Departmental Papers (ESE)
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Abstract
This paper applies an extension of classical averaging methods to hybrid dynamical systems, thereby achieving formally specified, physically effective and robust instances of all virtual bipedal gaits on a quadrupedal robot. Gait specification takes the form of a three parameter family of coupling rules mathematically shown to stabilize limit cycles in a low degree of freedom template: an abstracted pair of vertical hoppers whose relative phase locking encodes the desired physical leg patterns. These coupling rules produce the desired gaits when appropriately applied to the physical robot. The formal analysis reveals a distinct set of morphological regimes determined by the distribution of the body’s inertia within which particular phase relationships are naturally locked with no need for feedback stabilization (or, if undesired, must be countermanded by the appropriate feedback), and these regimes are shown empirically to analogously govern the physical machine as well. In addition to the mathematical stability analysis and data from physical experiments we summarize a number of extensive numerical studies that explore the relationship between the simple template and its more complicated anchoring body models.
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Sponsor Acknowledgements
This work was supported in part by NSF grant #1028237, and in part by ONR grant #N00014-16-1-2817, a Vannevar Bush Fellowship held by the last author, sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering.
Document Type
Journal Article
Subject Area
GRASP, Kodlab
Date of this Version
7-5-2018
Publication Source
The International Journal of Robotics Research
Volume
37
Issue
7
Start Page
743
Last Page
778
DOI
10.1177/0278364918779874
Copyright/Permission Statement
This is the accepted version of the document. The journal specifies:
"The above link and final published PDF are only for your personal use and non-profit teaching purposes and should not be posted online or otherwise distributed. If you wish to post your article on your personal website or institutional repository, you may use the accepted version. Please see the SAGE author sharing guidelines, linked below, for full details about appropriate use and version definitions."
Keywords
legged robots, dynamics, hybrid systems
Bib Tex
@article{de_vertical_2018, title = {Vertical hopper compositions for preflexive and feedback-stabilized quadrupedal bounding, pacing, pronking, and trotting}, volume = {37}, url = {https://doi.org/10.1177/0278364918779874}, doi = {10.1177/0278364918779874}, abstract = {This paper applies an extension of classical averaging methods to hybrid dynamical systems, thereby achieving formally specified, physically effective and robust instances of all virtual bipedal gaits on a quadrupedal robot. Gait specification takes the form of a three parameter family of coupling rules mathematically shown to stabilize limit cycles in a low degree of freedom template: an abstracted pair of vertical hoppers whose relative phase locking encodes the desired physical leg patterns. These coupling rules produce the desired gaits when appropriately applied to the physical robot. The formal analysis reveals a distinct set of morphological regimes determined by the distribution of the body’s inertia within which particular phase relationships are naturally locked with no need for feedback stabilization (or, if undesired, must be countermanded by the appropriate feedback), and these regimes are shown empirically to analogously govern the physical machine as well. In addition to the mathematical stability analysis and data from physical experiments we summarize a number of extensive numerical studies that explore the relationship between the simple template and its more complicated anchoring body models.}, number = {7}, journal = {The International Journal of Robotics Research}, author = {De, Avik and Koditschek, Daniel E.}, year = {2018}, pages = {743--778} }
Date Posted: 13 July 2018
This document has been peer reviewed.