A <trot> in a <quadrupedal robot> coordinates diagonal leg pairs: front-left with hind-right, and front-right with hind-left. The two pairs alternate their <stance phases> and <swing phases>. The pairing and relative timing define the pattern; the fraction of each cycle spent in contact can vary.

For an original periodic model, take cycle period $T$ and normalized cycle phase $u=t/T\pmod1$. Let the front-left/hind-right pair have phase zero and the other pair have phase $1/2$. Each foot remains in <stance phase> for fraction $\beta$ of the cycle. At $\beta=1/2$, one diagonal pair contacts while the other swings, apart from the idealized transition instants.

The contact-time consequences follow directly. For $\beta<1/2$, the diagonal-pair contacts do not overlap, and the fraction of the cycle with no foot contact is
$$
1-2\beta.
$$
For $\beta>1/2$, the intervals overlap, and the fraction with all four feet in contact is $2\beta-1$. Thus $\beta=0.4$ gives 20% no-contact time, while $\beta=0.6$ gives 20% four-foot overlap. The average number of contacting feet is $4\beta$ in either case, but an average does not describe the instantaneous support.

For stipulated $T=0.5\,\mathrm s$ and $\beta=0.6$, each foot's stance lasts $0.3\,\mathrm s$ and swing lasts $0.2\,\mathrm s$. Each pair overlaps the other for $0.05\,\mathrm s$ at each exchange, totaling $0.1\,\mathrm s$ per cycle. These are constructed timings, not measurements of a particular machine.

Two ideal diagonal point contacts have a <support polygon> reduced to a line segment. Static balance would require the projected <center of mass> to lie on that segment under the usual horizontal-plane assumptions, leaving no area margin to lateral disturbance. Dynamic motion additionally involves <contact forces>, <angular momentum>, <friction> and actuator limits. The contact and equilibrium models in the primary robotics text explain why a geometric schedule alone is insufficient.<Robotic Systems by Kris Hauser>[Chapter 12, Contact modeling and Equilibrium conditions]{ref}

A proposed robot trial records all foot-contact events, body motion and ground <contact forces> while commanding the diagonal pattern. It checks whether the planned duty fraction and phase offsets are realized and whether motion remains feasible. Contact timing identifies the <gait>; the force and motion records test its execution.


 Trot (source code)