Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots

Optimal locomotion for limbless crawlers

Limbless crawling is ubiquitous in biology, from cells to organisms. We develop and analyze a model for the dynamics of one-dimensional elastic crawlers, subject to active stress and deformation-dependent friction with the substrate. We find that the optimal active stress distribution that maximizes the crawler's center-of-mass displacement given a fixed amount of energy input is a traveling wave. This theoretical optimum corresponds to peristalsislike extension-contraction waves observed in biological organisms, possibly explaining the prevalence of peristalsis as a convergent gait across species. Our theory elucidates key observations in biological systems connecting the anchoring phase of a crawler to the retrograde and prograde distinction seen in peristaltic waves among various organisms. Using our optimal gait solution, we derive a scaling relation between the crawling speed and body mass, explaining experiments on earthworms with three orders of magnitude body mass variations. Our results offer insights and tools for optimal bioinspired crawling robots design with finite battery capacity.

Gait switching with phase reversal of locomotory waves in the centipedeScolopocryptops rubiginosus

Crawling using locomotory waves is a common method of locomotion for limbless and many-legged invertebrates and stimulates the biomimetic engineering of flexible locomotion. It is generally believed that the direction of locomotory waves is fixed for a given species. However, we found that a centipede,Scolopocryptops rubiginosus, flexibly generated its gait to allow for locomotory waves that varied in direction, depending on (i) locomotion speed and (ii) the physical conditions of terrain. We also found a new type of centipede's swimming gait unlike eel-like way known so far which is using posteriorly traveling waves of horizontal body undulation. The gait patterns of the centipede were examined in various conditions and analyzed how the waves switched in detailed. We showed that gait patterns were associated with control of stride length rather than stride frequency. Discussion was made on a possible scenario of the gait transition in the centipede compatible with our observations. This finding may give a hint at bio-inspired control of flexible gait switching in response to irregular terrain.

Peristalsis by pulses of activity

Peristalsis by actively generated waves of muscle contraction is one of the most fundamental ways of producing motion in living systems. We show that peristalsis can be modeled by a train of rectangular-shaped solitary waves of localized activity propagating through otherwise passive matter. Our analysis is based on the Fermi-Pasta-Ulam (FPU) type discrete model accounting for active stresses and we reveal the existence in this problem of a critical regime which we argue to be physiologically advantageous.

Gait-optimized locomotion of wave-driven soft sheets

Inspired by the robust locomotion of limbless animals in a range of environments, the development of soft robots capable of moving by localized swelling, bending, and other forms of differential growth has become a target for soft matter research over the last decade. Engineered soft robots exhibit a wide range of morphologies, but theoretical investigations of soft robot locomotion have largely been limited to slender bodied or one-dimensional examples. Here, we demonstrate design principles regarding the locomotion of two-dimensional soft materials driven by morphoelastic waves along a dry substrate. Focusing on the essential common aspects of many natural and man-made soft actuators, a continuum model is developed which links the deformation of a thin elastic sheet to surface-bound excitation waves. Through a combination of analytic and numerical methods, we investigate the relationship between induced active stress and self-propulsion performance of self-propelling sheets driven by FitzHugh-Nagumo type chemical waves. Examining the role of both sheet geometry and terrain geography on locomotion, our results can provide guidance for the design of more efficient soft crawling devices.

Parking 3-sphere swimmer: II. The long-arm asymptotic regime

The paper carries on our previous investigations on the complementary version of Purcell's rotator (sPr₃): a low-Reynolds-number swimmer composed of three balls of equal radii. In the asymptotic regime of very long arms, the Stokes-induced governing dynamics is derived, and then experimented in the context of energy-minimizing self-propulsion characterized in the first part of the paper.

An earthworm-inspired soft robot with perceptive artificial skin

The bodies of earthworms are composed of repeating deformable structural units, called metameres, that generate the peristaltic body motions required for limbless underground burrowing and above-ground crawling. Metameres are actuated by circular and longitudinal muscles that are activated synchronously by the animals' nervous systems. A significant number of the neural-motor feedback loops function with sensory input gathered by the animals' highly sensitive skins, which are embedded with light, pressure and chemical receptors. In this paper, adopting the basic mechanisms employed by earthworms, we propose a new type of pneumatically-driven soft robot that can travel inside pipes by mimicking the motions and replicating the functionalities of a single metamere. Furthermore, we introduce a sensing scheme for feedback control that mimics the mechanical sensory capabilities of an earthworm's skin, which was developed upon stretchable liquid circuits capable of measuring strain and detecting pressure variations. The suitability of the proposed approach is demonstrated through several controlled locomotion experiments, employing two different robotic prototypes.