Walking without Legs

Pardon? Is walking without legs possible? Well, if you stretch the definition a little...

There are quite a few terrestrial animals on Earth that have no legs; earthworms, legless lizards and particularly snakes come to mind. These are not evolutionary misfits whose leglessness will be their doom any day now. Snakes have been around for some 150 million years, after all. Limblessness in legless lizards seems to have evolved at least 8 times, also suggesting that 'not having a leg to stand on' is not necessarily a bad thing. It is probably a very good thing if your life style requires moving around in confined spaces where legs might hold you back, such as underground, in very dense growth and probably in crevasses between rocks. In fact, you may well wonder whether legless animals might be universal, found on many worlds across the universe.

If so, would all 'serpentiformes' or 'ophimorphs' (take your pick) move in the same way? That is debatable, as there may be one or two possible gaits that do not seem to be in use on Earth. How do animals without legs move on Earth? There are animals whose body length can vary, such as earthworms, but let's only look at those with a fixed body length, such as snakes. You can find more on that using Wikipedia etc., but here is a short summary.

The internet did not let me down in a search for interesting material. In the past I have found that some of my biomechanical ideas to design interesting life forms had also been invented by others designing robots, such as tetropters (radial flyers). In this case it was the other way around, and I came across a mechanical invention that might perhaps be 'biologified'. I found it on the website of the biorobotics laboratory of the Carnegie Mellon School of computer science, where they have lots of interesting material on the design of robotic snakes (there are other robot snake designers, but this site seems to cover all aspects).

Click to enlarge; copyright Gert van Dijk

Click to enlarge; source here

The basic element of robotic and live snakes is a segment (vertebrates are just as segmental as arthropods; the segments are just less apparent form the outside). In the picture above each segment is connected to the next with a universal joint, allowing movement up and down and sideways. The robotic snakes seem to have joints with just one axis of rotation (either up-down or sideways), but these alternate on consecutive joints. There is no movement along the longitudinal axis of the segments. Well, in animals there is almost always a bit of leeway, but not a lot; it's certainly not as if a segment could rotate 10 or 20 degrees along a longitudinal axis. It is tempting to adapt the design to allow more longitudinal rotation, and it would increase the 'alienness' of the design. (We need a word to describe how 'alien' an animal is compared to 'life as we know it'; 'alienosity'?)

Anyway, Earth's snakes can move in various ways. There is the 'rectilinear' mode, in which a bit of skin on the belly of the snake is lifted, moved forward, and put back on the ground again. The next bit of skin does the same thing but slightly out of phase, so you end up with a wave of skin rippling backwards along the belly of the beast. As the ripples push against the immobile earth, the snake moves forward. Think about this: part of the body, while lifted from the ground, swings forwards with respect to the centre of gravity of the body, and when it is on the ground it swings backwards: that is a description of what a leg does, if not what a leg is. A fine distinction, but an interesting one: do you define walking by its functional characteristics, or by the body parts that carry out the function? I tend to prefer the first option, but the consequence would be that snakes walk, and that departs too much from common use of 'walking'.

A very interesting snake gait is 'sidewinding'. Here, the snake lifts an entire segment of its body from the ground, moves it forwards, and puts it down again. You get the picture: a walking analogue again. The robotic snake does it too, with waves travelling down the body both in the up and down and sideways directions. In real life it is quite difficult to get a good understanding of how this works using just diagrams, but the videos shown here might help. Sidewinding provides snakes with their fastest way of locomotion: it is the 'running' of the snake world.

Now we get to the creative part: a gait snakes do not use. The robot's body is moved into a curve, so it lies in a plane. Now imagine that you change the direction of curvature a bit, so both ends of the animal would be lifted from the ground. That is not going to happen, as the uplifted ends of the body will fall towards the ground. The result is a C-shaped curve that rolls forward, a bit as how you would move a log by rolling it over the ground. I was struck by the creative beauty of this solution.

But before people trot off to design rolling metaserpents for their own worlds, they should think about why Earth's snakes don't do this. Rolling along the longitudinal axis of the body will cause the animals' head to spin quite literally. The poor animal will have difficulty in keeping its bearings. Regular readers may remember that there was a similar problem with cernuation. I wouldn't say this form of locomotion, which the robot designers called 'rolling', is impossible for animals, but the animal better have very sophisticated vestibular and equilibrium systems. Alternatively, or additioanlly, the head could do its own counter rotation, in the same way cernuating animals could temporarily keep their head still. Spinning ballerinas also rotate their head opposite their body to keep it still in space, and they are not alien (perhaps a tiny bit).

Here is another example of what 'rolling' can do: the designers have actually been able to make their robot climb a tree! Spectacular, isn't it?

