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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Format: | Article |
Language: | English |
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MDPI AG
2023-07-01
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Series: | Robotics |
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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. |
first_indexed | 2024-03-10T23:36:45Z |
format | Article |
id | doaj.art-877dbd08252343c79cd1d3b832d5d386 |
institution | Directory Open Access Journal |
issn | 2218-6581 |
language | English |
last_indexed | 2024-03-10T23:36:45Z |
publishDate | 2023-07-01 |
publisher | MDPI AG |
record_format | Article |
series | Robotics |
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 |