We introduce the Block Rearrangement Problem (BRaP), a challenging component of large warehouse management which involves rearranging storage blocks within dense grids to achieve a goal state. We formally define the BRaP as a graph search problem. Building on intuitions from sliding puzzle problems, we propose five search-based solution algorithms, leveraging joint configuration space search, classical planning, multi-agent pathfinding, and expert heuristics. We evaluate the five approaches empirically for plan quality and scalability. Despite the exponential relation between search space size and block number, our methods demonstrate efficiency in creating rearrangement plans for deeply buried blocks in up to 80x80 grids.

We study the problem of optimizing a guidance policy capable of dynamically guiding the agents for lifelong Multi-Agent Path Finding based on real-time traffic patterns. Multi-Agent Path Finding (MAPF) focuses on moving multiple agents from their starts to goals without collisions. Its lifelong variant, LMAPF, continuously assigns new goals to agents. In this work, we focus on improving the solution quality of PIBT, a state-of-the-art rule-based LMAPF algorithm, by optimizing a policy to generate adaptive guidance. We design two pipelines to incorporate guidance in PIBT in two different ways. We demonstrate the superiority of the optimized policy over both static guidance and human-designed policies. Additionally, we explore scenarios where task distribution changes over time, a challenging yet common situation in real-world applications that is rarely explored in the literature.

In multi-agent systems, when we account for the possibility of delays during execution, online planning becomes more complicated, as both execution and planning should be able to handle delays when agents are moving. Lifelong Multi-Agent Path Finding (LMAPF) is the problem of (re)planning the collision-free moves of agents to their goals in a shared space, while agents continuously receive new goals. PIE (Planning and Improving while Executing) is a recent approach to LMAPF which concurrently replans later parts of agents' trajectories while execution occurs. However, the execution is assumed to be perfect. Existing approaches either use policy-based methods to quickly coordinate agents every timestep with instant delay feedback, or deploy an execution policy to adjust a solution for delays on the fly. These approaches may introduce large amounts of unnecessary delays to agents due to their planner guarantees or simple delay-handling policies. In this paper, we extend PIE to define a framework for solving the lifelong MAPF problem with execution delays. We instantiate our framework with different execution and replanning strategies, and experimentally evaluate them. Overall, we find that this framework can substantially improve the throughput by up to a factor 3 for lifelong MAPF, compared to approaches that handle delays with simple execution policies.

Prioritised Planning (PP) is a popular approach for multi-agent and multi-robot navigation. In PP, collision-free paths are computed for one agent at a time, following a total order over the agents, called a priority ordering. Many MAPF algorithms follow this approach or use it in some way, including several state-of-the-art MAPF algorithms, although it is known that PP is neither complete nor optimal. In this work, we characterise the space of problems a PP algorithm can solve, and define the search problem of identifying whether a given MAPF problem is in that space. We call this search problem Prioritised MAPF (P-MAPF) and investigate its computational complexity, showing that it is generally NP-hard. Then, we develop a novel efficient search algorithm called Path and Priority Search (PaPS), which solves P-MAPF, providing guarantees of completeness and optimality. We next observe that PP algorithms operate with two primary degrees of freedom – the choice of priority ordering, and the choice of individual paths for agents. Accordingly, we further divide P-MAPF into two planning problems corresponding to the two degrees of freedom. We call them Priority-Function Constrained MAPF (PFC-MAPF), where the path choice is fixed while the priority ordering is not, and Priority Constrained MAPF (PC-MAPF), where the priority ordering is fixed while the path choice is not. We analyse these problems as well, and show how PaPS can be easily adapted to create algorithms that solve these problems optimally. We experiment with our algorithms in a range of settings, including comparisons with existing PP baselines. Our results show how the different degrees of freedom of PP-based algorithms affect their behaviour, and provide the first-known results for solution-quality optimality for PP-based algorithms on a popular MAPF benchmark set. The latter can be used as a lower bound for any PP algorithm.

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics that asks us to compute collision-free paths for a team of agents, all moving across a shared map. Although many works appear on this topic, all current algorithms struggle as the number of agents grows. The principal reason is that existing approaches typically plan free-flow optimal paths, which creates congestion. To tackle this issue, we propose a new approach for MAPF where agents are guided to their destination by following congestion-avoiding paths. We evaluate the idea in two large-scale settings: one-shot MAPF, where each agent has a single destination, and lifelong MAPF, where agents are continuously assigned new destinations. Empirically, we report large improvements in solution quality for one-short MAPF and in overall throughput for lifelong MAPF.

One area of research in multi-agent path finding is to determine how replanning can be efficiently achieved in the case of agents being delayed during execution. One option is to reschedule the passing order of agents, i.e., the sequence in which agents visit the same location. In response, we propose Switchable-Edge Search (SES), an A*-style algorithm designed to find optimal passing orders. We prove the optimality of SES and evaluate its efficiency via simulations. The best variant of SES takes less than 1 second for small- and medium-sized problems and runs up to 4 times faster than baselines for large-sized problems.

In applications of Multi-Agent Path Finding (MAPF), it is often the sum of planning and execution times that needs to be minimised (i.e., the Goal Achievement Time). Yet current methods seldom optimise for this objective. Optimal algorithms reduce execution time, but may require exponential planning time. Non-optimal algorithms reduce planning time, but at the expense of increased path length. To address these limitations we introduce PIE (Planning and Improving while Executing), a new framework for concurrent planning and execution in MAPF. We show how different instantiations of PIE affect practical performance, including initial planning time, action commitment time and concurrent vs. sequential planning and execution. We then adapt PIE to Lifelong MAPF, a popular application setting where agents are continuously assigned new goals and where additional decisions are required to ensure feasibility. We examine a variety of different approaches to overcome these challenges and we conduct comparative experiments vs. recently proposed alternatives. Results show that PIE substantially outperforms existing methods for One-shot and Lifelong MAPF.

