Optimal kite trajectory generation for ship traction: A comparison of numerical optimal control methods and a case study

This paper presents an overview of optimal trajectory generation for kite systems applied to ship traction, along with an illustrative case study. Motivated by the growing need for sustainable maritime propulsion, this paper begins by reviewing the fundamental principles of kite-assisted systems, their components, and the main challenges associated with their modeling and control. A special focus is placed on the optimal control formulation of the trajectory generation problem, highlighting general optimization strategies and transcription methods. Four major numerical approaches, GPOPS-II, ICLOCS2, CasADi, and MUSCOD, are critically reviewed, emphasizing their suitability for kite systems. A detailed case study is then conducted using CasADi combined with multiple shooting and IPOPT, with justification provided for this methodological choice. The obtained simulation results are analyzed, with particular attention to the trade-off between traction performance and energy consumption. The optimized figure-eight trajectory yields an average traction force of 980.35 kN for a 500 m 2 kite, corresponding to a wing loading of 1.96 kN/m 2 , with winch power consumption representing approximately 6% of the average mechanical power generated. A sensitivity analysis with respect to the true wind angle further confirms the robustness of the proposed approach. Finally, the paper identifies key research gaps and outlines future directions to improve the efficiency and robustness of kite-based ship traction systems.