Sampled-data robust HOCBF safety filtering with online residual-calibrated disturbance bounds for hydrofoil roll...

This paper develops a residual-calibrated sampled-data robust safety filter based on high-order control barrier functions (HOCBFs) for hydrofoil roll regulation under wave-induced disturbances and actuator constraints. Because the fin deflection is modeled as an actuator state, the roll-angle constraint has relative degree three with respect to the commanded fin-rate input. Combined with zero-order-hold implementation, this high-relative-degree structure requires safety enforcement beyond the sampling instants. We derive a sampled-data robust HOCBF condition in which disturbance amplitude, inter-sample disturbance increment, disturbance derivative, and inter-sample state drift enter as explicit tightening terms. The disturbance-related terms are constructed through a causal residual-proxy calibration module: sliding-window conformal quantiles provide local proxy radii, and residual-to-disturbance margins convert them into effective true-disturbance bounds. This separation prevents residual-proxy coverage from being misinterpreted as direct coverage of the physical disturbance. For the hydrofoil roll subsystem, the proposed RC-HOCBF-QP retains a scalar hard-first/soft-second interval structure under fin-deflection and fin-rate limits. The hard stage projects the nominal command onto the actuator-limited robust HOCBF interval whenever this interval is nonempty, whereas the two-stage lexicographic fallback is used only as a feasibility-aware fallback. Monte Carlo simulations evaluate fine-grid safety, actuator feasibility, proxy and true-disturbance coverage, hard infeasibility, slack activation, robust tightening, input-modification frequency, and input-energy trade-offs.