Continuous-Space Roadmap Generation for Mobile Robot Fleets with Distance Constraints and Geometry-Aware Discretization

We study a graph pathfinding problem Distance-$r$ Independent Unlabeled Multi-Agent Pathfinding, finding a set of collision-free paths between two sets where agents must stay at pairwise distance at least $r+1$ at all times. This additional constraint, generalizing collision modeling for classical MAPF, targets aspects of real-world multi-agent coordination. This additional distance constraint makes feasibility (i.e., whether a solution exists) PSPACE-complete, in contrast to standard (unlabeled) MAPF, where it can be decided in polynomial time. We address the challenge via two complementary approaches: (i) reduction-based optimal algorithms with a feasibility-preserving compression procedure, and (ii) a configuration generator-based search. Despite the hardness, empirical results show that our algorithm can handle hundreds of agents in a practical timeframe.

Mobile robot path planning methods are often constrained by vast search spaces, resulting in latency in samplingbased algorithms. Learning-based approaches frequently suffer from local region fragmentation and global topological inconsistency. To tackle the problem, we present the Connectivity- Preserving Region Proposal Network (CP-RPN), a segmentationguided model designed to predict compact and topologically connected candidate regions, significantly compressing the search space. Specifically, we design a segmentation model that leverages a Deformable Attention Transformer (DAT) to capture long-range dependencies for global connectivity, with a Deconvolutional decoder to preserve fine-grained spatial details. To guarantee the connectivity of the predicted mask, we design a composite loss function that combines Cross-Entropy loss for pixelwise supervision, a Connectivity-Aware loss to enhance local coherence, and a Topological Continuity loss based on persistent homology to enforce global connectivity. Building on these highconnectivity corridor-like regions, the Voronoi diagram is used to plan the path, backed by a local A* fallback mechanism to ensure robustness. Experimental results demonstrate that CPRPN reduces the candidate region size by over 60.13% compared to the MPT baseline and achieves deterministic low-latency planning (avg. 0.11s) with a 99.60% success rate, outperforming traditional sampling-based algorithms in stability.

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.