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A different switching surface stabilizing an existing unstable periodic gait: an analysis based on perturbation theory
Journal article   Peer reviewed

A different switching surface stabilizing an existing unstable periodic gait: an analysis based on perturbation theory

Ali Tehrani Safa, Aria Alasty and Mahyar Naraghi
Nonlinear dynamics, v 81(4), pp 2127-2140
01 Sep 2015
DOI: https://doi.org/10.1007/s11071-015-2130-1
Featured in Collection :   UN Sustainable Development Goals @ Drexel

Abstract

Engineering Engineering, Mechanical Mechanics Science & Technology Technology
Limit cycle walkers are known as a class of walking robots capable of presenting periodic repetitive gaits without having local controllability at all times during motion. A well-known subclass of these robots is McGeer's passive dynamic walkers solely activated by the gravity field. The mathematics governing this style of walking is hybrid and described by a set of nonlinear differential equations along with impulses. In this paper, by applying perturbation method to a simple model of these machines, we analytically prove that for this type of nonlinear impulsive system, there exist different switching surfaces, leading to the same equilibrium points (periodic solutions) with different stabilities. Furthermore, it has been shown that the number of existing periodic solutions depends on the characteristics of the switching surface.

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14 citations in Web of Science
16 citations in Scopus

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Collaboration types
Domestic collaboration
Web of Science research areas
Engineering, Mechanical
Mechanics
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