The Nautical δ-Corridor: A Connectivity-Preserving, Depth-Admissible Navigation Corridor for Autonomous Ship Navigation

Autonomous ships must show not only that their planned track is safe, but that the water they may need for an evasive manoeuvre is safe as well. This paper develops the nautical δ-corridor: a bounded, connected region of navigable water around a reference track on a bathymetric occupancy grid, in which the obstacle set is derived from the vessel’s dynamic draft and under-keel clearance policy, so that depth admissibility is an invariant of the construction rather than a measured outcome. Three phases build it: a distance-bounded expansion, a degree-based pruning yielding an anchor-protected 2-core, and an optional navigational refinement combining a minimum-width test, which removes regions reachable only through water narrower than the vessel can turn in, with a biconnectivity closure that guarantees no single cell can sever the corridor from the track. Four maritime extensions are introduced: a latitude-compensated metric, a half-width specified in nautical miles, a spatially adaptive envelope, and an asymmetric starboard reserve. Evaluation covers three physically defined scenarios—ocean passage, archipelago transit, and harbour approach—at four chart resolutions from 1002 to 10002 cells, against inflated-track, union-of-balls, and elastic-band baselines implemented under a common depth constraint. With δ fixed in nautical miles the envelope width varies by under 8% across a tenfold change in resolution, while a δ fixed in cells collapses tenfold. Degree-one pruning removes under 0.02% of the corridor whereas the width test removes up to 1.0%, showing that leaf removal alone does not eliminate single-access pockets; the closure then removes the few critical cells the width test itself creates. Sweeping the alteration angle shows what the starboard reserve buys: it leaves the standard 30° manoeuvre unchanged, but on the harbour approach a 90° alteration becomes executable from 55.3% of the track against 5.3% for a symmetric corridor spending the same total lateral allowance and occupying more area.