Convex Geometric Trajectory Tracking Using Lie Algebraic MPC for Autonomous Marine Vehicles

Controlling marine vehicles in challenging environ- ments 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 sce- narios involving ocean currents. Notably, our method substan- tially 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.