  Controlling marine vehicles in challenging environments is a complex task due
to the presence of nonlinear hydrodynamics and uncertain external disturbances.
Despite nonlinear model predictive control (MPC) showing potential in
addressing these issues, its practical implementation is often constrained by
computational limitations. In this paper, we propose an efficient controller
for trajectory tracking of marine vehicles by employing a convex error-state
MPC on the Lie group. By leveraging the inherent geometric properties of the
Lie group, we can construct globally valid error dynamics and formulate a
quadratic programming-based optimization problem. Our proposed MPC demonstrates
effectiveness in trajectory tracking through extensive-numerical simulations,
including scenarios involving ocean currents. Notably, our method substantially
reduces computation time compared to nonlinear MPC, making it well-suited for
real-time control applications with long prediction horizons or involving small
marine vehicles.
