January 04, 2014 / by Shai Revzen / In news

Why the Trot?

Research presented at SICB in 2014

Link to Paper

Professor Revzen has been working with his collaborator Samuel Burden on extending the theory of smooth oscillators (differential equations having smooth vector fields and limit cycle behavior) to “hybrid” oscillators which aren’t smooth, or even continuous. This research is of interest for many applications. One such application is to legged locomotion (of animals, people, robots, etc.) – it is convenient to model locomotion as a piecewise-smooth oscillator with discontinuities in its vector field resulting from ground-leg contact, as this removes the need to explicitly model extremely complicated impact dynamics.

In January of 2014, we gave a talk at the annual meeting of the Society for Integrative and Comparative Biology in Austin, TX to present an application of this research.

Consider the following observation. When represented in state space, the set of states representing “multiple-contact” events (when more than one leg contacts the ground simultaneously) constitute a set of measure zero. Therefore, generically speaking, we would not expect to observe this behavior in animals – yet, we do. The purpose of this talk at SICB was to explain how the aforementioned theory of hybrid oscillators may help to explain this phenomenon.


The trot and pace gaits of quadrupeds and the alternating tripod gait of running hexapods are just the most familiar of the many multiple contact gaits that multilegged animals utilize. We define “multiple contact gaits” to be those in which multiple legs touch down with near simultaneity. Arguments of collision angle suggest that such gaits are inherently less energetically efficient than rotary gallops and metachronal gaits. We present new results from dynamical systems theory which suggest that multiple contact gaits benefit from a unique, hitherto unknown, form of stability which makes them particularly robust to uncertainties in muscle actuation and ground traction. We conjecture that this advantage, conferred by the inherent the structure of the mechanical dynamics, accounts at least in part for the convergent appearance of multiple contact gaits across virtually all terrestrial animal taxa.

Authors : Shai Revzen, Samuel Burden, Matthew Kvalheim