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics that asks us to compute collision-free paths for a team of agents, all moving across a shared map. Existing scalable approaches struggle as the number of agents grows, as they typically plan free-flow optimal paths, which creates congestion. To tackle this issue, we propose a new approach for MAPF where agents are guided to their destination by following congestion-avoiding paths. Empirically, we report large improvements in overall throughput for lifelong MAPF while coordinating more than ten thousand agents.

Prioritised Planning (PP) is a family of incomplete and sub-optimal algorithms for multi-agent and multi-robot navigation. In PP, agents compute collision-free paths in a fixed order, one at a time. Although fast and usually effective, PP can still fail, leaving users without explanation or recourse. In this work, we give a theoretical and empirical basis for better understanding the underlying problem solved by PP, which we call Priority Constrained MAPF (PC-MAPF). We first investigate the complexity of PC-MAPF and show that the decision problem is NP-hard. We then develop Priority Constrained Search (PCS), a new algorithm that is both complete and optimal with respect to a fixed priority ordering. We experiment with PCS in a range of settings, including comparisons with existing PP baselines, and we give first-known results for optimal PC-MAPF on a popular benchmark set.

In applications of Multi-Agent Path Finding (MAPF), it is often the sum of planning and execution times that needs to be minimised (i.e., the Goal Achievement Time). Yet current methods seldom optimise for this objective. Optimal algorithms reduce execution time, but may require exponential planning time. Non-optimal algorithms reduce planning time, but at the expense of increased path length. To address these limitations we introduce PIE (Planning and Improving while Executing), a new framework for concurrent planning and execution in MAPF. We first show how PIE for one-shot MAPF improves practical performance compared to sequential planning and execution.We then adapt PIE to Lifelong MAPF, a popular application setting where agents are continuously assigned new goals and where additional decisions are required to ensure feasibility. We examine a variety of different approaches to overcome these challenges and we conduct comparative experiments vs. recently proposed alternatives. Results show that PIE substantially outperforms existing methods for One-shot and Lifelong MAPF.

Multi-Agent Path Finding (MAPF) is the problem of planning collision-free paths for multiple agents in a shared environment. In this paper, we propose a novel algorithm MAPF-LNS2 based on large neighborhood search for solving MAPF efficiently. Starting from a set of paths that contain collisions, MAPF-LNS2 repeatedly selects a subset of colliding agents and replans their paths to reduce the number of collisions until the paths become collision-free. We compare MAPF-LNS2 against a variety of state-of-the-art MAPF algorithms, including Prioritized Planning with random restarts, EECBS, and PPS, and show that MAPF-LNS2 runs significantly faster than them while still providing near-optimal solutions in most cases. MAPF-LNS2 solves 80% of the random-scenario instances with the largest number of agents from the MAPF benchmark suite with a runtime limit of just 5 minutes, which, to our knowledge, has not been achieved by any existing algorithms.

Multi-Train Path Finding (MTPF) is a coordination problem that asks us to plan collision-free paths for a team of moving agents, where each agent occupies a sequence of locations at any given time. MTPF is useful for planning a range of real-world vehicles, including rail trains and road convoys. MTPF is closely related to another coordination problem known as k-Robust Multi-Agent Path Finding (kR-MAPF). Although similar in principle, the performance of optimal MTPF algorithms in practice lags far behind that of optimal kR-MAPF algorithms. In this work, we revisit the connection between them and reduce the performance gap. First, we show that, in many cases, a valid kR-MAPF plan is also a valid MTPF plan, which leads to a new and faster approach for collision resolution. We also show that many recently introduced improvements for kR-MAPF, such as lower-bounding heuristics and symmetry reasoning, can be extended to MTPF. Finally, we explore a new type of pairwise symmetry specific to MTPF. Our experiments show that these improvements yield large efficiency gains for optimal MTPF.

During Multi-Agent Path Finding (MAPF) problems, agentscan be delayed by unexpected events. To address suchsituations recent work describes k-Robust Conflict-BasedSearch (k-CBS): an algorithm that produces coordinated andcollision-free plan that is robust for up tokdelays. In thiswork we introducing a variety of pairwise symmetry break-ing constraints, specific tok-robust planning, that can effi-ciently find compatible and optimal paths for pairs of con-flicting agents. We give a thorough description of the newconstraints and report large improvements to success rate ina range of domains including: (i) classic MAPF benchmarks;(ii) automated warehouse domains and; (iii) on maps fromthe 2019 Flatland Challenge, a recently introduced railwaydomain wherek-robust planning can be fruitfully applied toschedule trains.

Multi-Agent Path Finding (MAPF) is the challenging problem of computing collision-free paths for multiple agents. Algorithms for solving MAPF can be categorized on a spectrum. At one end are (bounded-sub)optimal algorithms that can find high-quality solutions for small problems. At the other end are unbounded-suboptimal algorithms that can solve large problems but usually find low-quality solutions. In this paper, we consider a third approach that combines the best of both worlds: anytime algorithms that quickly find an initial solution using efficient MAPF algorithms from the literature, even for large problems, and that subsequently improve the solution quality to near-optimal as time progresses by replanning subgroups of agents using Large Neighborhood Search. We compare our algorithm MAPF-LNS against a range of existing work and report significant gains in scalability, runtime to the initial solution, and speed of improving the solution.

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.