+|| Nico ||
Nico can do a basic alternating diagonal walk, as decribed on our quadruped locomotion page. Nico's legs were designed to work in a similar manner to mammalian legs, oriented for pushing directly downwards against the force of gravity. They also perform "mirror-image" front-to-back bending, which allows a wide range of versatility in emulating different animal gaits.
The basic walk places body weight on alternating diagonals in a 4-beat fashion. LF+RR legs alternate in supporting the body with RF+LR. There is a period of time with 2 diagonal legs firmly planted on the ground, performing the power stroke [straight and moving backwards], while the other 2 legs are suspended in the recovery phase [bent and moving forwards]. Then, the suspended legs come down into the power stroke, while the other diagonal lifts and recovers. The walk is actually very similar to the trot, which is a 2-beat gait, but in the walk the front leg slightly precedes the rear leg during recovery, giving the gait a 4-time beat.
<| Timing Diagrams
The diagram at the right shows the timing relationships for the 8 servos that control Nico's legs when doing a Diagonal Walk gait. In this case, the "forward-backward" servos are the ones mounted in-board, and the "up-down" servos are the ones mounted out-board. This is an upright femur stance, as described on our Leg Geometry Variations page.
We have been experimenting with different timing and geometry arrangements, and this diagram actually shows a 2-beat walk, rather than the 4-beat walk discussed above. This is really equivalent to the "trot", and is easier to illustrate, but a slight relative shift in phase between front and rear legs of the same diagonal, as discussed below, will produce the 4-beat cadence. As the walk gets slower, stability is better with 4-beat phasing rather than 2-beat.
Movement shifts from diagonal to diagonal - LF+RR, alternating with RF+LR. 2 legs at a time support, while the other 2 lift. As shown here, the gait begins with the RF+LR recovery stroke. The femurs [in-board servos] move forward while the tibias [out-board servos] lift. Simultaneous with maximum lift, as shown at time t1, the legs of the opposite diagonal are half-way through their power stroke moving backwards. Once the suspended legs come down and start moving backwards, the opposite diagonal undergoes its own suspension phase. Movement of the 2 diagonals is exactly 180 degrees out-of-phase. The cycle repeats, and forward motion continues.
The horse diagram shows the various positions of both diagonals on one convenient diagram. The times corresponding to t1 and t3 are the center positions, where one leg is suspended while its contralateral counterpart provides support.
In summary, in the walk, the legs of one diagonal lift up and move forward together, while the other diagonal is grounded and provides the backwards power stroke. The 2 diagonals then alternate roles, always working exactly 180 degrees out of phase with each other. When one set of legs is at the high point of elevation, the other set is straight downwards under the body, positioned to provide maximum support. The overall action results in steady forward movement, with alternating phases of dynamic stability on 2 legs. Momentum drives the body forward and keeps it relatively level. Variations in phasing are dicussed below.
<| Variations and Stability
Variations on the Theme. Leg phasing can be varied to produce different results, and with Nico we are experimenting with different arrangements of up-down time versus forward-backward time versus relative phasing.
In the situation shown here, the power stroke is somewhat longer than the recovery stroke, but this can be varied. The legs are down for longer than they are up, which gives better stability at slower speeds, but as the forward velocity picks up, the up-down times could be made more equal. Typically, in animal walking, there is an overlap period of upwards to 25% of the total gait when all legs are down simultaneously and pulling backwards together. This period is longer for slower speeds, and vice versa. This occurs around times t2 and t4 on the above diagram.
Overlap also occurs in human bipedal walking, where the suspended heel typically comes down before the toe of the other foot leaves the ground. As forward speed increases, this overlap decreases. During fast running, overlap disappears as both legs are in suspension simultaneously part of the time.
Diagonal Walk Stability. Stability in the diagonal walk gait is "dynamic", rather than static as in the creep. When 2 legs of 4 are both suspended, the animal or mechanical animal would totter unstably if it weren't for forward momentum. Therefore, the 2-beat alternating diagonal walk is more stable as the forward velocity increases. Same thing with bipedal walking - it is hard to be stable when one leg is held statically-suspended away from the body, but much easier when going forward fast.
One thing of note in the alternating diagonal walk is that, whenever 2 legs go into suspension during the recovery stroke, the 2 alternate diagonal [down] legs are "half-way" through their backward power stroke, and are positioned directly under Nico's "hip" and "shoulder" joints, thus providing maximal support. This is illustrated at times t1 and t3 of the diagram above. From a biomorphic viewpoint, the legs are straight here, so the bones [mechanical members] are bearing the major weight, rather than the muscles [servo motors], thus conserving energy and improving stamina.
Alternating Tripods. At higher speeds, a 2-time gait provides good stability, since forward momentum helps out. At slower speeds, momentum is not as much a factor, but stability can be improved by changing the phasing to produce a 4-time beat. This is shown by Jake's dog walk on another page.
Here, the walk can be thought of as moving from one "dynamic tripod" to another, rather than between alternating diagonals - note especially Jake positions 3, 5, and 7. In the 4-beat walk, the front leg of the non-supporting diagonal is lifted slightly before the rear leg, so the rear leg temporarily forms a tripod with the down-diagonal - see Jake positions 1, 5, and 9. The rear leg then "pushes off" so that the suspended front leg comes down to form a new, forward-translated tripod with the same down-diagonal. There is still a period when both legs are suspended simultaneously, but it is shorter than in the 2-beat gait described above, and any potential unstable teeter-tottering will be lessened.
This variation is easily brought about by a slight phase change in the timing relationships of the 2-beat gait shown above - namely, advance the phase of the front leg so it starts its suspension phase slightly ahead of the rear leg of the same diagonal. The variations described here are some of the future work planned for Nico, as he learns to improve his walking abilities.