Robust MAPF

The coordination of Automated Guided Vehicles (AGVs) in high-density industrial environments represents a critical challenge within Logistics 4.0, as traditional traffic management methods often lead to inefficiencies caused by negotiation-based priority assignment. To overcome the resulting limitations, this paper presents an innovative AGV traffic management system based on a Lifelong Multi-Agent Path Finding (L-MAPF) algorithm operating on roadmaps generated with Non-Uniform Rational B-Splines (NURBS) curves. The approach guarantees locally optimal coordination and ensures safe operation of large and heterogeneous AGVs. Building on this concept, the proposed framework integrates a modified version of the Bounded Horizon Conflict Based Search (CBS) technique within a Rolling Horizon Conflict Resolution strategy, utilizing an extended time horizon for each agent to enable effective conflict resolution in corridors identified by a topological map. In contrast to state-of-the-art methods for AGV fleet traffic management, the proposed solution is designed for real-world, non-standardized (i.e., non-grid-like) industrial settings characterized by narrow bidirectional corridors and high-traffic density, where AGVs of various sizes and capabilities operate simultaneously. Key contributions include an anytime conflict resolution strategy with adaptive time horizon regulation, an execution layer for safe and standard-compliant interaction with real AGVs, and an advanced mechanism for deadlock detection and resolution. Experimental results obtained in realistic industrial environments demonstrate higher throughput, with improvements of up to 11% over a conventional rule-based traffic management system, a state-of-the-art industrial method, and a priority-based L-MAPF variant, while maintaining continuous operation and improved efficiency.

Many research fields share a common structure: a set of agents, each pursuing its own goal, whose actions must be coordinated so that no two of them conflict. Multi-Agent Path Finding (MAPF) is a concrete instance of this structure, with applications from warehouses to road traffic and airports. Much of MAPF research assumes discrete time, circular agents sharing one spatial graph, a single goal per agent, and that an agent must remain at its goal once reached, precluding heterogeneous fleets, non-geometric conflicts, task sequences, and agents that move on after completing them. We generalise the MAPF formulation to lift these assumptions, and present Anytime-Optimal Continuous-time Conflict-Based Search (AOC-CBS), an exact and solution-complete solver for it. AOC-CBS guarantees the eventual return of an optimal solution, while reporting an incumbent with a known optimality gap upper bound throughout its runtime; it is configurable with a portfolio of repair functions, one of which we introduce (Tier-Prioritized Safe Interval Path Planning), and can exploit multiple processor cores. We demonstrate AOC-CBS on a mixed fleet of non-convex agents moving along smooth, kinodynamically feasible trajectories. Preliminary experiments against the exact solver OC-CBS, on well-known benchmarks and roadmaps we sample from them, show AOC-CBS is comparable at finding optimal solutions while extending scalability from the tens to the hundreds of agents when a bounded optimality gap is accepted.

Automated warehouses face a fundamental trade-off between maximizing storage density and achieving high retrieval throughput. While puzzle-based storage (PBS) architectures increase capacity by eliminating aisles, coordinating multiple robots in these high-density spaces is computationally challenging due to the potential for deadlocks. This paper introduces a novel multi-robot formulation for the ``ordered storage and retrieval problem at maximum capacity''. The focus is on rectangular grids accessible from a single boundary, where loads need to be first stored up to full capacity and then efficiently retrieved, given a planned departure sequence. This work bridges the gap between geometric feasibility and execution efficiency by leveraging the properties of relocation-free arrangements. These properties guide an online, prioritized multi-agent path-finding algorithm, which is the main contribution of this work. Unlike general centralized planners, the approach exploits the specific invariants of the storage arrangement to guarantee completeness and prevent deadlocks, enabling scalability. Experiments demonstrate that the method achieves near-linear improvement in makespan with respect to the number of robots, up to $m = C$, where $C$ is the grid width. Crucially, the algorithmic overhead of supporting robustness is negligible; the system handles uncertainty in departure sequences using robust storage arrangements with no significant penalty in execution speed compared to the non-robust baseline.

