Gaits and Central Pattern Generators

A gait is a pattern of leg timing. In a trot, diagonal legs move together. In a pace, legs on the same side do. In a bound, front and back pairs alternate. Animals produce these rhythms with circuits in the spinal cord called central pattern generators, and robots can copy the idea with coupled oscillators.

Gait Stride frequency Coupling strength

Coupled oscillators

Each leg $i$ has a phase $\phi_i$ that advances at the stride frequency $f$. Coupling pulls each pair toward its target phase difference $\Delta_{ij}$ for the chosen gait, a Kuramoto-style model:

$$\dot\phi_i = 2\pi f + k \sum_{j} \sin\!\big(\phi_j - \phi_i - \Delta_{ij}\big)$$

A leg is in stance, on the ground, during part of each cycle, its duty factor.

What to notice

Scramble the phases and the coupling pulls them back into the gait within a few strides. With zero coupling they never sync. Switching gaits only changes the target phase differences, so the transition is smooth. The footfall diagram shows the result: in a walk at least two or three feet are always down, while in a gallop there are moments with all four in the air. Legged robots often use CPGs as a base rhythm, adjusted by feedback from the feet.