Course-Keeping Control for Ship Great Circle Routes Based on Finsler Geometry and Conformal Vector Fields
Copyright © 2026 Yanjun Zeng. Published by Nan Yang Academy of Sciences Pte. Ltd.
This is an open access article under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) License.
Abstract
To address the anisotropic navigation costs caused by environmental disturbances in ocean navigation, this study introduces Finsler geometry and conformal vector field theory to maintain the course of ocean vessels on great circle routes. Based on Finsler geometry, an effective metric for ship navigation is constructed, and a generalized great circle geodesic incorporating environmental losses is built. A globally smooth course field is constructed using a conformal vector field to solve for continuously differentiable desired course commands. A hierarchical course-maintaining control architecture is established, creating an integrated theoretical system encompassing navigation space modeling, course command generation, and closed-loop course control. Experimental results show that under weak disturbance conditions, the proposed method can output continuous and smooth course commands, completely eliminating course jumps and track oscillations. Under moderate disturbance conditions, the average steady-state error of the ship's course is reduced to 0.35° and the average amplitude of rudder angle fluctuation is reduced to 1.68°, representing reductions of 68.75% and 60.09%, respectively, compared to the control group. Under strong disturbance and long-duration operation conditions, the average daily energy consumption of the ship is reduced to 21.4 t of standard fuel per day, achieving an energy saving effect of 22.18%. In summary, this method can accurately adapt to the anisotropic characteristics of ocean navigation, effectively improve heading tracking accuracy, reduce rudder wear and navigation energy consumption, and demonstrate excellent robustness and engineering practicality.
Keywords: Finsler Geometry, Conformal Vector Field, Great Circle Route, Course Maintenance, Ship Path Tracking
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