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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} }

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Date Posted: 13 July 2018

This document has been peer reviewed.