Multi-Agent Path Finding for Precedence-Constrained Goal Sequences

**Read paper on the following link:** https://ifaamas.org/Proceedings/aamas2022/pdfs/p1464.pdf **Abstract:** With the rising demand of deploying robot teams in autonomous warehouses and factories, the Multi-agent Path Finding (MAPF) problem has drawn more and more attention. However, the classical MAPF problem focuses on navigating agent teams to reach single goal locations while avoiding collisions, and thus it cannot plan the case in which each agent is associated with a sequence of goal locations, and precedence constraints across goal sequences should be respected. Planning with these goal sequences and precedence constraints is important in real-world multi-agent systems. For example, a mobile robot needs to move an inventory pod to several stations for delivering different packages, which is captured by a sequence of goal locations, and another robot can only pick up a package after it has been delivered to the corresponding station, which can be modeled as precedence constraints across goal sequences. In this paper, we formalize the Multi-Agent Path Finding with Precedence Dependency (MAPF-PD) problem along with two algorithms to systematically solve this problem: Conflict-Based Search with Precedence Dependency (CBS-PD) is a complete and optimal algorithm; and Priority-Based Search with Precedence Dependency (PBS-PD) is an incomplete and suboptimal algorithm but shows great scalability and obtains near-optimal solutions in practice. Our experimental results show that our algorithms can scale to dozens of agents with hundreds of goal locations and precedence constraints.

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 of this approach is that in MAPF the agents must reach a configuration in which all agents are at their targets simultaneously. Coordinating the agents’ paths such that they occupy their targets at the same time is needlessly restrictive for LMAPF. Techniques have been proposed to indirectly mitigate this drawback. In this position paper, 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 MAPF for Lifelong (MAPF4L) and propose how to solve it by modifying several existing MAPF algorithms. A limited experimental evaluation identifies some cases where using a MAPF4L algorithm can improve the system throughput significantly.

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 3-SAT problem (which is known to be an NP-complete problem) to the problem at hand. In particular, for an arbitrary 3-SAT formula we procedurally construct a dedicated graph with specific start and goal vertices and show that the given 3-SAT formula is satisfiable iff the corresponding path finding instance has a solution.

The 2D Multi-Agent Path Finding (MAPF) problem aims at finding collision-free paths for a number of agents, from a set of start locations to a set of goal positions in a known 2D environment. MAPF has been studied in theoretical computer science, robotics, and artificial intelligence over several decades, due to its importance for robot navigation. It is currently experiencing significant scientific progress due to its relevance in automated warehousing (such as those operated by Amazon) and in other contemporary application areas. In this paper, we demonstrate that some recently developed MAPF algorithms apply more broadly than currently believed in the MAPF research community. In particular, we describe the 3D Pipe Routing (PR) problem, which aims at placing collision-free pipes from given start locations to given goal locations in a known 3D environment. The MAPF and PR problems are similar: a solution to a MAPF instance is a set of blocked cells in x-y-t space, while a solution to the corresponding PR instance is a set of blocked cells in x-y-z space. We show how to use this similarity to apply several recently developed MAPF algorithms to the PR problem, and discuss their performance on real-world PR instances. This opens up a new direction of industrial relevance for the MAPF research community.

Multi-Robot-Arm Motion Planning (M-RAMP) is a challenging problem featuring complex single-agent planning and multi-agent coordination. Recent advancements in extending the popular Conflict-Based Search (CBS) algorithm have made large strides in solving Multi-Agent Path Finding (MAPF) problems. However, fundamental challenges remain in applying CBS to M-RAMP. A core challenge is the existing reliance of the CBS framework on conservative "complete" constraints. These constraints ensure solution guarantees but often result in slow pruning of the search space -- causing repeated expensive single-agent planning calls. Therefore, even though it is possible to leverage domain knowledge and design incomplete M-RAMP-specific CBS constraints to more efficiently prune the search, using these constraints would render the algorithm itself incomplete. This forces practitioners to choose between efficiency and completeness. In light of these challenges, we propose a novel algorithm, Generalized ECBS, aimed at removing the burden of choice between completeness and efficiency in MAPF algorithms. Our approach enables the use of arbitrary constraints in conflict-based algorithms while preserving completeness and bounding sub-optimality. This enables practitioners to capitalize on the benefits of arbitrary constraints and opens a new space for constraint design in MAPF that has not been explored. We provide a theoretical analysis of our algorithms, propose new "incomplete" constraints, and demonstrate their effectiveness through experiments in M-RAMP.