And finally, a robot that is not very prominently displayed on their site. They call it the 'skin drive', and about the only information is that it uses its entire skin to move. From looking at the video, it seems to have flexible rubbery skin, and underneath that there must be series of elements that can be stuck out radially and retracted again. I guess that waves of extraction and retraction march backwards across the body, as if you would push successive fingers against a sheet of rubber. If these fingertips find enough traction against the ground, they will stay in place, and the body as a while will be pushed forwards. It is a bit like 'rectilinear' snake movement, but not exactly the same. I wonder where the inventors will take it, or where its evolution will lead to.

Furaha Swamp Scene II

If this scene looks a bit familiar, that is because I posted previous versions of it as well, in November 2009. This version is updated though, and so is still worth viewing, or so I hope. The end is a bit rough: the 'Fish' is visible for a short while only, which is intentional, and so I thought I could get away with a limited amount of detail. There is a better quality version on the site: simply go to the plant page and select the arrox tree.

Click to enlarge; copyright plant image Gert van Dijk

Here is a short 'making of'. The plants were all designed with XFrog, a program aimed wholly at structures that branch and grow, i.e., plants. The various rules and settings can be quite complex, but it allows very good control over the characteristics of any plant you create with it. There are not many good plant editors about. One of the few other candidates is the plant editor inside Vue, but that is unfortunately geared towards changing and mutating existing plants, and does not allow the creation of a plant from scratch. Vue has the advantage that it allows its own plants to move in a breeze, which certainly adds to the liveliness of a scene.
The image above shows one of the flowering plants in the swamp scene, as it looks inside XFrog.

Click to enlarge

The next stage is to produce a suitable environment, for which I use Vue Infinite. Basically you start with a 'terrain', which in this case is the ground with some grooves in it to hold streams. Vue allows the user to define 'ecosystems' as collections of 3D objects that are placed according to rules. For instance, one such system could be limited to high points in the terrain. In this swamp scene the arrox trees only grow on such relatively high ground. The marsh growths, with reeds etc., are limited to medium height zones, while in this case hardly anything grows in the lowest ones. That is on purpose, as they would be obscured by muddy water anyway.
Once the playing filed is ready, the camera is set to fly through the scene, and to produce a ray-traced image 24 times a second, or more. A simple scene lasting 4 seconds may take about 10 hours, so a short film of one minute takes many nights of lonely processing (for the computer, that is; I will be asleep).
And then it is a matter of turning the individual frames into films, for which I use VirtualDub. The resulting clips are much too large to show on the internet so they have to be compressed, at the loss of quality. Adding sound and titles adds to the fun, for which I use Adobe's Premiere (Elements).

And there we are; a Furahan scene that does not actually look that alien. One reason for this is that plants may yield less obvious visual 'alienness' than animals. Regardless , I could not resist putting in an animal at the end. a specimen of a 'Fishes IV' species. I do not yet know how to make the parts of their body move, something that would add greatly to the visual quality of the film. But this is the level of my animation skills at present. I do not think that I will try to become good at it, as there is too little time for that.

Click to enlarge. From left to right, typical examples of species from the Fishes IV, V and VI groups. Copyright Gert van Dijk

But I guess that some of you will want to know more about the various 'Fishes', that are just called that by Furahan people because the word came easily, not because it is biologically correct. In this sense the early Horizonists seem to have gone for the old custom of labelling just about any type of water animal a 'Fish'. 'Crayfish' and 'starfish' come to mind as well. I will not go into the early development of Fishes I, II and II, that follow one another in geological time. Not so for Fishes IV, V and VI, shown above in a rough sketch. Here is a quote from an authoritative source, Nyoroge's "Broad Stokes":

"From this point on hexapod evolution becomes more complex. ‘Fishes III’ gave rise to three new groups, ‘Fishes IV, V and VI’, all of which had three pairs of fins. This has caused a great deal of confusion. There are two schools of thought trying to explain the ‘Fishes III Division’, as the debate has become known. The ‘Hexaphile School’ holds that Fishes IV, V and VI evolved separately from multifinned ancestors, and have three pairs of limbs in common, because three pairs of limbs are innately superior to any other number, without actually explaining in much detail why this should be the case. The ‘Monophyletic School’ contends that all three groups have three pairs simply because they all stem from a single ancestor. This is somewhat surprising in view of other differences between Fishes IV, V and VI, which do not suggest a common ancestry. The ‘Contingency View’, which has been gaining strength lately, holds that there is no innate advantage in any number of limbs, and that all three groups have the same number of limbs by accident. Molecular Cladisticians keep silent about the matter, due to a lack of clear evidence one way or the other."

