Analytical insights into optimality and resonance in fish swimming

Kohannim, Saba; Iwasaki, Tetsuya

doi:10.1098/rsif.2013.1073

Cited by 24 publications

(26 citation statements)

References 41 publications

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“…Scaling parameters are of great importance in describing the dominant physics of locomotion. The Strouhal (St) number St(=f A/U) is one such parameter that has been used widely to characterize aquatic locomotion [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] when the inertial fluid effects are dominant (high swimming velocities or large body sizes). The Strouhal number relates swimming speed U to the tail-beat frequency f and tail-beat amplitude (tip-to-tip excursion of the tail) A.…”

Section: Introductionmentioning

confidence: 99%

On the rules for aquatic locomotion

et al. 2017

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We present unifying rules governing the efficient locomotion of swimming fish and marine mammals. Using scaling and dimensional analysis, supported by new experimental data, we show that efficient locomotion occurs when the values of the Strouhal (St) number St(=f A/U) and A * (=A/L), two nondimensional numbers that relate forward speed U , tail-beat amplitude A, tail-beat frequency f , and the length of the swimmer L are bound to the tight ranges of 0.2-0.4 and 0.1-0.3, respectively. The tight range of 0.2-0.4 for the St number has previously been associated with optimal thrust generation. We show that the St number alone is insufficient to achieve optimal aquatic locomotion, and an additional condition on A * is needed. More importantly, we show that when swimming at minimal power consumption, the Strouhal number of a cruising swimmer is predetermined solely by the shape and drag characteristics of the swimmer. We show that diverse species of fish and cetaceans cruise indeed with the St number and A * predicted by our theory. Our findings provide a physical explanation as to why fast aquatic swimmers cruise with a relatively constant tail-beat amplitude of approximately 20% of the body length, and their swimming speed is nearly proportional to their tail-beat frequency.

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Section: Introductionmentioning

confidence: 99%

On the rules for aquatic locomotion

et al. 2017

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“…For instance, modeling and gait analyses within our framework have supported the hypotheses that carangiform fish exploit body-fluid resonance for efficient swimming [30] and two representative gaits of batoids, undulation and oscillation [31], result from energy optimization under round and triangular shapes of large pectoral fins [32], [33]. In the field of engineering, our framework is useful for proof-of-concept designs of mechanical rectifiers.…”

Section: Discussionmentioning

confidence: 99%

Dynamical Model and Optimal Turning Gait for Mechanical Rectifier Systems

Kohannim

Iwasaki

2017

IEEE Trans. Automat. Contr.

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Abstract-Animal locomotion can be viewed as mechanical rectification due to the dynamics that convert periodic body movements to a positive average thrust, resulting in a steady locomotion velocity. This paper considers a general multi-body mechanical rectifier under continuous interactions with the environment, with full rotation and translation in three dimensional space. The equations of motion are developed with respect to body coordinates to allow for direct analysis of maneuvering dynamics. The paper then formulates and solves an optimal turning gait problem for a mechanical rectifier traveling along a curved path, with propulsive forces generated by periodic body deformation (gait). In particular, the gait is optimized to minimize a quadratic cost function, subject to constraints on average locomotion velocity and average angular velocity. The problem is proven to reduce to two separate, tractable minimization problems solvable for globally optimal solutions. The first problem solves for the optimal shape offset that results in turning, while the other solves for the optimal gait that results in locomotion along a straight path. A case study of a locomotor in a fluid environment is presented to demonstrate the utility of the method for robotic locomotor design.

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“…Experiments have shown that a natural walking stride conforms to the resonant frequency of the limbs when they are modeled as pendulums (Holt, Hamill, & Anders, 1991;Wagenaar & van Emmerik, 2000). Mathematical analysis of inertial swimmers (high Reynolds number swimming) supports the existence of resonance peaks when considering muscle tension (Kohannim & Iwasaki, 2014), travel speed, and efficiency (Gazzola, Argentina, & Mahadevan, 2015) with respect to frequency. Animals can also tune the resonance frequency of their bodies.…”

Section: Introductionmentioning

confidence: 86%

Exploiting natural dynamics for gait generation in undulatory locomotion

Ludeke¹,

Iwasaki²

2019

International Journal of Control

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Robotic vehicles inspired by animal locomotion are propelled by interactive forces from the environment resulting from periodic body movements. The pattern of body oscillation (gait) can be mimicked from animals, but understanding the principles underlying the gait generation would allow for flexible and broad applications to match and go beyond the performance of the nature's design. We hypothesize that the traveling-wave oscillations, often observed in undulatory locomotion, can be characterized as a natural oscillation of the locomotion dynamics, and propose a formal definition of the natural gait for locomotion systems. We first identify the dynamics essential to undulatory locomotion, and define the mode shape of natural oscillation by the free response of an idealized system. We then use bodyenvironment resonance to define the amplitude and frequency of the oscillations. Explicit formulas for the natural gait are derived to provide insight into the mechanisms underlying undulatory locomotion. An example of leech swimming illustrates how undulatory gaits similar to those observed can be produced as the natural gait, and how they can be modulated to achieve a variety of swim speeds.

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Analytical insights into optimality and resonance in fish swimming

Cited by 24 publications

References 41 publications

On the rules for aquatic locomotion

On the rules for aquatic locomotion

Dynamical Model and Optimal Turning Gait for Mechanical Rectifier Systems

Exploiting natural dynamics for gait generation in undulatory locomotion

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