Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots

Peristalsis, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a ``phase coordination'' principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed

An earthworm-like modular soft robot for locomotion in multi-terrain environments

Robotic locomotion in subterranean environments is still unsolved, and it requires innovative designs and strategies to overcome the challenges of burrowing and moving in unstructured conditions with high pressure and friction at depths of a few centimeters. Inspired by antagonistic muscle contractions and constant volume coelomic chambers observed in earthworms, we designed and developed a modular soft robot based on a peristaltic soft actuator (PSA). The PSA demonstrates two active configurations from a neutral state by switching the input source between positive and negative pressure. PSA generates a longitudinal force for axial penetration and a radial force for anchorage, through bidirectional deformation of the central bellows-like structure, which demonstrates its versatility and ease of control. The performance of PSA depends on the amount and type of fluid confined in an elastomer chamber, generating different forces and displacements. The assembled robot with five PSA modules enabled to perform peristaltic locomotion in different media. The role of friction was also investigated during experimental locomotion tests by attaching passive scales like earthworm setae to the ventral side of the robot. This study proposes a new method for developing a peristaltic earthworm-like soft robot and provides a better understanding of locomotion in different environments

Mathematical models for biological motility: From peristaltic crawling to plant nutations

In this thesis we propose mathematical models for the motility of one-dimensional crawlers moving along a line and for growing slender plant organs, which are applied to the study of peristaltic crawling and nutations of plant shoots, respectively. The first chapter contains a theoretical analysis of metameric worm-like robotic crawlers, and it investigates optimal actuation strategies. Our main result is that peristalsis, i.e., muscle extension and contraction waves propagating along the body, is an optimal actuation strategy for locomotion. We give a rigorous mathematical proof of this result by solving analytically the optimal control problem in the regime of small deformations. We show that phase coordination arises from the geometric symmetry of a 1D system, exactly in the periodic case and approximately, due to edge-effects, in the case of a crawler of finite length. In the second chapter we introduce the general framework of morphoelastic rods to model elongating slender plant organs. This chapter is intended as preparatory to the third one, where we derive a rod model that is exploited to investigate the role of mechanical deformations in circumnutating plant shoots. We show that, in the absence of endogenous cues, spontaneous oscillations might arise as system instabilities when a loading parameter exceeds a critical value. Moreover, when oscillations of endogenous nature are present, their relative importance with respect to the ones associated with the former mechanism varies in time, as the biomechanical properties of the shoot change. Our findings suggest that the relative importance of exogenous versus endogenous oscillations is an emergent property of the system, and that elastic deformations play a crucial role in this kind of phenomena

Limit cycles for dynamic crawling locomotors with periodic prescribed shape

We study the asymptotic evolution of a family of dynamic models of crawling locomotion, with the aim to introduce a well-posed characterization of a gait as a limit behaviour. The locomotors, which might have a discrete or continuous body, move on a line with a periodic prescribed shape change, and might possibly be subject to external forcing (e.g. crawling on a slope). We discuss how their behaviour is affected by different types of friction forces, including also set-valued ones such as dry friction. We show that, under mild natural assumptions, the dynamics always converge to a relative periodic solution. The asymptotic average velocity of the crawler yet might still depend on its initial state, so we provide additional assumption for its uniqueness. In particular, we show that the asymptotic average velocity is unique both for strictly monotone friction forces, and also for dry friction, provided in the latter case that the actuation is sufficiently smooth (for discrete models) or that the friction coefficients are always nonzero (for continuous models). We present several examples and counterexamples illustrating the necessity of our assumptions

Dynamical systems : mathematical and numerical approaches

Proceedings of the 13th Conference „Dynamical Systems - Theory and Applications" summarize 164 and the Springer Proceedings summarize 60 best papers of university teachers and students, researchers and engineers from whole the world. The papers were chosen by the International Scientific Committee from 315 papers submitted to the conference. The reader thus obtains an overview of the recent developments of dynamical systems and can study the most progressive tendencies in this field of science