Lifelong Multi-Agent Path Finding (LMAPF) requires generating collision-free paths for large agent fleets under strict real-time constraints. Reactive frameworks such as PIBT and Enhanced PIBT (EPIBT) scale effortlessly to thousands of agents through rule-based, step-by-step coordination but suffer from severe temporal myopia, making them ineffective in scenarios where long-horizon reasoning is essential. RHCR plans windowed paths over multi-step horizons but incurs substantial planning overheads that hinder scalability. TP tackles both challenges by planning only subsets of agents at each timestep, yet its applicability is restricted to highly structured maps. To achieve long-horizon planning at scale across general maps, we propose Path Updates over Staggered Horizons (PUSH), a LMAPF planner capable of coordinating thousands of agents in under a second while planning over multi-step horizons. PUSH combines the key advantages of PIBT, RHCR, and TP. Like TP, PUSH reduces computational complexity by planning only a subset of agents at each timestep using staggered planning windows. Unlike TP, however, PUSH plans RHCR-style windowed paths in general maps without relying on restrictive map assumptions. To maintain high throughput in congested environments, PUSH further integrates EPIBT-inspired priority inheritance, backtracking, and anytime improvements into its windowed planning. Empirical evaluations across two realistic MAPF scenarios requiring long-horizon reasoning show that PUSH scales to the same massive agent loads as EPIBT (e.g., 10k agents) while achieving significantly higher system throughput than all baselines.

Lifelong Multi-Agent Path Finding (LMAPF) requires repeatedly planning collision-free paths for agents that continuously receive new goals upon reaching their current ones. While many learning-based planners have been proposed for LMAPF, most rely on oversimplified kinematic assumptions that may overlook motion constraints critical to real-world performance. In this work, we study a more realistic LMAPF model derived from many real-world automated warehouse systems, termed LMAPF-R2, which incorporates robust safety constraints and in-place rotation constraints. These constraints substantially increase coordination difficulty, particularly in highly constrained spaces. To address these challenges, we propose Search-Aided Joint Reinforcement Learning (SJRL). We first augment neural policies with Causal PIBT, a single-step search-based planner that resolves agents' collisions and propagates their intentions. We then introduce a unified RL formulation that jointly optimizes agent and environment policies, where the environment policy learns graph edge costs to provide global movement guidance via backward Dijkstra search. Experiments demonstrate that SJRL achieves significant improvements over the strong search-based planner, Causal-PIBT, across multiple high-density maps. We further validate SJRL in a challenging mixed-reality warehouse environment with 8 physical robots and 248 virtual robots.

Multi-Agent Path Finding (MAPF) is a problem that requires computing collision-free paths for a set of agents from their start locations to designated goal locations. The problem has broad applications in domains where teams of robots must operate in a coordinated manner. ORCA* is a real time MAPF solver that assigns for each timestep a velocity for each agent. Due to its real time nature, it is myopic to future deadlocks that result from current decisions. ORCA*-MAPF attempts to remedy this limitation by introducing fallback mechanisms when deadlocks are detected. However, post hoc interventions often introduce significant flowtime overhead. In this paper, we introduce C-ORCA* and C-ORCA*-MAPF, continuous space MAPF algorithms that incorporate agents' entire spatial trajectory and their spatial dependencies to proactively prevent deadlocks from occurring, thus avoiding the high flowtime overhead associated with post hoc corrections in ORCA*-MAPF. The C-ORCA* family of algorithms significantly outperform previous state-of-the-art in terms of solve rate, runtime, and flowtime.

We study strategic space- and time-constrained cooperation between two self-interested agents through the Intermittent Strategic Cooperation-Based Two-Agent Path Planning (IC2PP) problem, a shortest-path game on graphs in which agents navigate toward individual targets while optionally cooperating at specific nodes to reduce their own travel times. Although such cooperation can strictly benefit both agents, it is strategically fragile: agents may deviate at any point along their paths. Modeled as a 2-player game, we characterize the structure of Pure Nash Equilibrium (PNE) joint strategies in IC2PP, and show that stable cooperation must follow a highly constrained form. We further prove that at least one PNE exists in every instance of IC2PP, and present a polynomial-time algorithm for enumerating all relevant PNEs. When multiple equilibria arise, we study coordination mechanisms based on bargaining-theoretic selection concepts and empirically compare equilibrium outcomes in terms of individual travel times and social welfare.

Local guidance has recently proven to be a powerful driver of empirical performance in real-time, suboptimal multi-agent pathfinding (MAPF), improving the scalable configuration-based solver LaCAM. By injecting informative spatiotemporal cues around each agent, local guidance mitigates congestion, reduces waiting, and remains scalable enough even with tight time budgets, yielding state-of-the-art performance for one-shot MAPF. This study asks whether the same benefits can be lifted to the lifelong setting (LMAPF), where tasks arrive continuously and improvements in per-step plans can increase task completion throughput over long horizons. We propose LLLG, a Lifelong version of LaCAM enhanced with Local Guidance, which employs a receding-horizon windowed planning framework and warm-starts guidance from the previous solution at each timestep. Our method scales effectively, maintains high throughput even in compact, dense environments, and surpasses existing planners, thereby pushing the frontier of real-time, lifelong MAPF.

