Ocean Current-Harnessing Stage-Gated MPC: Monotone Cost Shaping and Speed-to-Fly for Energy-Efficient AUV Navigation

Autonomous Underwater Vehicles (AUVs) are a highly promising technology for ocean exploration and diverse offshore operations, yet their practical deployment is constrained by energy efficiency and endurance. To address this, we propose Current-Harnessing Stage-Gated MPC, which exploits ocean currents via a per-stage scalar which indicates the "helpfulness" of ocean currents. This scalar is computed along the prediction horizon to gate lightweight cost terms only where the ocean currents truly aids the control goal. The proposed cost terms, that are merged in the objective function, are (i) a Monotone Cost Shaping (MCS) term, a help-gated, non-worsening modification that relaxes along-track position error and provides a bounded translational energy rebate, guaranteeing the shaped objective is never larger than a set baseline, and (ii) a speed-to-fly (STF) cost component that increases the price of thrust and softly matches ground velocity to the ocean current, enabling near zero water-relative "gliding". All terms are C1 and integrate as a plug-and-play in MPC designs. Extensive simulations with the BlueROV2 model under realistic ocean current fields show that the proposed approach achieves substantially lower energy consumption than conventional predictive control while maintaining comparable arrival times and constraint satisfaction.