Energy-Optimal Control for Autonomous Underwater Vehicles Using Economic Model Predictive Control

Improving endurance is important for autonomous underwater vehicles (AUVs) as it affects the operational cost and application range of the vehicle. In this article, we propose an economic model predictive control (EMPC)-based controller to reduce the control energy of AUVs while performing waypoint tracking. The proposed EMPC controller optimizes stage costs capturing the control energy consumed within the prediction horizon and a terminal cost approximating the energy-to-go, the energy required to reach the desired waypoint from the end of the prediction horizon. To approximate the energy-to-go, we partition it into the dynamic and static segments based on the operational characteristics of the optimal vehicle maneuver obtained from off-line trajectory optimization using direct collocation (DC). To account for the disturbances caused by ocean currents, we adopt the energy-to-go to a virtual Earth-fixed frame that transforms the drift in the vehicle location to the drift in the desired waypoint. Theoretical and numerical analyses of the approximated energy-to-go reveal that the proposed controller can balance the tradeoffs among energy components spent for vehicle surge, heave, and yaw controls in consideration of vehicle dynamics. Simulations under different flow conditions are conducted to compare the proposed approach with DC and a line-of-sight (LOS) guidance-based approach that optimizes vehicle surge speed for energy minimization. Through simulations, it is shown that the proposed approach achieves near-optimal performance as DC and outperforms the LOS-based approach.