Trot

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 $u=t/T(\mathrm{mod}1)$. 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 isFor $\beta >1/2$, 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.^[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.