  Low-propulsion vessels can take advantage of powerful ocean currents to
navigate towards a destination. Recent results demonstrated that vessels can
reach their destination with high probability despite forecast errors. However,
these results do not consider the critical aspect of safety of such vessels:
because of their low propulsion which is much smaller than the magnitude of
currents, they might end up in currents that inevitably push them into unsafe
areas such as shallow areas, garbage patches, and shipping lanes. In this work,
we first investigate the risk of stranding for free-floating vessels in the
Northeast Pacific. We find that at least 5.04% would strand within 90 days.
Next, we encode the unsafe sets as hard constraints into Hamilton-Jacobi
Multi-Time Reachability (HJ-MTR) to synthesize a feedback policy that is
equivalent to re-planning at each time step at low computational cost. While
applying this policy closed-loop guarantees safe operation when the currents
are known, in realistic situations only imperfect forecasts are available. We
demonstrate the safety of our approach in such realistic situations empirically
with large-scale simulations of a vessel navigating in high-risk regions in the
Northeast Pacific. We find that applying our policy closed-loop with daily
re-planning on new forecasts can ensure safety with high probability even under
forecast errors that exceed the maximal propulsion. Our method significantly
improves safety over the baselines and still achieves a timely arrival of the
vessel at the destination.
