FREE SHIPPING over $40
OVER 10000 FIVE-STAR REVIEWS
5% OFF ALL SUBSCRIPTIONS
100% HAPPINESS GUARANTEE
Analyze Diet
0
Journal of computational and nonlinear dynamics2015; 11(2); 0210081-2100812; doi: 10.1115/1.4030622

Passive Dynamics Explain Quadrupedal Walking, Trotting, and Tölting.

Abstract: This paper presents a simplistic passive dynamic model that is able to create realistic quadrupedal walking, tölting, and trotting motions. The model is inspired by the bipedal spring loaded inverted pendulum (SLIP) model and consists of a distributed mass on four massless legs. Each of the legs is either in ground contact, retracted for swing, or is ready for touch down with a predefined angle of attack. Different gaits, that is, periodic motions differing in interlimb coordination patterns, are generated by choosing different initial model states. Contact patterns and ground reaction forces (GRFs) evolve solely from these initial conditions. By identifying appropriate system parameters in an optimization framework, the model is able to closely match experimentally recorded vertical GRFs of walking and trotting of Warmblood horses, and of tölting of Icelandic horses. In a detailed study, we investigated the sensitivity of the obtained solutions with respect to all states and parameters and quantified the improvement in fitting GRF by including an additional head and neck segment. Our work suggests that quadrupedal gaits are merely different dynamic modes of the same structural system and that we can interpret different gaits as different nonlinear elastic oscillations that propel an animal forward.
Get Full Text
Publication Date: 2015-08-26 PubMed ID: 27222653PubMed Central: PMC4844082DOI: 10.1115/1.4030622Google Scholar: Lookup
The Equine Research Bank provides access to a large database of publicly available scientific literature. Inclusion in the Research Bank does not imply endorsement of study methods or findings by Mad Barn.
LinkedInCopy
  • Journal Article

Summary

This research summary has been generated with artificial intelligence and may contain errors and omissions. Refer to the original study to confirm details provided. Submit correction.

The paper under discussion presents a basic dynamic model which can simulate quadrupedal movements such as walking, trotting and tölting. The model is based on the spring loaded inverted pendulum (SLIP) and successfully matches experimental results obtained from Warmblood and Icelandic horses.

Model Concept and Components

  • The research proposes a simplified dynamic model to emulate various types of quadrupedal motion like walking, tölting, and trotting. This model takes inspiration from the bipedal spring-loaded inverted pendulum (SLIP) model.
  • It consists of a distributed mass placed on four massless legs. Each leg has a distinct state – it can be in ground contact, withdrawn for swinging or prepared for touch down with a particular angle of attack.

Gait Generation

  • With the change in starting states relevant to the simulation, the model can generate different gaits. Gaits essentially denote periodic movements that vary depending upon interlimb coordination patterns.
  • To reproduce movement accurately, the model does not require an external force or control. Contact patterns and ground reaction forces (GRFs) evolve naturally from the initial conditions set in the model.

Optimization and Performance

  • Identifying the correct system parameters through optimization, this model closely aligns with the experimental data of vertical GRFs obtained from real Warmblood horses while walking and trotting and from Icelandic horses while tölting.
  • The researchers conducted a thorough study to examine model sensitivity with relation to all states and parameters. Particularly significant was their effort to measure how much better the model recreated GRFs when an additional segment for head and neck was incorporated.

Interpretation and Significance

  • Based on the research, it is suggested that different quadrupedal gaits are in fact varied dynamic modes of a similar structural system. Different gaits can be viewed as differing elastic oscillations that drive an animal forward, propelling its movement in a non-linear manner.
  • This insight could potentially contribute to the ongoing studies in motion kinetics and dynamics pertaining to mammals and offers a simple yet effective model to understand and simulate complex mammal gaits.

