Analytical insights into optimality and resonance in fish swimming

Robot motor learning shows emergence of frequency-modulated, robust swimming with an invariant Strouhal number

Fish locomotion emerges from diverse interactions among deformable structures, surrounding fluids and neuromuscular activations, i.e. fluid-structure interactions (FSI) controlled by fish's motor systems. Previous studies suggested that such motor-controlled FSI may possess embodied traits. However, their implications in motor learning, neuromuscular control, gait generation, and swimming performance remain to be uncovered. Using robot models, we studied the embodied traits in fish-inspired swimming. We developed modular robots with various designs and used central pattern generators (CPGs) to control the torque acting on robot body. We used reinforcement learning to learn CPG parameters for maximizing the swimming speed. The results showed that motor frequency converged faster than other parameters, and the emergent swimming gaits were robust against disruptions applied to motor control. For all robots and frequencies tested, swimming speed was proportional to the mean undulation velocity of body and caudal-fin combined, yielding an invariant, undulation-based Strouhal number. The Strouhal number also revealed two fundamental classes of undulatory swimming in both biological and robotic fishes. The robot actuators were also demonstrated to function as motors, virtual springs and virtual masses. These results provide novel insights in understanding fish-inspired locomotion.

Numerical Investigation of Dimensionless Parameters in Carangiform Fish Swimming Hydrodynamics

Research into how fish and other aquatic organisms propel themselves offers valuable natural references for enhancing technology related to underwater devices like vehicles, propellers, and biomimetic robotics. Additionally, such research provides insights into fish evolution and ecological dynamics. This work carried out a numerical investigation of the most relevant dimensionless parameters in a fish swimming environment (Reynolds Re, Strouhal St, and Slip numbers) to provide valuable knowledge in terms of biomechanics behavior. Thus, a three-dimensional numerical study of the fish-like lambari, a BCF swimmer with carangiform kinematics, was conducted using the URANS approach with the k-ω-SST transition turbulence closure model in the OpenFOAM software. In this study, we initially reported the equilibrium Strouhal number, which is represented by St∗, and its dependence on the Reynolds number, denoted as Re. This was performed following a power-law relationship of St∝Re(-α). We also conducted a comprehensive analysis of the hydrodynamic forces and the effect of body undulation in fish on the production of swimming drag and thrust. Additionally, we computed propulsive and quasi-propulsive efficiencies, as well as examined the influence of the Reynolds number and Slip number on fish performance. Finally, we performed a vortex dynamics analysis, in which different wake configurations were revealed under variations of the dimensionless parameters St, Re, and Slip. Furthermore, we explored the relationship between the generation of a leading-edge vortex via the caudal fin and the peak thrust production within the motion cycle.

Flexible tensegrity wing design and insights in principles of swimming kinematics of batoid rays

A novel tensegrity wing design is first proposed which can emulate the kinematic waves of the pectoral fin of batoid rays and has a simple structure for manufacture. The attitude control and the regulation of wing natural frequency are realized by wing morphing. Then analytical insights in batoid ray swimming are gained by analyzing the analytical wing (cable)-fluid interaction model, whose parameters are determined based on the biological data. The stride length (traveled distance per cycle normalized by the body length (BL)) is shown to be almost invariant among different-sized rays if the phase and amplitude of wing flexion angles remain unchanged. This result is supported by biological data, 1.5 and 1.47 respectively for the manta ray and cownose ray, though their flapping frequencies (0.15-0.45 Hz and 0.64-1.25 Hz respectively) and body sizes (1.25 m and 0.15 m respectively) are very different, and similar to the expression for the carangiform fish swimming. In other words, the swimming kinematics of two different swimming forms are described by a similar analytical equation when the body resonance is exploited. The fluid force and cable tension are both found to be proportional to the fourth power of the body size and the square of the wing flapping frequency, which may tell that the flapping frequency of the manta ray (BL = 1.25 m) is much smaller than that of the cownose ray (BL = 0.15 m) is to avoid both the large actuation tension and fluid force density due to the size increase.

Scaling of swimming performance in baleen whales

The scale-dependence of locomotor factors have long been studied in comparative biomechanics, but remain poorly understood for animals at the upper extremes of body size. Rorqual baleen whales include the largest animals, but we lack basic kinematic data about their movements and behavior below the ocean surface. Here we combined morphometrics from aerial drone photogrammetry, whale-borne inertial sensing tag data, and hydrodynamic modeling to study the locomotion of five rorqual species. We quantified changes in tail oscillatory frequency and cruising speed for individual whales spanning a threefold variation in body length, corresponding to an order of magnitude variation in estimated body mass. Our results showed that oscillatory frequency decreases with body length (∝ length−0.53) while cruising speed remains roughly invariant (∝ length0.08) at 2 m s−1. We compared these measured results for oscillatory frequency against simplified models of an oscillating cantilever beam (∝ length−1) and an optimized oscillating Strouhal vortex generator (∝ length−1). The difference between our length-scaling exponent and the simplified models suggests that animals are often swimming non-optimally in order to feed or perform other routine behaviors. Cruising speed aligned more closely with an estimate of the optimal speed required to minimize the energetic cost of swimming (∝ length0.07). Our results are among the first to elucidate the relationships between both oscillatory frequency and cruising speed and body size for free-swimming animals at the largest scale.

Scaling in Free-Swimming Fish and Implications for Measuring Size-at-Time in the Wild

This study was motivated by the need to measure size-at-age, and thus growth rate, in fish in the wild. We postulated that this could be achieved using accelerometer tags based first on early isometric scaling models that hypothesize that similar animals should move at the same speed with a stroke frequency that scales with length-1, and second on observations that the speed of primarily air-breathing free-swimming animals, presumably swimming 'efficiently', is independent of size, confirming that stroke frequency scales as length-1. However, such scaling relations between size and swimming parameters for fish remain mostly theoretical. Based on free-swimming saithe and sturgeon tagged with accelerometers, we introduce a species-specific scaling relationship between dominant tail beat frequency (TBF) and fork length. Dominant TBF was proportional to length-1 (r2 = 0.73, n = 40), and estimated swimming speed within species was independent of length. Similar scaling relations accrued in relation to body mass-0.29. We demonstrate that the dominant TBF can be used to estimate size-at-time and that accelerometer tags with onboard processing may be able to provide size-at-time estimates among free-swimming fish and thus the estimation of growth rate (change in size-at-time) in the wild.