In warehouse logistics, parcels released from the outfeed of an automated storage system must be routed through conveyor networks to workstations. Beyond collision avoidance, practical operations impose an additional requirement of order-contiguous arrivals: at each delivery point, parcels belonging to the same order must arrive as a consecutive block in the arrival sequence to reduce downstream re-sorting effort. We formalize this problem as online multi-agent path finding with order-contiguity (online MAPF-OC), where agents (i.e., parcels) appear over time and exit upon delivery. To efficiently solve online MAPF-OC, we propose Dual-Ordering Prioritized Planning (DOPP), a complete polynomial-time algorithm with a three-level structure that (i) searches order-level arrival sequences, (ii) refines agent-level priorities, and (iii) synthesizes feasible solutions via prioritized planning. Experiments on various conveyor-network layouts, including those derived from actual warehouses, demonstrate DOPP's practical scalability and ability to generate high-quality plans within tight time budgets.

Decentralized multi-agent path finding (MAPF) routes a team of agents on a shared grid, each acting from its own local view. The standard solution trains one shared neural policy with Proximal Policy Optimization (PPO), a popular on-policy reinforcement learning algorithm. Such a policy works well on clean observations, but a small input perturbation on one agent often changes its action, which then blocks a neighbour, and the team jams. In this paper we present two training recipes that keep the same network and the same deployment loop, yet make the policy hold up under perturbed observations. The first recipe, Adv-PPO, trains the shared policy against worst-case perturbations of its own input and selects the checkpoint by performance under adversarial perturbation. The second recipe, Adv-PPO+MACER, fine-tunes that checkpoint with a small on-policy smoothness term whose gradient follows the certified radius of randomized smoothing. On POGEMA with 8x8 maps and four agents, the unprotected PPO policy reaches 95.8% clean success but only 2.5% under the strongest attack. Adv-PPO recovers worst-case success to 59.2% at one percentage point of clean cost. Adv-PPO+MACER recovers it to 77.5% +/- 6.0% across three independent seeds at less than one percentage point of clean cost. We support these numbers with per-attack curves, a certified action-stability sanity check (which measures the smoothed-policy wrapper, not the deployed argmax policy), and side-by-side rollout storyboards that show the failure mode and the fix inside one environment instance.

Multi-agent pathfinding (MAPF) is a widely used abstraction for multi-robot trajectory planning problems, where multiple homogeneous agents move simultaneously within a shared environment. Although solving MAPF optimally is NP-hard, scalable and efficient solvers are critical for real-world applications such as logistics and search-and-rescue. To this end, the research community has proposed various decentralized suboptimal MAPF solvers that leverage machine learning. Such methods frame MAPF (from a single agent perspective) as a Dec-POMDP where at each time step an agent has to decide an action based on the local observation and typically solve the problem via reinforcement learning or imitation learning. We follow the same approach but additionally introduce a learnable communication module tailored to enhance cooperation between agents via efficient feature sharing. We present the Local Communication for Multi-agent Pathfinding (LC-MAPF), a generalizable pre-trained model that applies multi-round communication between neighboring agents to exchange information and improve their coordination. Our experiments show that the introduced method outperforms the existing learning-based MAPF solvers, including IL and RL-based approaches, across diverse metrics in a diverse range of (unseen) test scenarios. Remarkably, the introduced communication mechanism does not compromise LC-MAPF's scalability, a common bottleneck for communication-based MAPF solvers.

During the execution of Multi-Agent Path Finding (MAPF) plans in real-life applications, the MAPF assumption that the fleet's movement is perfectly synchronized does not apply. Since one or more of the agents may become delayed due to internal or external factors, it is often necessary to use a robust execution method to avoid collisions caused by desynchronization. Robust execution methods - such as the Action Dependency Graph (ADG) - synchronize the execution of risky actions, but often at the expense of increased plan execution cost, because it may require some agents to wait for the delayed agents. In such cases, the execution's cost can be reduced while still preserving safety by finding a new plan either by rescheduling (reordering the agents at crossroads) or the more general replanning capable of finding new paths. However, these operations may be costly, and the new plan may not even lead to lower execution cost than the original plan: for example, the two plans may be the exact same. Therefore, we estimate the benefit that can be achieved by single replanning in scenarios with delayed agents given an immediate state of the execution with a fully connected feed-forward neural network. The input to the neural network is a set of newly designed ADG-based features describing the robust execution's state and the impact of potential delays, and the output is an estimated benefit achievable by replanning. We train and test the network on a new labeled dataset containing 12,000 experiments, and we show that our proposed method is capable of reducing the impact of delays by up to 94.6% of the achievable reduction.