Cite This Article

APA
Gan Z, Wiestner T, Weishaupt MA, Waldern NM, David Remy C. (2015). Passive Dynamics Explain Quadrupedal Walking, Trotting, and Tölting. J Comput Nonlinear Dyn, 11(2), 0210081-2100812. https://doi.org/10.1115/1.4030622

Publication

Journal of computational and nonlinear dynamics
ISSN: 1555-1415
NlmUniqueID: 101629392
Country: United States
Language: English
Volume: 11
Issue: 2
Pages: 0210081-2100812

Researcher Affiliations

Gan, Zhenyu
  • Robotics and Motion Laboratory, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 e-mail:  ganzheny@umich.edu.
Wiestner, Thomas
  • Equine Department, Vetsuisse Faculty, University of Zurich, Zurich CH-8057, Switzerland e-mail:  twiestner@vetclinics.uzh.ch.
Weishaupt, Michael A
  • Equine Department, Vetsuisse Faculty, University of Zurich, Zurich CH-8057, Switzerland e-mail:  mweishaupt@vetclinics.uzh.ch.
Waldern, Nina M
  • Equine Department, Vetsuisse Faculty, University of Zurich, Zurich CH-8057, Switzerland e-mail:  nwaldern@vetclinics.uzh.ch.
David Remy, C
  • Robotics and Motion Laboratory, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 e-mail:  cdremy@umich.edu.

