SAGE: Ergodic Control for Autonomous and Adaptive Inspection of Subsea Infrastructure

Subsea Christmas Trees (XTs) are underwater structures that use valves for directing oil flow, needing constant inspection. But not every valve carries the same risk at the same time: a valve with a suspected leak needs to be revisited far more often than one with a clean history, and that risk picture changes during the mission as new leaks are found. To handle this, we present SAGE (Semantic and Adaptive Generative Ergodicity), an ergodic-control architecture that allocates vehicle time in proportion to a live, sensor-derived risk distribution rather than a scripted route. We study a two-XT scenario, with five valves in total, and compare a fixed-loop A* tour against SAGE. Both methods can be tuned to spend similar total time near a high-risk valve, but only ergodic control also checks it more often: in simulation, a dominant-risk valve was revisited every 5.8 s under ergodic control against a fixed 8.1 s for every valve under A*, regardless of risk, so a leak can go unnoticed for barely two-thirds as long. Because the tracked distribution is recomputed rather than planned once, a newly detected leak shifts vehicle behavior on the next control cycle with no explicit re-planning step and no operator in the loop, which a fixed tour cannot do without a discrete re-route. We derive the ergodic control law behind this behavior and report simulation results on the five-valve scenario.