Optimal tracking control of an Autonomous Underwater Vehicle: A PMP approach

Anil B; Sneha Gajbhiye

doi:10.1016/j.isatra.2023.12.002

Optimal tracking control of an Autonomous Underwater Vehicle: A PMP approach

ISA Trans. 2024 Feb:145:298-314. doi: 10.1016/j.isatra.2023.12.002. Epub 2023 Dec 4.

Authors

Anil B¹, Sneha Gajbhiye²

Affiliations

¹ Department of Electrical Engineering, Indian Institute of Technology Palakkad, Kanjikkode, Kerala, India, 678623. Electronic address: 122004002@smail.iitpkd.ac.in.
² Department of Electrical Engineering, Indian Institute of Technology Palakkad, Kanjikkode, Kerala, India, 678623.

PMID: 38057173
DOI: 10.1016/j.isatra.2023.12.002

Abstract

This paper addresses the optimal tracking control problem of an Autonomous Underwater Vehicle (AUV) using Pontryagin's Minimum Principle (PMP). The formulation uses a choice of Hamiltonian function using the desired control objective with AUV dynamics acting as dynamic constraints. We first develop PMP based on AUV kinematics and then extend it to the dynamics to arrive at optimal thrusts and moments. Necessary conditions for optimality are derived for both the models using PMP, which results in optimal trajectories that simultaneously minimize the tracking error as well as the control cost, thereby arriving at energy optimality. It was observed that the adjoint variables (costates) are indeed the momenta in the inertial and body-fixed frames. At the kinematic level, this forms a stable solution. The developed methodology is applied to both 2D and 3D AUV model with disturbances due to inputs and ocean currents. Numerical simulations are carried out with the derived control laws for a given trajectory tracking target. Quantitative evaluation of the performance and comparison of the controller is done using Mean Square Error(MSE) and Total Variation(TV) measures. The proposed control laws are found to achieve the desired control objectives.

Keywords: Autonomous Underwater Vehicle; Optimal tracking control; Pontryagin’s Minimum Principle.