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.

Portfolio-based algorithm selection can help in choosing the best suited algorithm for a given task while leveraging the complementary strengths of the candidates. Solving the Multi-Agent Path Finding (MAPF) problem optimally has been proven to be NP-Hard. Furthermore, no single optimal algorithm has been shown to have the fastest runtime for all MAPF problem instances, and there are no proven approaches for when to use each algorithm. To address these challenges, we develop MAPFASTER, a smaller and more accurate deep learning based architecture aiming to be deployed in fleet management systems to select the fastest MAPF solver in a multi-robot setting. MAPF problem instances are encoded as images and passed to the model for classification into one of the portfolio's candidates. We evaluate our model against state-of-the-art Optimal-MAPF-Algorithm selectors, showing +5.42% improvement in accuracy while being 7.1× faster to train. The dataset, code and analysis used in this research can be found at https://github.com/jeanmarcalkazzi/mapfaster.

In Multi-Agent Path Finding (MAPF), we are asked to plan collision-free paths for teams of moving agents. Among the leading methods for optimal MAPF is Conflict-Based Search (CBS), an algorithmic family which has received intense attention in recent years and for which large advancements in efficiency and effectiveness have been reported. Yet all of the recent CBS gains come from reasoning over pairs of agents only. In this paper, we show how to further improve CBS by reasoning about more than two agents at the same time. Our new cluster reasoning techniques allow us to generate stronger bounds for CBS and to identify more bypasses (alternative cost-equivalent paths), which reduce the number of nodes in the CBS conflict tree.

We address conflict reasoning in generalizations of multi-agent path finding (MAPF). We assume items placed in vertices of an undirected graph with at most one item per vertex. Items can be relocated across edges while various constraints depending on the concrete type of MAPF must be satisfied. We recall a general problem formulation that encompasses known types of item relocation problems such as multi-agent path finding (MAPF) and token swapping (TSWAP). We show how to express new types of relocation problems in the general problem formulation. We thoroughly evaluate a novel solving method for item relocation that combines satisfiability modulo theory (SMT) with conflict-based search (CBS). CBS is interpreted in the SMT framework where we start with the basic model and refine the model with a collision resolution constraint whenever a collision between items occurs. The key difference between the standard CBS and the SMT-based modification of CBS (SMT-CBS) is that the standard CBS branches the search to resolve the collision while SMT-CBS iteratively adds a single disjunctive collision resolution constraint. Our experimental evaluation revealed that although SMT-CBS performs better than CBS in small densely occupied instances of variants of MAPF, it is outperformed on large sparsely occupied environments. The performed analysis shows that individual paths in large environments of relocation instances can be found faster using simple A*-based algorithm than by the SMT solver. On the other hand the SMT solver performs better when many conflicts between items need to be resolved.

Multi-Agent Path Finding (MAPF) is an important problem with a variety of applications. Its aim is to find collision-free paths for agents having separate start and goal positions. This work proposes a new lexicographic bi-objective MAPF considering different task types, where agents are divided into two kinds to perform critical and acritical tasks. This is common in practical intelligent warehousing scenarios where a critical/acritical-task-performing agent (called c-agent and a-agent, respectively) may represent a full-load/no-load one or the one conducting urgent/non-urgent tasks. The primary objective is to minimize the sum-of-costs of c-agents, while the secondary objective is to minimize the sum-of-costs of a-agents. Two MAPF algorithms are modified to fit and solve the concerned problem for the first time. Moreover, four improvement strategies are embedded to the proposed algorithms and proved to be effective in solving MAPF problems with different task types.

