Energy-optimal linear quadratic tracking control for unmanned underwater vehicles in offshore aquaculture fish net-pen visual inspection

Unmanned underwater vehicles (UUVs) have been deployed for fish net-pen visual inspection (FNVI) in offshore aquaculture. Limited energy capacity of onboard power supplies constrains the UUV’s working range and operating time. To minimize the energy consumption by the UUV during the FNVI of the Blue Endeavour Project (an offshore salmon farm of the New Zealand King Salmon Company), an energy-optimal linear quadratic tracking (EO-LQT) control scheme is proposed in this paper. For EO-LQTs implementation, a new Linear-Parameter-Varying (LPV) system that approximates the nonlinear UUV dynamics model with an accuracy of approximately 99% regardless of the operating points in real-time, with the modified versions of Bhāskara I’s sine approximation and Shirali’s cosine approximation, is developed. The use of the Lagrangian under the Principle of Least Action with the UUV’s kinetic energy and the non-quadratic thruster power function in the EO-LQT performance index (PI) is demonstrated. The steps to solve the Hamilton-Jacobi-Bellman (HJB) equation with the non-quadratic Hamiltonian H are detailed to derive the new analytical EO-LQT optimal control form. Five EO-LQT controllers with different PIs are tested against the conventional LQT (CO-LQT) controller in both high-fidelity simulations under simulated disturbance speed up to 0.9 m/s and pool experiments, reducing energy consumption up to 37.1%. As key comparison metrics for the pose tracking and energy consumption, the mean-absolute-error (MAE) and T200 thruster power function are used to validate the effectiveness of the proposed EO-LQT controllers, compared to the CO-LQT controller.