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Science (New York, N.Y.)1986; 231(4743); 1292-1294; doi: 10.1126/science.3945823

Symmetry in running.

Abstract: Symmetry plays a key role in simplifying the control of legged robots and in giving them the ability to run and balance. The symmetries studied describe motion of the body and legs in terms of even and odd functions of time. A legged system running with these symmetries travels with a fixed forward speed and a stable upright posture. The symmetries used for controlling legged robots may help in elucidating the legged behavior of animals. Measurements of running in the cat and human show that the feet and body sometimes move as predicted by the even and odd symmetry functions.
Publication Date: 1986-03-14 PubMed ID: 3945823DOI: 10.1126/science.3945823Google Scholar: Lookup
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  • Journal Article
  • Research Support
  • Non-U.S. Gov't

Summary

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This research paper discusses the importance of symmetry in the motion control of legged robots and its potential applications in understanding legged animal behavior. It demonstrates that certain symmetrical patterns used in robot leg control can lead to stable running and balance, noted in both cat and human locomotion.

Understanding Symmetry in Running

  • The researchers studied symmetry in the context of robotic locomotion, focusing on the motion of the body and legs.
  • They explored these motions through the use of even and odd functions of time which, when used to describe the motion, simplify the execution of stability and forward motion.
  • It was observed in the study that legged systems operating under these symmetrical patterns could achieve a consistent forward speed while maintaining an upright posture.

Applications of Symmetry in Robotics

  • The insights gained from understanding symmetry in movement can be applied to improve the movement and balance of legged robots.
  • By mimicking the symmetrical movement patterns in walking or running, robots could potentially achieve greater stability, improved balance, and more natural, lifelike motion.

Connection to Animal Behavior

  • Interestingly, the study found that the symmetries used in controlling legged robots share similarities with the legged behavior observed in animals, specifically cats and humans.
  • The findings suggest that the feet and body of these animals sometimes move in accordance with the even and odd symmetry functions used to describe robot motion.
  • This implies that there may be universal patterns of symmetry underlying the legged locomotion of both robots and biological organisms, providing valuable insights into the principles governing legged movement as a whole.

Implications and Potential Research

  • This research opens the door for further exploration of the patterns of symmetry inherent in legged locomotion, both in terms of robotics and animal movement.
  • Better understanding these patterns could potentially lead to advancements in improvement of legged robot design and control.
  • Additionally, the study could provide valuable insights into the locomotion of animals, aiding in fields such as veterinary science, animal biology, and understanding the evolution of movement patterns.

Cite This Article

APA
Raibert MH. (1986). Symmetry in running. Science, 231(4743), 1292-1294. https://doi.org/10.1126/science.3945823

Publication

ISSN: 0036-8075
NlmUniqueID: 0404511
Country: United States
Language: English
Volume: 231
Issue: 4743
Pages: 1292-1294

Researcher Affiliations

Raibert, M H

    MeSH Terms

    • Animals
    • Automation
    • Cats
    • Horses
    • Leg / physiology
    • Movement
    • Running

    Citations

    This article has been cited 5 times.
    1. Clark KP, Meng CR, Stearne DJ. 'Whip from the hip': thigh angular motion, ground contact mechanics, and running speed. Biol Open 2020 Oct 21;9(10).
      doi: 10.1242/bio.053546pubmed: 32917763google scholar: lookup
    2. Wilshin S, Haynes GC, Porteous J, Koditschek D, Revzen S, Spence AJ. Morphology and the gradient of a symmetric potential predict gait transitions of dogs. Biol Cybern 2017 Aug;111(3-4):269-277.
      doi: 10.1007/s00422-017-0721-2pubmed: 28631166google scholar: lookup
    3. Wei X, Long Y, Wang C, Wang S. A Critical Characteristic in the Transverse Galloping Pattern. Appl Bionics Biomech 2015;2015:631354.
      doi: 10.1155/2015/631354pubmed: 27087773google scholar: lookup
    4. Gu J, Ye Z, Rae-Grant T, Wang S, Zhao D, Hester J, Webster-Wood VA, Yao L. Optimization and control of actuator networks in variable geometry truss systems using genetic algorithms. Nat Commun 2025 Sep 30;16(1):8432.
      doi: 10.1038/s41467-025-63373-7pubmed: 41028748google scholar: lookup
    5. Gong M, Liu Y, Cao Z, Gao B. Strength and Push Gait Asymmetry in Skeleton Athletes. J Hum Kinet 2025 Apr;97:13-25.
      doi: 10.5114/jhk/193480pubmed: 40463313google scholar: lookup