'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?