This study informs the design of future multi-agent pathfinding (MAPF) and multi-robot motion planning (MRMP) algorithms by guiding choices based on constraint classification for constraint-based search algorithms. We categorize constraints as conservative or aggressive and provide insights into their search behavior, focusing specifically on vanilla Conflict-Based Search (CBS) and Conflict-Based Search with Priorities (CBSw/P). Under a hybrid grid-roadmap representation with varying resolution, we observe that aggressive (priority constraint) formulations tend to solve more instances as agent count or resolution increases, whereas conservative (motion constraint) formulations yield stronger solution quality when both succeed. Findings are synthesized in a decision flowchart, aiding users in selecting suitable constraints. Recommendations extend to Multi-Robot Motion Planning (MRMP), emphasizing the importance of considering topological features alongside problem, solution, and representation features. A comprehensive exploration of the study, including raw data and map performance, is available in our public GitHub Repository.

We study practical approaches to solving the token swapping (TSWAP) problem optimally in this paper. In TSWAP, we are given an undirected graph with colored vertices. A colored token is placed in each vertex. A pair of tokens can be swapped between adjacent vertices. The goal is to perform a sequence of swaps so that token and vertex colors agree across the graph. The minimum number of swaps is required in the optimization variant of the problem. We observed similarities between the TSWAP problem and multi-agent path finding (MAPF) where instead of tokens we have multiple agents that need to be moved from their current vertices to given unique target vertices. The difference between both problems consists in local conditions that state transitions (swaps/moves) must satisfy. We developed two algorithms for solving TSWAP optimally by adapting two different approaches to MAPF - conflict-based search (CBS) and SAT-based approach that uses multi-value decision diagrams (MDD-SAT). This constitutes the first attempt to design optimal solving algorithms for TSWAP. Experimental evaluation on various types of graphs shows that the reduction to SAT scales better than CBS in optimal TSWAP solving. It has been also demonstrated that TSWAP instances are easier to solve than corresponding similar MAPF instances.

We describe an attempt to unify search-based and compilation-based approaches to multi-agent path finding (MAPF) through satisfiability modulo theories (SMT). The task in MAPF is to navigate agents in an undirected graph to given goal vertices so that they do not collide. We rephrase Conflict-Based Search (CBS), one of the state-of-the-art algorithms for optimal MAPF solving, in the terms of SMT. This idea combines SAT-based solving known from MDD-SAT, a SAT-based optimal MAPF solver, at the low level with conflict elimination of CBS at the high level. Where the standard CBS branches the search after a conflict occurs, we refine the propositional model with a disjunctive constraint instead. Our novel algorithm called SMT-CBS hence does not branch at the high-level but incrementally extends the propositional model that is consulted with the SAT solver at each iteration. We experimentally compare SMT-CBS with CBS and MDD-SAT.

The task in the multi-agent path finding problem (MAPF) is to find paths for multiple agents, each with a different start and goal position, such that agents do not collide. A successful optimal MAPF solver is the conflict-based search (CBS) algorithm. CBS is a two level algorithm where special conditions ensure it returns the optimal solution. Solving MAPF optimally is proven to be NP-hard, hence CBS and all other optimal solvers do not scale up. We propose several ways to relax the optimality conditions of CBS trading solution quality for runtime as well as bounded-suboptimal variants, where the returned solution is guaranteed to be within a constant factor from optimal solution cost. Experimental results show the benefits of our new approach; a massive reduction in running time is presented while sacrificing a minor loss in solution quality. Our new algorithms outperform other existing algorithms in most of the cases.

Multi-agent path finding (MAPF) is the problem of planning a set of non-colliding paths for a set of agents so that each agent reaches its individual goal location following its path. A mutex from classical planning is a constraint forbidding a pair of facts to be both true or a pair of actions to be executed simultaneously. In the context of MAPF, mutexes are used to rule out the simultaneous occurrence of a pair of agents in a pair of locations, which can prune the search space. Previously mutex propagation had been integrated into conflict-based search (CBS), a major search-based approach for solving MAPF optimally. In this paper, we introduce mutex propagation into the compilation-based (SAT-based) solver MDD-SAT, an alternative to search-based solvers. Our experiments show that, despite mutex propagation being computationally expensive, it prunes the search space significantly so that the overall performance of MDD-SAT is improved.