Radial Robots

'Radial robots'; for a title that isn't too bad. I was tempted to add words with 'r' such as 'rampaging' or 'ravaging', but I resisted, as that ran the risk of rather ruining the effect, rendering it ridiculous.

Back to the matter at hand. When I first thought of a radial walking pattern, resulting in Furahan spidrids, I was content to visualise the gait by writing some programmes in Matlab. The results are shown on the Furaha page, and some were featured in the blog as well (here and here). I never imagined I would see really see spidrids walk. Literally, of course, I never will, unless creative bioengineering kits become available quickly, which is unlikely. But walking robots have emerged on the scene since I thought of the spidrids, and among them radial leg designs, as opposed to bilateral symmetry, seem to be quite popular. You can even buy kits to build one yourself. As these designs probably evolved independently, it is interesting to see how parallel these forms of evolution have become: convergent speculation? I therefore surveyed the internet to see whether their anatomy and gaits resembled those of Furahan spidrids. As most of the robots out there seem to be hexapods, I made a quick hexapod version of my originally octapod spidrids (if you need information on spidrids, go to the land section of the Furaha site and select 'walking with...'). A mutation, if you will.

Mutated spidrid; copyright Gert van Dijk

And here it is. I cannot call it a spidrid any longer, as that name evoked spiders, and therefore eight legs. Suggestions are welcome. The beasty walks with the simplest possible gait: that is a double tripod gait, in which the six legs are divided into two groups of three. The three legs of a group move in unison, and the two groups are exactly out of phase. Provided that each leg touches the ground longer than it is off it, there will always be at least three lags on the ground (either that or six). This gait, together with sprawling legs, provides excellent stability. As discussed previously, this is useful for very small animals, soupy atmospheres or a very low walking velocity. It also doesn't require subtle neural control, making it suitable for today's rather dumb robots. It is also a bit boring, which is why my spidrids walk with different gaits, but that is another matter.

Click to enlarge; copyright Gert van Dijk

Next, a scheme to show how the joint anatomy works. Spidrids are very simple: there is a joint at the 'hip', in which the entire leg can rotate clockwise or anti-clockwise. The rotation axis is vertical, indicated by a shiny metal axis and a red arrow. All other joints are simple hinges allowing the segments of the leg to be stretched or bent, and the axes are horizontal, indicated by more shiny axes and blue arrows. Now that the basic spidrid anatomy and gait are clear, it is time to see whether the robot creators have evolved completely different approaches, or whether they evolved the same ideas.

The first video is of a hexapod robot from this YouTube source. As soon as you see it move you will see that its leg anatomy is exactly that of the spidrid: there is one vertical axis at the hip, and the leg itself only contains horizontal axes. The gait is simple as well, in that the legs move in two sets of three, just like the animation above. I like the clunking sound it makes, as if a whole battalion of Cybermen comes clunking down the street. It does one thing my spidrid animations do not (as yet): it changes gait, in the sense that it moves from a circular rotation to walking again (I could have programmed that, but that is a lot of work...).

Here is another one (source here), and this one has a more biological feel to it, in the sense that the movements seem smoother and less mechanical. It does have the same basic anatomy though. Its gaits seem more diverse.

Just to show that radial robots are not restricted to six legs, here is an eight-legged one (source here), more reminiscent of the original spidrids. With eight legs there are many ways to move the legs, and the risks of falling are diminished, as it is easier to spread weight-bearing evenly around the centre of gravity.

Click to enlarge; source here

Finally, just a look at this one suggest a radical departure from the norm. It has four legs, but that is not the point, as it still clearly has a radial anatomy. The legs do not seem to be attached in the usual fashion: where they touch the body the joint seems to be a simple hinge with a horizontal axis. In fact, all its joints seem to have horizontal axes. So how does it move its legs in more than one direction? How can it walk if all its legs can do is stretch and shorten? The answer lies in its design: this robot is fundamentally different. It is part of a project in which the robot has an internal representation of its body, so it can learn to move once more after its legs have been damaged. In short, it is a lot more intelligent than its dumb brethren. If you want interesting movements, always add a brain (an insect type of brain will do).

And this video shows how it moves: it tilts its body, and that takes the place of (anti)clockwise leg rotations. By varying the tilt of its body the reach of its legs becomes much more varied than with an immobile body. In fact, with the anatomy it has, body tilt is the only way forward (pun intended). What a clever design! I love it.

Does this mean that the 'usual' radial design is flawed? I think not. There are good reasons why this design was invented several times, for robots as well as spidrids: it is simple and allows good mobility. Now, if the robots develop more interesting and sophisticated gaits, we are in business: model spidrids in your own home; what more could you wish for?