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Passive dynamics explain quadrupedal walking, trotting, and tölting


Gan, Zhenyu; Wiestner, Thomas; Weishaupt, Michael A; Waldern, Nina M; David Remy, C (2015). Passive dynamics explain quadrupedal walking, trotting, and tölting. Journal of Computational and Nonlinear Dynamics, 11(2):online.

Abstract

This paper presents a simplistic passive dynamic model that is able to create realistic quadrupedal walking, tölting, and trotting motions. The model is inspired by the bipedal spring loaded inverted pendulum (SLIP) model and consists of a distributed mass on four massless legs. Each of the legs is either in ground contact, retracted for swing, or is ready for touch down with a predefined angle of attack. Different gaits, that is, periodic motions differing in interlimb coordination patterns, are generated by choosing different initial model states. Contact patterns and ground reaction forces (GRFs) evolve solely from these initial conditions. By identifying appropriate system parameters in an optimization framework, the model is able to closely match experimentally recorded vertical GRFs of walking and trotting of Warmblood horses, and of tölting of Icelandic horses. In a detailed study, we investigated the sensitivity of the obtained solutions with respect to all states and parameters and quantified the improvement in fitting GRF by including an additional head and neck segment. Our work suggests that quadrupedal gaits are merely different dynamic modes of the same structural system and that we can interpret different gaits as different nonlinear elastic oscillations that propel an animal forward.

Abstract

This paper presents a simplistic passive dynamic model that is able to create realistic quadrupedal walking, tölting, and trotting motions. The model is inspired by the bipedal spring loaded inverted pendulum (SLIP) model and consists of a distributed mass on four massless legs. Each of the legs is either in ground contact, retracted for swing, or is ready for touch down with a predefined angle of attack. Different gaits, that is, periodic motions differing in interlimb coordination patterns, are generated by choosing different initial model states. Contact patterns and ground reaction forces (GRFs) evolve solely from these initial conditions. By identifying appropriate system parameters in an optimization framework, the model is able to closely match experimentally recorded vertical GRFs of walking and trotting of Warmblood horses, and of tölting of Icelandic horses. In a detailed study, we investigated the sensitivity of the obtained solutions with respect to all states and parameters and quantified the improvement in fitting GRF by including an additional head and neck segment. Our work suggests that quadrupedal gaits are merely different dynamic modes of the same structural system and that we can interpret different gaits as different nonlinear elastic oscillations that propel an animal forward.

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1 citation in Web of Science®
1 citation in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:05 Vetsuisse Faculty > Veterinary Clinic > Equine Department
Dewey Decimal Classification:570 Life sciences; biology
630 Agriculture
Language:English
Date:2015
Deposited On:01 Feb 2016 11:43
Last Modified:30 Apr 2016 07:43
Publisher:The American Society of Mechanical Engineers
ISSN:1555-1415
Publisher DOI:https://doi.org/10.1115/1.4030622

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