehouse automation environment.
Multi-robot assembly systems are becoming increasingly appealing in manufacturing due to their ability to automatically, flexibly, and quickly construct desired structural designs. However, effectively planning for these systems in a manner that ensures each robot is simultaneously productive, and not idle, is challenging due to (1) the close proximity that the robots must operate in to manipulate the structure and (2) the inherent structural partial orderings on when each part can be installed. In this paper, we present a task and motion planning framework that jointly plans safe, low-makespan plans for a team of robots to assemble complex spatial structures. Our framework takes a hierarchical approach that, at the high level, uses Mixed-integer Linear Programs to compute an abstract plan comprised of an allocation of robots to tasks subject to precedence constraints and, at the low level, builds on a state-of-the-art algorithm for Multi-Agent Path Finding to plan collision-free robot motions that realize this abstract plan. Critical to our approach is the inclusion of certain collision constraints and movement durations during high-level planning, which better informs the search for abstract plans that are likely to be both feasible and low-makespan while keeping the search tractable. We demonstrate our planning system on several challenging assembly domains with several (sometimes heterogeneous) robots with grippers or suction plates for assembling structures with up to 23 objects involving Lego bricks, bars, plates, or irregularly shaped blocks.
Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents from their start locations to end locations. We consider an extension to this problem, Precedence Constrained Multi-Agent Path Finding (PC-MAPF), wherein agents are assigned a sequence of planning tasks that contain precedence constraints between them. PC-MAPF has various applications, for example in multi-agent pickup and delivery problems where some objects might require multiple agents to collaboratively pickup and move them in unison. Precedence constraints also arise in warehouse assembly problems where before a manufacturing task can begin, its input resources must be manufactured and delivered. We propose a novel algorithm, Precedence Constrained Conflict Based Search (PC-CBS), which finds makespan-optimal solutions for this class of problems. PC-CBS utilizes a Precedence-Constrained Task-Graph to define valid intervals for each planning task and updates them when precedence conflicts are encountered. We benchmark the performance of this algorithm over various warehouse assembly, and multi-agent pickup and delivery tasks, and use it to evaluate the sub-optimality of a recently proposed efficient baseline.
In the Multi-Agent Path Finding (MAPF) problem, the goal is to find non-colliding paths for agents in an environment, such that each agent reaches its goal from its initial location. In safety-critical applications, a human supervisor may want to verify that the plan is indeed collision-free. To this end, a recent work introduces a notion of explainability for MAPF based on a visualization of the plan as a short sequence of images representing time segments, where in each time segment the trajectories of the agents are disjoint. Then, the explainable MAPF problem asks for a set of non-colliding paths that admits a short-enough explanation. Explainable MAPF adds a new difficulty to MAPF, in that it is NP-hard with respect to the size of the environment, and not just the number of agents. Thus, traditional MAPF algorithms are not equipped to directly handle explainable-MAPF. In this work, we adapt Conflict Based Search (CBS), a well-studied algorithm for MAPF, to handle explainable MAPF. We show how to add explainability constraints on top of the standard CBS tree and its underlying A* search. We examine the usefulness of this approach and, in particular, the tradeoff between planning time and explainability.
In Lifelong Multi-Agent Path Finding (L-MAPF) a team of agents performs a stream of tasks consisting of multiple locations to be visited by the agents on a shared graph while avoiding collisions with one another. L-MAPF is typically tackled by partitioning it into multiple consecutive, and hence similar, "one-shot" MAPF queries, as in the Rolling-Horizon Collision Resolution (RHCR) algorithm. Therefore, a solution to one query informs the next query, which leads to similarity with respect to the agents' start and goal positions, and how collisions need to be resolved from one query to the next. Thus, experience from solving one MAPF query can potentially be used to speedup solving the next one. Despite this intuition, current L-MAPF planners solve consecutive MAPF queries from scratch. In this paper, we introduce a new RHCR-inspired approach called exRHCR, which exploits experience in its constituent MAPF queries. In particular, exRHCR employs an extension of Priority-Based Search (PBS), a state-of-the-art MAPF solver. The extension, which we call exPBS, allows to warm-start the search with the priorities between agents used by PBS in the previous MAPF instances. We demonstrate empirically that exRHCR solves L-MAPF instances up to 39% faster than RHCR, and has the potential to increase system throughput for given task streams by increasing the number of agents a planner can cope with for a given time budget.