Periodical Body Deformations are Optimal Strategies for Locomotion

Giraldi, Laëtitia; Jean, Frédéric

doi:10.1137/19m1280120

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…Given an initial position y 0 , a single iteration of the gait will displace the locomotor to γy 0 . be evaluated in the long-time limit [23], so that optimality is considered only among limit-cycles. Example of this limit-cycle optimization have been discussed, for instance, for the Chaplygin sleigh [16,36] and for a model of quasistatic crawling [9].…”

Section: Introductionmentioning

confidence: 99%

Limit cycles for dynamic crawling locomotors with periodic prescribed shape

Gidoni

Margheri

Rebelo

2023

Z. Angew. Math. Phys.

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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.

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Section: Introductionmentioning

confidence: 99%

Limit cycles for dynamic crawling locomotors with periodic prescribed shape

Gidoni

Margheri

Rebelo

2023

Z. Angew. Math. Phys.

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“…A rigorous proof of the well-posedness and uniqueness of the asymptotic behaviour of the system is not only relevant per se, but can also be seen as a preliminary step to gait optimization. Indeed, since gaits can be properly defined only as an asymptotic property of a periodic input, gait optimization must also be evaluated in the long-time limit [23], so that optimality is considered only among limit-cycles. Example of this limit-cycle optimization have been discussed, for instance, for the Chaplygin sleigh [16,37] and for a model of quasistatic crawling [9].…”

Section: Introductionmentioning

confidence: 99%

Limit cycles for dynamic crawling locomotors with periodic prescribed shape

Gidoni¹,

Margheri²,

Rebelo³

2022

Preprint

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We study the asymptotic behaviour of a family of dynamic models of crawling locomotion, with the aim of characterizing a gait as a limit property. 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.

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“…However, optimization is central to control theory. In a recent work [27] it is shown that, for a quadratic optimization problem for an equivariant locomotion system with two controls, the optimal controls are periodic. Thus, a possible future research direction is to apply the ideas highlighted in this paper to the study of the relative periodic orbits obtained from such periodic optimal controls.…”

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confidence: 99%

Control of locomotion systems and dynamics in relative periodic orbits

Fassò

Passarella

Zoppello

2020

Journal of Geometric Mechanics

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The connection between the dynamics in relative periodic orbits of vector fields with noncompact symmetry groups and periodic control for the class of control systems on Lie groups known as '(robotic) locomotion systems' is well known, and has led to the identification of (geometric) phases. We take an approach which is complementary to the existing ones, advocating the relevance-for trajectory generation in these control systems-of the qualitative properties of the dynamics in relative periodic orbits. There are two particularly important features. One is that motions in relative periodic orbits of noncompact groups can only be of two types: either they are quasi-periodic, or they leave any compact set as t → ±∞ ('drifting motions'). Moreover, in a given group, one of the two behaviours may be predominant. The second is that motions in a relative periodic orbit exhibit 'spiralling', 'meandering' behaviours, which are routinely detected in numerical integrations. Since a quantitative description of meandering behaviours for drifting motions appears to be missing, we provide it here for a class of Lie groups that includes those of interest in locomotion (semidirect products of a compact group and a normal vector space). We illustrate these ideas on some examples (a kinematic car robot, a planar swimmer).

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Periodical Body Deformations are Optimal Strategies for Locomotion

Cited by 3 publications

References 25 publications

Limit cycles for dynamic crawling locomotors with periodic prescribed shape

Limit cycles for dynamic crawling locomotors with periodic prescribed shape

Limit cycles for dynamic crawling locomotors with periodic prescribed shape

Control of locomotion systems and dynamics in relative periodic orbits

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