Exploiting natural dynamics for gait generation in undulatory locomotion

Abstract

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.

Towards the optimization of passive undulatory locomotion on land: mathematical and physical models

“…Contrarily, in [ 24 ] for dry frictional environment, it is found that at resonance, the speed of undulatory locomotion decreases and the power increases. More recently, in [ 37 ], for viscous friction, the resonance frequency is defined as the frequency at which the speed of a system is maximized with minimum actuation effort for undulatory locomotion. In this section we study the correlation between the input frequency and the resulting speed.…”

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

“…The author emphasizes that the analytical fluid force model ( 4) is greatly simplified and cannot, for example, describe the pressure or shear force variation across the wings or body obeying the Bernoulli's principle as shown in figures 14(a) and (b) in [16] or other hydrodynamic characteristics of the swimming. It is only used in our study as well as other studies [21,23,[32][33][34][35]37] to give an approximation of the fluid force acting on the wing or body in the study of wing-or body-fluid interaction which allows us to study the response of wing kinematics to the tension and fluid force, to investigate the influence of resonance exploitation of wing natural modes on wing oscillation amplitude, the total thrust and the muscle power consumption, and to derive the analytical relationships of swimming kinematics and kinetics (the results in sections 4.1 and 4.2). For example, simulation showed that when the actuation frequency of the wing was 0.5 Hz, off the resonance frequency 0.29 Hz, the peak power of the middle tensegrity fin rays increased by more than 70%, but both the wing peak-to-peak oscillation .…”

Repetitive Learning Control for Body Caudal Undulation with Soft Sensory Feedback

“…By synchronizing body undulation frequency with the flow, fish swim efficiently, harnessing energy from the fluid and converting it into propulsion (Beal et al, 2006; Akanyeti et al, 2016; Liao and Akanyeti, 2017). The oscillation of the caudal fin emerges as one of the most efficient propulsion modes in terms of transport costs (Rayner, 1986; Ludeke and Iwasaki, 2019), and underwater speeds are enhanced significantly (Block et al, 1992), resulting in passive propulsion even in deceased fish specimens (Liao et al, 2003).…”