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.
Publication Date: 2015-08-26 PubMed ID: 27222653PubMed Central: PMC4844082DOI: 10.1115/1.4030622Google Scholar: Lookup
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Summary
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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 Each leg has a distinct state – it can be in ground contact, withdrawn for swinging or prepared for touch down with a particular angle of attack.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
Researcher Affiliations
- Robotics and Motion Laboratory, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 e-mail: ganzheny@umich.edu.
- Equine Department, Vetsuisse Faculty, University of Zurich, Zurich CH-8057, Switzerland e-mail: twiestner@vetclinics.uzh.ch.
- Equine Department, Vetsuisse Faculty, University of Zurich, Zurich CH-8057, Switzerland e-mail: mweishaupt@vetclinics.uzh.ch.
- Equine Department, Vetsuisse Faculty, University of Zurich, Zurich CH-8057, Switzerland e-mail: nwaldern@vetclinics.uzh.ch.
- Robotics and Motion Laboratory, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 e-mail: cdremy@umich.edu.
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