References

This article includes 30 references
  1. Cavagna GA, Kaneko M. Mechanical Work and Efficiency in Level Walking and Running. J. Physiol. 268(2), pp. 467–481.
    doi: 10.1113/jphysiol.1977.sp011866pmc: PMC1283673pubmed: 874922google scholar: lookup
  2. McGeer T. Passive Dynamic Walking. Int. J. Rob. Res. 9(2), pp. 62–82.
    doi: 10.1177/027836499000900206google scholar: lookup
  3. Seyfarth A, Geyer H, Günther M, Blickhan R. A Movement Criterion for Running. J. Biomech. 35(5), pp. 649–655.
    doi: 10.1016/S0021-9290(01)00245-7pubmed: 11955504google scholar: lookup
  4. Cavagna GA, Heglund NC, Taylor CR. Mechanical Work in Terrestrial Locomotion: Two Basic Mechanisms for Minimizing Energy Expenditure. Am. J. Physiol. 233(5), pp. R243–R261.
    pubmed: 411381
  5. Mochon S, McMahon TA. Ballistic Walking: An Improved Model. Math. Biosci. 52(3), pp. 241–260.
    doi: 10.1016/0025-5564(80)90070-Xgoogle scholar: lookup
  6. Garcia M, Chatterjee A, Ruina A, Coleman M. The Simplest Walking Model: Stability, Complexity, and Scaling. ASME J. Biomech. Eng. 120(2), pp. 281–288.
    doi: 10.1115/1.2798313pubmed: 10412391google scholar: lookup
  7. Kuo AD. Stabilization of Lateral Motion in Passive Dynamic Walking. Int. J. Rob. Res. 18(9), pp. 917–930.
    doi: 10.1177/02783649922066655google scholar: lookup
  8. Geyer H, Seyfarth A, Blickhan R. Compliant Leg Behaviour Explains Basic Dynamics of Walking and Running. Proc. R. Soc. B 273(1603), pp. 2861–2867.
    doi: 10.1098/rspb.2006.3637pmc: PMC1664632pubmed: 17015312google scholar: lookup
  9. Farley CT, Glasheen J, McMahon TA. Running Springs-Speed and Animal Size. J. Exp. Biol. 185, pp. 71–86.
    pubmed: 8294853
  10. Full RJ, Koditschek DE. Templates and Anchors: Neuromechanical Hypotheses of Legged Locomotion on Land. J. Exp. Biol. 202(23), pp. 3325–3332.
    pubmed: 10562515
  11. Lee CR, Farley CT. Determinants of the Center of Mass Trajectory in Human Walking and Running. J. Exp. Biol. 201(21), pp. 2935–2944.
    pubmed: 9866878
  12. Pandy MG. Simple and Complex Models for Studying Muscle Function in Walking. Philos. Trans. R. Soc. London, Ser. B 358(1437), pp. 1501–1509.
    doi: 10.1098/rstb.2003.1338pmc: PMC1693253pubmed: 14561341google scholar: lookup
  13. Smith AC, Berkemeier MD. Passive Dynamic Quadrupedal Walking. International Conference on Robotics and Automation (ICRA) Albuquerque, NM, Apr. 20–25. Vol. 1, pp. 34–39.
    doi: 10.1109/ROBOT.1997.620012google scholar: lookup
  14. Remy CD, Buffinton KW, Siegwart RY. Stability Analysis of Passive Dynamic Walking of Quadrupeds. Int. J. Rob. Res. 29(9), pp. 1173–1185.
    doi: 10.1177/0278364909344635google scholar: lookup
  15. Remy CD, Hutter M, Siegwart R. Passive Dynamic Walking With Quadrupeds-Extensions Towards 3D. International Conference on Robotics and Automation (ICRA) Anchorage, AK, May 3–7, pp. 5231–5236.
    doi: 10.1109/ROBOT.2010.5509408google scholar: lookup
  16. McGuigan MP, Wilson AM. The Effect of Gait and Digital Flexor Muscle Activation on Limb Compliance in the Forelimb of the Horse Equus Caballus. J. Exp. Biol. 206(8), pp. 1325–1336.
    doi: 10.1242/jeb.00254pubmed: 12624168google scholar: lookup
  17. Clayton HM, Schamhardt HC, Willemen MA, Lanovaz JL, Colborne GR. Kinematics and Ground Reaction Forces in Horses With Superficial Digital Flexor Tendinitis. Am. J. Vet. Res. 61(2), pp. 191–196.
    doi: 10.2460/ajvr.2000.61.191pubmed: 10685692google scholar: lookup
  18. Remy CD, Buffinton K, Siegwart R. A Matlab Framework for Efficient Gait Creation. 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) San Francisco, CA, Sep. 25–30, pp. 190–196.
    doi: 10.1109/IROS.2011.6094452google scholar: lookup
  19. Gan Z, Remy CD. A Passive Dynamic Quadruped That Moves in a Large Variety of Gaits. International Conference on Intelligent Robots and Systems (IROS) Chicago, IL, Sep. 14–18.
    doi: 10.1109/IROS.2014.6943255google scholar: lookup
  20. Hof AL. Scaling Gait Data to Body Size. Gait Posture 4(3), pp. 222–223.
    doi: 10.1016/0966-6362(95)01057-2google scholar: lookup
  21. Weishaupt MA, Hogg HP, Wiestner T, Denoth J, Stüssi E, Auer JA. Instrumented Treadmill for Measuring Vertical Ground Reaction Forces in Horses. Am. J. Vet. Res. 63(4), pp. 520–527.
    doi: 10.2460/ajvr.2002.63.520pubmed: 11939313google scholar: lookup
  22. Griffin TM, Kram R, Wickler SJ, Hoyt DF. Biomechanical and Energetic Determinants of the Walk–Trot Transition in Horses. J. Exp. Biol. 207(24), pp. 4215–4223.
    doi: 10.1242/jeb.01277pubmed: 15531642google scholar: lookup
  23. Herr HM, McMahon TA. A Trotting Horse Model. Int. J. Rob. Res. 19(6), pp. 566–581.
    doi: 10.1177/027836490001900602google scholar: lookup
  24. Chatzakos P, Papadopoulos E. Parametric Analysis and Design Guidelines for a Quadruped Bounding Robot. Mediterranean Conference on Control and Automation (MED’07) pp. 1–6.
  25. Weishaupt M, Waldern N, Kubli V, Wiestner T. Effects of Shoeing on Breakover Forces in Icelandic Horses at Walk, Tölt and Trot. Equine Vet. J. 46(S46), pp. 51–51.
    doi: 10.1111/evj.12267_156google scholar: lookup
  26. Bogisch S, Peinen KG-V, Wiestner T, Roepstorff L, Weishaupt M. Influence of Velocity on Horse and Rider Movement and Resulting Saddle Forces at Walk and Trot. Comp. Exercise Physiol. 10(1), pp. 23–32.
    doi: 10.3920/CEP13025google scholar: lookup
  27. Vorstenbosch M, Buchner H, Savelberg H, Schamhardt H, Barneveld A. Modeling Study of Compensatory Head Movements in Lame Horses. Am. J. Vet. Res. 58(7), pp. 713–718.
    pubmed: 9215445
  28. Waldern N, Wiestner T, Peinen KV, Álvarez C, Roepstorff L, Johnston C, Meyer H, Weishaupt M. Influence of Different Head-Neck Positions on Vertical Ground Reaction Forces, Linear and Time Parameters in the Unridden Horse Walking and Trotting on a Treadmill. Equine Vet. J. 41(3), pp. 268–273.
    doi: 10.2746/042516409X397389pubmed: 19469234google scholar: lookup
  29. Buchner H, Savelberg H, Schamhardt H, Barneveld A. Inertial Properties of Dutch Warmblood Horses. J. Biomech. 30(6), pp. 653–658.
    doi: 10.1016/S0021-9290(97)00005-5pubmed: 9165402google scholar: lookup
  30. Hoyt DF, Taylor CR. Gait and the Energetics of Locomotion in Horses. Nature 292(5820), pp. 239–240.
    doi: 10.1038/292239a0google scholar: lookup

