Hierarchical PIwFF–Koopman-Based Offset-Free MPC for AUV Trajectory Tracking: Simulation and Pool Experiments

Abstract

Accurate trajectory tracking of autonomous underwater vehicles (AUVs) is challenging because nonlinear hydrodynamics, actuator constraints, and persistent plant–model mismatch degrade controller performance. This paper proposes a hierarchical proportional-integral with feedforward (PIwFF)–Koopman-based offset-free model predictive control (MPC) for trajectory tracking of the Xplorer-mini AUV. The outer PIwFF loop converts pose-tracking errors and reference pose rates into body-fixed velocity commands using a proportional-integral structure augmented with a velocity feedforward term to anticipate reference motion, while the inner Koopman-based MPC tracks the velocity/lifted-state commands with actuator and velocity constraints enforced by construction. A cascade stability analysis establishes uniform ultimate boundedness (UUB) of the tracking errors under standard MPC assumptions. To reduce persistent velocity-output bias caused by finite-dimensional Koopman approximation errors, unmodeled dynamics, and unknown persistent disturbances, the inner MPC is augmented with an output-error integrator. DMDc and eDMDc are compared as prediction models; although eDMDc improves open-loop prediction accuracy, DMDc is selected for closed-loop control because it provides comparable tracking performance at a lower computational cost. Furthermore, a preview command is introduced for time-varying references. Simulation and pool experiments demonstrate that the proposed controller reduces steady-state bias and improves trajectory tracking relative to the PIwFF–Koopman-based nominal MPC and PID–PID baselines under the tested conditions.