'Zigzag / zagzig' and 'zagzig / zagzig' robots (Walking Machines V)

I have not discussed the theme of walking machines for a long time: the last post on that subject was published back in 2010, but dealt with 'radial robots', meant as toys. As you will know the word robot was derived from 'worker', so it is fitting to go back to posts on robots meant to do proper work (here).

The lack of interest was not because no progress is being made; quite the contrary. There is so much improvement that robots are slowly taking on aspects of animals, and the reason for that is en ever-increasing subtlety of control of the movement. The word 'cybernetics' has its origin in a Greek word for 'steersman', and 'steering' all aspects of movement is a key concept in walking, regardless of whether you are talking about an animal or a machine. The other major theme is mechanics, of course. For some background on leg design, see here and here.

You are probably familiar with 'Big Dog', a walking robot made by Boston Dynamics. That company has developed a range of robots meant to aid the military. The video above shows the level of control their robots have these days: clearly, this thing, the 'legged squad support system' (LS3) can hold its won on difficult terrain and follows its human master on its own. There are more YouTube videos (and with better quality) that are found on YouTube after a search for 'Boston Dynamics'.

Here is another one: a 'cheetah' running very fast on a treadmill. It is tethered and the power source is external, but is still an amazing sight. It is interesting to see how the engineers handled the problem of elongating stride length. Running mammals generally have legs with  three major segments; the foot can be seen as a fourth, minor segment. Cheetahs obtain an additional lengthening of their strides by flexing and extending their bodies as well during the stride. Now compare that to the cheetah robot: it does have a flexing body, but the legs have only two segments and the foot appears to be something like a rubber ball only.

Their latest attempt is called 'WildCat', which is apparently based on the cheetah design. This time both the front legs and the hind legs seem to be linked to the main body by a flexible joint, instead of the legs being fixed to the body directly as was the case for LS3. As a result, the setup is beginning to resemble the setup of shoulder and pelvic girdles common to vertebrates.

The legs still consist of two segments only. Seen from a level of control, having only two segments makes it much easier to find out where the foot should be, as only two angles have to be controlled, and each foot position can be reached with only one combination of angles. If you add another segment, each foot position can be reached in an infinite combination of joint angles. I wonder whether the lack of a foot is due to similar considerations: adding another segment, even a short one, probably adds a considerable computing overhead. 

Another interesting aspects is how the engineers chose the directions where the knees and elbows point to. In an earlier post I discussed whether legs should start with a segment pointing forwards (a 'zig') or backwards (a 'zag'). The next segment than points the other way. The upper arm (humerus) of mammal front legs points backwards and the forearm forwards, so the mammal front leg is a 'zagzig'. Hind legs, in the same jargon, are 'zigzags'. The formula for the entire mammal is a 'zagzig / zigzag'. Are you still there? (Mind you, this is just a simplification paving the way to look at robots; if you include the scapula, -a zig!- and label all three segments, mammals are 'zigzagzig /zigzagzig' animals.)

Now have a look at the LS3 again. Its mid leg joints point away from the body, just the opposite of the mammalian leg bone pattern. The LS3 is a 'zigzag / zagzig' walker. WildCat, in contrast, is a 'zagzig / zagzig' walker. I have no idea why the engineers  chose the designs they did, but the results strengthens my feeling that there is no basic overwhelming advantage inherent in the current mammal pattern. During evolution sideways-pointing legs were turned to have the plane of the leg parallel to that of the body, and in this turn front legs turned backwards and hind legs forwards. Evolution might well have resulted in a different pattern, that of LS3. At least it prevents knocking elbows into knees! Those who wish to add more 'alienosity' to their animals might consider departing from the Earth vertebrate pattern. Have a look at LS3, WildCat, or, of course, at an older post in this blog to see what might be done.

Finally, a word on gaits. Walking consists of a repeated cycle of leg movements, and a gait is nothing more than the phase differences between the various legs. The basic gait of LS3 is a trot, in which front left and right hind legs move together as one pair, and the other two legs from the other pair, moving exactly half a cycle out of phase. If this is confusing go the Furaha 'walking with...' page, where the major gaits are explained. The engineers of Boston Dynamics have managed to proceed beyond the trot, so the thing can bound and gallop as well. I am very surprised though that it seems to use a trot when it is walking very slowly. You would expect a 'walk', which in this context also is a defined gait. The various gaits used by animals have important energy consequences, and a trot is more expensive than a gait. I wonder how much further 'evolution' will take these robots. More segments? More efficient gaits? More legs, even?  

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?

Walking machines

The world of mechanics and robotics proved to contain some interesting analogues and even inspiration for speculative biological creations. That worked for flying animals, both of the heavier than air and of the lighter than air variety. No wonder that the thought came up that walking and other terrestrial modes of transportation could undergo the same treatment.

So, are there interesting mechanical contraptions out there that deserve to be 'biologified'? (I just invented that word but checked it on Google to be certain. Unfortunately, I was not the first: 'biologify' has 3 hits and its derived noun 'biologification' already has 91. Oh well...).

Well, the result of my search is a bit less dramatic than held for the flying animals, but there are some intriguing inventions out there. If you type in words such as 'walking machines' or 'robot insect' into Google, you will find many hits. Most concern toys with usually a high number of legs, of which only a few are lifted at a time. Most are not at all sophisticated in the sense of having integrated sensory and motor systems with balancing reflexes. No neural control at all, sadly. Instead there is just a motor and some mechanical bits and pieces that turn a rotary motion into steps. If you look at them, you realise how complicated and advanced biological walking really is. Still, that does not mean that people cannot have fun with these machines, and watching them is good fun as well. Just have a look at the following clunker:




I found it on YouTube, where it is labelled as a walking machine at "Burning Man '07" You can see that there are at least four legs on the ground at any time, so no delicate balancing tricks here. There doesn't seem to be much in the way of a suspension either, so it might pay to bring a soft cushion.

A more advanced machine is the so-called 'walking tractor'. From what I read, it was a design by a Finnish company meant for the logging industry, but the company apparently no longer exists. You can see they followed the double tripod design, in which three legs are always on the ground. This one apparently had advanced computerised controls. Here it comes:



A walker that really is beginning to look like an animal is the 'Big Dog' by Boston Dynamics. It is supposed to help soldiers cross difficult terrain. A very convincing demonstration occurs halfway in the video: someone kicks it, and it obviously has the reflexes to deal with that. If it steps in a hole, it can even deal with that without falling too. It is lengthy, but worthwhile:



I found it extremely impressive. Well, for a machine, that is. It is not impressive for an animal, which shows how much cybernetics still have to catch up...

None of these machines provide new inspiration in the sense of something that biology hasn't come up with yet. Surely there is something of interste for those who do speculative biology? Yes, there is: in the first place, machines such as the clunker shown above do hold some interest, as their legs work as 'pantographs': there is a system of bars linked together with movable joints, and no biological leg works like that. I will keep that subject for another entry, and that will also deal with Theo Jansens 'standbeesten'.

I will close with something for which I do not think there is a biological analogue, and I rather doubt the design idea lends itself will for biologification. It is a tripod walk. You will probably be disappointed know, seeing that tripod walkers go back as far as HG Wells in 'The war of the worlds'. (By the way, walking with odd numbers of legs might also merit a blog entry one day: there are pentapod walkers on Furaha, not to mention Epona!) But the design here has a twist. Almost literally, in fact. Its home page is here It is very creative and very crazy at the same time, so I cannot help but like it! Does anyone think it makes sense for an animal to move like this?