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In recent years, the use of autonomous undersea vehicles (AUVs) for highly time-critical at-sea operations involving surface ships has received increased attention, magnifying the importance of optimal interception. Finding the optimal route to a moving target is a challenging procedure. In this work, we describe and apply our exact time-optimal path planning methodology and the corresponding software to such ship interception problems. A series of numerical ship interception experiments is completed in the southern littoral of Massachusetts, namely in Buzzards Bay and Vineyard Sound around the Elizabeth Islands and Martha's Vineyard. Ocean currents are estimated from a regional ocean modeling system. We show that complex coastal geometry, ship proximity, and tidal current phases all play key roles influencing the time-optimal vehicle behavior. Favorable or adverse currents can shift the optimal route from one island passage to another, and can even cause the AUV to remain nearly stationary until a favorable current develops. We also integrate the Kelvin wedge wake model into our path planning software, and show that considering wake effects significantly complicates the shape of the time-optimal paths, requiring AUVs to execute sequences of abrupt turns and tacking maneuvers, even in highly idealized scenarios. Such behavior is reminiscent of ocean animals swimming in wakes. In all cases, it is shown that our level set partial differential equations successfully guide the time-optimal vehicles through regions with the most favorable currents, avoiding regions with adverse effects, and accounting for the ship wakes when present. |
