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

2026-07-03

AI Summary

This study addresses the challenge of balancing efficiency and maneuverability in multi-fin oscillatory-propulsion underwater robots during cruising. The authors propose a novel approach that embeds a Strouhal number constraint (St = 0.25–0.35) directly into the objective function of model predictive control (MPC). Grounded in first-principles fluid dynamics, this method enables direct optimization of energy efficiency within the MPC framework by integrating a quasi-steady hydrodynamic model and a two-stage non-convex optimization algorithm, achieving real-time operation at 25 Hz on onboard hardware. Experimental results demonstrate an 8.8%–32% reduction in mechanical power consumption across cruising speeds of 0.1–0.3 m/s, successful execution of high-speed maneuvers up to 0.4 m/s—unattainable with conventional methods—and precise tracking of commanded forces.

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.

Problem

• Strouhal number
• flapping locomotion
• energy efficiency
• underwater vehicle
• multi-fin propulsion

Innovation

• Strouhal-aware MPC
• flapping locomotion
• energy-efficient control
• soft fin propulsion
• nonconvex optimization