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.

翻译：在复杂环境中控制航行器是一项艰巨任务，这源于非线性水动力学和不确定外部干扰的存在。尽管非线性模型预测控制（MPC）在应对这些问题上展现出潜力，但其实际应用常受计算资源限制所约束。本文提出一种高效控制器，通过采用基于李群上的凸误差状态MPC实现航行器轨迹跟踪。利用李群固有的几何性质，我们能够构建全局有效的误差动力学模型，并建立基于二次规划的优化问题。通过包含海流场景在内的广泛数值仿真，所提出的MPC方法在轨迹跟踪中展现出有效性。值得注意的是，与非线性MPC相比，本方法显著降低了计算时间，使其特别适用于具有长预测时域或涉及小型航行器的实时控制应用。