Time-Preserving Geometric Smoothing for Near-Threshold Large-Disk Multi-Agent Path Finding

Grid-based multi-agent path finding (MAPF) solvers scale to large teams, but their discrete schedules may not provide high-quality continuous finite-radius motions near the square-grid corner-passing threshold. We study endpoint-time-preserving geometric smoothing for disk agents at radius 0.35. We establish an embedded-graph corner-passing threshold for synchronized finite-radius local passes and derive the square-grid radius rc=2/4. Finite-radius realizations are formulated as Lipschitz trajectories, and we prove that standard four-neighbor schedules without vertex conflicts or head-on edge swaps are pairwise continuously feasible up to this threshold. The smoother replaces windows by shortcuts only when speed, obstacle-clearance, pairwise continuous-collision detection, and length checks pass. Accepted shortcuts preserve endpoint times, schedule-level makespan, discrete arrival records, and discrete sum-of-costs while enforcing geometric length non-increase; the strict-decrease subset yields the reported geometric sum-of-costs reductions. Across six MovingAI map settings, LaCAM solves 575 benchmark instances; 570 smoothed trajectories pass finite-radius validation, with median geometric sum-of-costs reductions of 9.9% on the main slice and 11.2% on the five-map extension. A targeted 100-agent radius sweep further supports the threshold interpretation by showing a clean feasibility transition around the predicted corner-passing radius. The results support time-preserving smoothing as a validated geometric-quality layer for scalable grid planners.