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Analysis of Multi-Legged Animal + Robot Gaits

Index:
|> Hexapod Gaits
|> Octopod Gaits
|> Movies and Animations - Spider Walking

<| Hexapod Gaits

The figure shown below was adapted from the following paper by Cynthia Ferrell - "Robust and Adaptive Locomotion of an Autonomous Hexapod" (1994), in Proceedings From Perception to Action Conference, Lausanne, Switzerland, 66-77. These gaits were developed for Hannibal, an MIT robot with 6 legs, 19 DOF, over 60 sensors, and 8 computers.

The Tripod Gait is the best-known hexapod gait. A tripod consists of the front-back legs on one side and the middle leg on the opposite side. For each tripod, the legs are lifted, lowered, and moved forwards and backwards in unison. During walking, a hexapod uses its 2 tripods not unlike a bi-ped stepping from one foot to the other - the weight is simply shifted alternately from one tripod to the other. Since 3 legs are on the ground at all times, this gait is both "statically" and "dynamically" stable. The movement scheme is easily visualized by examining the following figure - the numbers adjacent to the legs in the body diagram correspond to timepoints on the graph.

[Hexapod gaits]

In the Wave Gait, all legs on one side are moved forward in succession, starting with the rear-most leg. This is then repeated on the other side. Since only 1 leg is ever lifted at a time, with the other 5 being down, the animal is always in a highly-stable posture.

One conjectures that the Wave cannot be speeded up very much. If you try to shorten the suspenson phases, the steps will get shorter, and/or the legs will have to pump faster. If you try to overlap the suspension phases, this would entail lifting adjacent legs simultaneously, and lead to partial collapse of that part of the body.

The final stride is the Ripple Gait. At first glance the timing of this gait looks somewhat complicated, however, the key to understanding is to recognize that, on each side a local wave comprising non-overlapping lift phases is being performed, and that the 2 opposite side waves are exactly 180 degrees out of phase with one another. For instance, if L3 and R3 are considered to represent the start of each local wave, then notice that R3 starts to move exactly in the middle of the L3-L2-L1 side wave.

Speed. If step size is held constant, the Tripod gait will be fastest, completing a cycle in 2 time beats, while the Wave gait is slowest at 6 beats. By overlapping the local side waves, the Ripple comes in at a fast 3 time beats per cycle, although the phasing-offset actually produces 6 mini-beats overall.

Stability. The Wave will be most stable, since it keeps the most legs on the ground at all phases of the stride. It will probably also be the easiest to adjust during movement over uneven terrain. The Ripple is next most-stable. At most, only 2 legs are ever off the ground at the same time. Only 1 leg per side is ever lifted at a time, and when it is, its direct contralateral counterpart is down - compare L3 and R3 at times (1) and (4). Furthermore, because of the phase offsets between sides, no 2 legs are ever in full suspension at any time - eg, when R3 is up, L2 is just coming down and L1 is just starting to raise. The Tripod, although fastest, will also be the least stable, since it always has 3 legs in suspension.


<| Octopod Gaits

It has proven to be very difficult to find good info about octopod gaits on the web - especially for spiders, the most common octopod.

Scorpion. The picture below shows the gait timing of an 8-legged real-life scorpion, as described in the following paper from Fraunhofer Institut Autonome intelligente Systeme (AiS), written by B.Klaassen, R.Linnemann, D.Spenneberg, & F.Kirchner, "Biomimetic Walking Robot Scorpion: Control and Modelling", SIRS'2001, and which can be downloaded here: Team Bar - Scorpion

[Scorpion gait]

This gait is similar to both the hexapod tripod and ripple gaits, but is a level more complicated. Here legs on opposite sides work together as "tetrapods" rather than tripods, but rather than all moving together, the 4 legs in each tetrapod move in a wave-like succession. The upper timing diagram shows the sequence for one tetrapod: R4-L3-R2-L1. Note that the legs firing in succession are on alternating sides, and the lift phases overlap significantly.

As shown here, approximately half-way through the period just described, the alternate tetrapod consisting of legs L4-R3-L2-R1 begins its sequence of wave-like lifts. Thus, you have a wave sequence within each tetrapod, plus the 2 tetrapods working "approximately" 180 degrees out of phase with each other. Notice there is a period in the middle of each tetrapod wave when all 4 legs are airborne simultaneously, but that the first leg will be coming down about the same time as the last leg is starting to lift. Therefore, the period over which all 4 legs are lifted "simultaneously" is relatively short. Also, during this entire time, all 4 legs of the other tetrapod are firmly grounded, providing a stable platform. Overall, the diagram indicates that each leg is down about 2/3 of the time.

In summary, the real-life scorpion utilizes alternating tetrapods, which function somewhat like a cross between the hexapod tripod and ripple/wave gaits. The following site shows a geared robotic arrangement that performs an alternating tetrapod gait.