Citations

This article has been cited 8 times.
  1. Kamimura T, Sato K, Aoi S, Higurashi Y, Wada N, Tsuchiya K, Sano A, Matsuno F. Three Characteristics of Cheetah Galloping Improve Running Performance Through Spinal Movement: A Modeling Study. Front Bioeng Biotechnol 2022;10:825638.
    doi: 10.3389/fbioe.2022.825638pubmed: 35497345google scholar: lookup
  2. Yamada T, Aoi S, Adachi M, Kamimura T, Higurashi Y, Wada N, Tsuchiya K, Matsuno F. Center of Mass Offset Enhances the Selection of Transverse Gallop in High-Speed Running by Horses: A Modeling Study. Front Bioeng Biotechnol 2022;10:825157.
    doi: 10.3389/fbioe.2022.825157pubmed: 35295643google scholar: lookup
  3. Usherwood JR. Legs as linkages: an alternative paradigm for the role of tendons and isometric muscles in facilitating economical gait. J Exp Biol 2022 Mar 8;225(Suppl_1).
    doi: 10.1242/jeb.243254pubmed: 35258605google scholar: lookup
  4. Kamimura T, Aoi S, Higurashi Y, Wada N, Tsuchiya K, Matsuno F. Dynamical determinants enabling two different types of flight in cheetah gallop to enhance speed through spine movement. Sci Rep 2021 May 5;11(1):9631.
    doi: 10.1038/s41598-021-88879-0pubmed: 33953253google scholar: lookup
  5. Kashiri N, Abate A, Abram SJ, Albu-Schaffer A, Clary PJ, Daley M, Faraji S, Furnemont R, Garabini M, Geyer H, Grabowski AM, Hurst J, Malzahn J, Mathijssen G, Remy D, Roozing W, Shahbazi M, Simha SN, Song JB, Smit-Anseeuw N, Stramigioli S, Vanderborght B, Yesilevskiy Y, Tsagarakis N. An Overview on Principles for Energy Efficient Robot Locomotion. Front Robot AI 2018;5:129.
    doi: 10.3389/frobt.2018.00129pubmed: 33501007google scholar: lookup
  6. Egenvall A, Engström H, Byström A. Kinematic effects of the circle with and without rider in walking horses. PeerJ 2020;8:e10354.
    doi: 10.7717/peerj.10354pubmed: 33240661google scholar: lookup
  7. Polet DT, Bertram JEA. An inelastic quadrupedal model discovers four-beat walking, two-beat running, and pseudo-elastic actuation as energetically optimal. PLoS Comput Biol 2019 Nov;15(11):e1007444.
    doi: 10.1371/journal.pcbi.1007444pubmed: 31751339google scholar: lookup
  8. Sellers WI, Hirasaki E. Quadrupedal locomotor simulation: producing more realistic gaits using dual-objective optimization. R Soc Open Sci 2018 Mar;5(3):171836.
    doi: 10.1098/rsos.171836pubmed: 29657790google scholar: lookup
Subscribe to our newsletter
Join 99,970 horse owners like you who receive our email updates on horse health and nutrition.