Paper: “Passive Dynamics Explain Quadrupedal Walking, Trotting, and Tölting”
Authors: Zhenyu Gan, Thomas Wiestner, Michael A. Weishaupt, Nina M. Waldern, and C. David Remy
Journal: Journal of Computational and Nonlinear Dynamics, 2016
This study demonstrates that a simple passive dynamic model with elastic legs can accurately reproduce the primary natural gaits of horses: walking, trotting, and tölting. The authors developed a planar quadrupedal model with a distributed mass and massless springs for legs, incorporating phases for stance, swing, and readiness for touchdown. Different gaits emerge by selecting appropriate initial conditions and model parameters, without any active control or preprogrammed coordination.
Using a single-shooting optimization framework, the model’s predicted ground reaction forces (GRFs) and contact timings were closely matched to experimental treadmill data from both Warmblood and Icelandic horses. The results show that each gait is characterized by unique footfall patterns and force profiles that arise directly from the system’s passive mechanics. Notably, the model can fit not only symmetrical gaits like walk and trot but also the tölting gait unique to Icelandic horses, simply by adjusting initial states. An extended version of the model, which includes a head and neck segment, further improves prediction accuracy, particularly for walking.
A sensitivity analysis highlights how parameters such as leg stiffness, body inertia, and the center of mass affect the emergence and quality of each gait. The findings support the concept that natural quadrupedal gaits represent distinct dynamic modes of a single compliant mechanical system, and they suggest new approaches for the design and control of legged robots.
Reference
@article{gan2016passive,
title={Passive dynamics explain quadrupedal walking, trotting, and tölting},
author={Gan, Zhenyu and Wiestner, Thomas and Weishaupt, Michael A. and Waldern, Nina M. and Remy, C. David},
journal={Journal of Computational and Nonlinear Dynamics},
volume={11},
number={2},
pages={021008},
year={2016},
doi={10.1115/1.4030622}
}