Simulated Arachnid. We did find a paper on simulated arachnid gaits produced using genetic algorithms by Gary Parker: "Generating Arachnid Robot Gaits with Cyclic Genetic Algorithms", in Genetic Programming 1998: Proceedings of the Third Annual Conference, pp 576-583. This paper can be downloaded here. The following figure shows a few of the successful gaits discovered.

[evolved octopod gaits]

The first gait is the "Alternating Cartesian Table" gait used by many of the large walkers seen at the SAE Walking Machine competitions. In the second, adjacent legs in the corners work in unison, and the result is similar to the "Alternating Diagonal" gait used by walking and trotting quadrupeds. The third gait is called the "Quadripod Gait" by Parker, and is essentially the same as the alternating tetrapod gait shown above for the scorpion. These are all 2-beat gaits, which would advance the animal or robot at the same speed. However, a little thought shows they are not all quite as stable as one another. The Cartesian gait will have a little front-back instability in the second position, while the Diagonal will have a little off-diagonal-axis wobble. The Tetrapod should be marginally better than either of the others.

Cross-Species Similarities. The last 2 gaits support the idea put forth by R.J. Full that species all across the animal kingdom use legs together in certain combinations that produce analogous results - namely, "... 1 human leg works like 2 dog legs, 3 cockroach legs and 4 crab legs ...". In the most basic gait, a human steps from 1 leg to the other, a dog or horse from 1 diagonal to the other, a roach or beetle from 1 tripod to the other, and a crab or scorpion from 1 tetrapod to the other. Raibert found a similar result relating quadruped gaits to a virtual biped gait. Different structures can work together in functionally-equivalent ways.

Although we did not specifically find it in the literature, it is easy to see how the wave and ripple gaits of the hexapod shown above can be extended to 8 [or more] legs.

Real Spider. So far, we have not found very much on the web concerning gaits of living spiders, when on land.

However, Friedrich Barth describes locomotion of the hunting spider Cupiennius salei (large adult, 14 cm = 5.6 in) in the book "A Spider's World, Senses and Behavior", chapter XXIV, pub Springer (2002). The characteristic gait of this spider is the alternating tetrapod (4-2-3-1 sequence), as illustrated in the figure at the right. Leg numbering is as above for the scorpion. Although the leg traces are ordered differently between the figures, the scorpion [above] and spider gaits are essentially the same. When walking at 10 cm/sec, Barth says Cupiennius uses the 4-2-3-1 leg sequence about 68% of the time, but it also employs a 4-1-3-2 sequence about 15% of the time, and a 4-3-1-2 sequence about 13% of the time.

The figure illustrates that a given leg is grounded for about 60-70% of the total step, and there is always a period of overlap (about 15-20%) where adjacent ipsilateral legs are grounded. As can be seen, on transitioning from one tetrapod to the other, there is typically a period when at least 3 (and sometimes 4) legs on a given side are grounded simultaneously. Overall, at least 6 legs are grounded at all times during the transitions. This overlap will clearly improve the stability of the gait, and will probably increase the endurance of the animal.

  • Also, analysis of spider jumping by David Hill: "Targeted Jumps ...".
  • Misc: simulation

  • <| Animations and Movies

    The following sites have multi-legged walker animations: various MIT robots, dinosaur, salamander, misc, hexapod tripod/ripple/wave, and Cyber Spider.

    Home Movies. We recently caught and made movies of two tiny (3/16", 5 mm) jumping spiders - apparently (salticidae) Sitticus Palustris. This wasn't the easiest, as these spiders are very small and move fast. The images were captured in AVI format using a Logitech QuickCam VC, at 160x240 and 320x120 resolution, and at up to 50 fps. The camera was moved by hand to follow the action. The movies were edited using VirtualDub.
    1 [Salticidae Sitticus Palustris]
    2
    3
    4
    Sitticus Palustris
    (about 10X normal size
    + normal-size bottom
    left, just a little speck)

    Spider Walking Sequences. The following two files show the same 5-sec walking sequence (50 fps capture) - some walking and some turning:

  • Jumping Spider Walking [1] (normal speed) - 680 KByte AVI file.
  • Jumping Spider Walking [1] - slow (playback at 1/5 normal speed) - 680 KByte AVI file.

    The following two files show the same 2-sec walking sequence (50 fps capture):

  • Jumping Spider Walking [2] (normal speed) - 300 KByte AVI file.
  • Jumping Spider Walking [2] - slow (playback at 1/5 normal speed) - 300 KByte AVI file.

    Meticulous analysis of the slow-speed movies reveals a basic tetrapod gait. The spider takes very quick steps, and the pace is a slightly irregular stop-n-go. Same-position legs on opposite sides are seen to move essentially 180 degrees out-of-phase with each other. In addition, same-side legs typically move in pairs, #1 and #3 together, approximately counter-phase to #2 and #4.

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    © Oricom Technologies, July 2002, updated Jan 2003