Compare the trot, where there are never 3 legs down simultaneously, to position 5 of the walk and to the characteristic leg position of the creep. Basically, the faster walks can take advantage of body inertia and "dynamic stability", while the slower walks must relie upon a 3-legged tripod for "static stability". By forming stable-tripods with their legs some of the time, quadrupeds are emulating the stability inherent in the tripod gait of 6-legged hexapod animals, which includes the vast majority of insects and other arthropods.

<| Nico-II Slow Walk. For Nico-II, we've tried implementing some slower walks, taking advantage of items (a) and (b) above. Basically, this involves extending the amount of time each leg is on the ground, and also slightly delayed the timing of the rear legs with respect to the front legs. This is shown in the diagram to the right. Two complete steps are shown here.

Note that, at the beginning of its power stroke (ie, grounded period), a leg is at its furthest forward position.

Same-Side Overlap. The grounded time for each leg is set at 60% of the total gait time, and the airborne time is 40%. This produces an overlap of the 2 legs on the same side of the body during 20% of the gait. To accomplish the 60-40 ratio, the legs must move a little faster during the recovery stroke (up), than during the power stroke (down). In fact, if you watch animals walking slowly, you'll notice they characterisitcally move their airborne legs forward at a faster rate, compared to the grounded legs moving backwards. This is not difficult, since an airborne leg is unloaded.

Notice that the same-side overlaps occur at the start of the front-leg power stroke (ie, when fully forward) and the end of the rear-leg power stroke (ie, when fully backward). This increases stability of the animal by extending the time that both legs on the same side are far apart and forming part of a "tripod" with one of the legs on the other side.

Same-Side "Gap". Also, notice in the diagram here, that the front leg on a side (eg, LF at time = 0.6) lifts off for its recovery stroke exactly coincident with the rear leg on the same side (eg, LR) touching down for its power stroke. This works when the feet don't clash, but in real animals, the front leg may lift off slightly before the rear leg grounds - and this will produce a "gap" in the timing diagram, with both same-side legs off the ground at the same time. This is more of a problem in short bodies with relatively long legs that can clash - compare Jake the terrier at positions 4 and 8.

Stability Tripod. In general, the points on the timing diagram (ie, times 0.1, 0.6, 1.1, etc) where the 2 feet on one side are far apart (and overlap in grounding) correspond to both feet on the other side being near the center. Although both of these may be in the air simultaneously, one is impacting the ground while other is leaving it, so the net result is to have a well-formed stability triangle much of the time during the slow gait. See Jake the terrier at positions 2, 3, 5, 7 and 9.

Retarded Rear-Leg Timing. In addition to the foregoing, note the relative timing of the legs: (a) comparable legs on opposite sides (eg, LF and RF) begin their power strokes exactly every half-cycle of the gait (eg, at the 0.0 and 0.5 timing marks), but (b) the start of the rear-leg power strokes are retarded by 10% (ie, occur at the 0.1 and 0.6 marks), as a result of the 60-40 grounded-airborne ratio. In other words, in order to improve stability at slow speeds, the period of grounded overlapping of the legs is lengthened, but at the same time the relative timing between strokes becomes more complex. This is comparable to the progression from tripod to ripple to wave gait in hexapods. The diagram at the right shows a slow walk in a coyote in the wild. The tripod position of the legs is evident. What is also clear is the extent to which the timing of the front-legs precedes that of the rear-legs. In this case, the RF leg is already half-way back through its power stroke, but the RR leg has barely finished its rearward travel. Likewise, the LF leg is half-way forward during its recovery stroke, yet the LR leg is still coming down to the ground. While the rear-leg timing shown in the diagram above is retarded by 10%, in this case it appears to be about 20-25% of the total gait period. From the symmetry, it's clear that the comparable legs on opposite sides are working 180 degrees out-of-phase with each other, but that both rear-legs are significantly retarded in timing with regards the fronts.

<| Progression to the Creep. We can keep decreasing the airborne period of each leg, increasing the overlap period of same-side legs, and increasing the retardation of the rear-leg power strokes .... until we get to the Creep gait, at which point the airborne period of each leg will be reduced to 25% of the gait period, and the retardation will be ____ (??? - left as an exercise). Generally, as these factors are all implemented together, the period of the gait will also increase. The gait will slow down. In Creep gait, only one leg at a time is lifted and stepped forwards in recovery stroke, and for best stability this always starts with a rear-leg, followed by stepping of the leg directly in front. This is then repeated on the other side. In the diagram to the right, the stepping order is RR-RF-LR-LF. We've done a stability analysis on the Creep, and found that only one of the 6 possible step-sequences for a quadruped will produce a stable gait. Interesting. Notice how, in the diagram at the right, the points in time corresponding to positions 4 and 8 of Jake's walk are always centered within the overlapping periods of the opposite-side legs. Interestingly, this same "conceptual" matter of leg timing (ie, same-side overlap simultaneous with opposite-side lift+impact) occurs far back in the evolution of animal locomotion. Bugs have apparently been using it for 400,000,000 years. The Creep Gait has the best stability of all the gaits, since only 1 leg is ever lifted at a time, and 3 legs are always on the ground. The downside to "implementing" the Creep (or any gait with overlap between same-side feet) is that the movements of the grounded legs must be closely matched, else the legs will work against each other. In fact, this is only possible if the foot velocities and leg geometries exactly match (ie, the legs work like the sides of a shifting parallelogram), which isn't really a simple task to accomplish. Oh well, no one ever said evolution of robot walking was gonna be trivial.

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