Stability of a Groucho-Style Bounding Run in the Sagittal Plane

This paper develops a three-degree-of-freedom sagittal-plane hybrid dynamical systems model of a Groucho-style bounding quadrupedal run. Simple within-stance controls using a modular architecture yield a closed-form expression for a family of hybrid limit cycles that represent bounding behavior over...

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Main Authors: Jeffrey Duperret, Daniel E. Koditschek
Format: Article
Language:English
Published: MDPI AG 2023-07-01
Series:Robotics
Subjects:
Online Access:https://www.mdpi.com/2218-6581/12/4/109
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author Jeffrey Duperret
Daniel E. Koditschek
author_facet Jeffrey Duperret
Daniel E. Koditschek
author_sort Jeffrey Duperret
collection DOAJ
description This paper develops a three-degree-of-freedom sagittal-plane hybrid dynamical systems model of a Groucho-style bounding quadrupedal run. Simple within-stance controls using a modular architecture yield a closed-form expression for a family of hybrid limit cycles that represent bounding behavior over a range of user-selected fore-aft speeds as a function of the model’s kinematic and dynamical parameters. Controls acting on the hybrid transitions are structured so as to achieve a cascade composition of in-place bounding driving the fore-aft degree of freedom, thereby decoupling the linearized dynamics of an approximation to the stride map. Careful selection of the feedback channels used to implement these controls affords infinitesimal deadbeat stability, which is relatively robust against parameter mismatch. Experiments with a physical quadruped reasonably closely match the bounding behavior predicted by the hybrid limit cycle and its stable linearized approximation.
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spelling doaj.art-877dbd08252343c79cd1d3b832d5d3862023-11-19T02:55:22ZengMDPI AGRobotics2218-65812023-07-0112410910.3390/robotics12040109Stability of a Groucho-Style Bounding Run in the Sagittal PlaneJeffrey Duperret0Daniel E. Koditschek1Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USADepartment of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USAThis paper develops a three-degree-of-freedom sagittal-plane hybrid dynamical systems model of a Groucho-style bounding quadrupedal run. Simple within-stance controls using a modular architecture yield a closed-form expression for a family of hybrid limit cycles that represent bounding behavior over a range of user-selected fore-aft speeds as a function of the model’s kinematic and dynamical parameters. Controls acting on the hybrid transitions are structured so as to achieve a cascade composition of in-place bounding driving the fore-aft degree of freedom, thereby decoupling the linearized dynamics of an approximation to the stride map. Careful selection of the feedback channels used to implement these controls affords infinitesimal deadbeat stability, which is relatively robust against parameter mismatch. Experiments with a physical quadruped reasonably closely match the bounding behavior predicted by the hybrid limit cycle and its stable linearized approximation.https://www.mdpi.com/2218-6581/12/4/109legged robotsmodular control architecturessimplified models
spellingShingle Jeffrey Duperret
Daniel E. Koditschek
Stability of a Groucho-Style Bounding Run in the Sagittal Plane
Robotics
legged robots
modular control architectures
simplified models
title Stability of a Groucho-Style Bounding Run in the Sagittal Plane
title_full Stability of a Groucho-Style Bounding Run in the Sagittal Plane
title_fullStr Stability of a Groucho-Style Bounding Run in the Sagittal Plane
title_full_unstemmed Stability of a Groucho-Style Bounding Run in the Sagittal Plane
title_short Stability of a Groucho-Style Bounding Run in the Sagittal Plane
title_sort stability of a groucho style bounding run in the sagittal plane
topic legged robots
modular control architectures
simplified models
url https://www.mdpi.com/2218-6581/12/4/109
work_keys_str_mv AT jeffreyduperret stabilityofagrouchostyleboundingruninthesagittalplane
AT danielekoditschek stabilityofagrouchostyleboundingruninthesagittalplane