Strouhal-Aware Model Predictive Control for Efficient Multi-Fin Flapping Locomotion

Yuya Hamamatsu; Zixi Chen; Maarja Kruusmaa; Asko Ristolainen

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arXiv · 2607.03216

Strouhal-Aware Model Predictive Control for Efficient Multi-Fin Flapping Locomotion

Yuya Hamamatsu·Zixi Chen·Maarja Kruusmaa·Asko Ristolainen

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Abstract

Efficient flapping propulsion hinges on operating within a narrow Strouhal number window, a principle nature has converged upon for maximum thrust-to-power ratio. We translate this bioinspired empirical rule into real-time control, demonstrating it on an autonomous underwater vehicle driven by four soft fins. The proposed Strouhal-aware Model Predictive Control (MPC) enhances a quasi-steady hydrodynamic model with an explicit penalty for Strouhal deviation, solving the resulting nonconvex problem via a two-stage sampling and gradient optimization that runs onboard at 25 Hz. Pool and field trials show that the controller keeps each fin within the optimal Strouhal corridor (0.25-0.35) while precisely tracking commanded forces. This results in a mean reduction in mechanical power of 8.8\% to 32\% throughout the cruising range of 0.1 to 0.3 m/s. The proposed method also allows for a velocity of 0.4 m/s, which is unattainable for a baseline of the conventional inverse model. The results confirm that embedding first-principle flow physics into an MPC objective yields tangible endurance gains without sacrificing agility, offering a generic pathway to energy-aware locomotion in next-generation multifin robots.

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Yuya Hamamatsu, Zixi Chen, Maarja Kruusmaa, Asko Ristolainen. 2026-07-03. Strouhal-Aware Model Predictive Control for Efficient Multi-Fin Flapping Locomotion. https://arxiv.org/abs/2607.03216

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