Subject:
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Tripod Robots
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Newsgroups:
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lugnet.robotics
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Date:
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Sat, 2 Apr 2005 17:00:03 GMT
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Original-From:
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PeterBalch <peterbalch@compuserve.STOPSPAMMERScom>
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Viewed:
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1246 times
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Hi Danny
I too have often wondered what gaits would work but never found anything
even theoretical on the web, let alone actual hardware.
In War Of The Worlds, they're described walking:
"A [lightning] flash, and it came out vividly, heeling over one way with
two feet in the air, to vanish and reappear almost instantly as it seemed,
with the next flash, a hundred yards nearer. Can you imagine a milking
stool tilted and bowled violently along the ground? That was the impression
those instant flashes gave. But instead of a milking stool imagine it a
great body of machinery on a tripod stand."
I suppose a rotating gait could be made to work but it would very tricky. A
"one-legged-man on crutches" gait might work but would require dynamic
balancing while the centre leg was the only support. There are toy robots
that use the gait but the centre "leg" is the whole body of the robot with
an enormous foot - imagine something the shape of R2D2.
What's really needed is a gait like a horse walking - the four legs are
90deg out of phase (120deg for a tripod) so at any instant only one leg is
off the ground.
It seems to me that only two gaits are possible - let's call them the 2(13)
and the 123 gaits.
The 2(13) gait is the "one-legged-man on crutches":
++++++ ++++++++ ++++++++ ++++++++ ++++++++ ++++++++
++++++++ ++++++++
++++++++ ++++++++ ++++++++ ++++++++ ++++++++ ++++++++
++++++++ ++++++++
++++++ ++++++++ ++++++++ ++++++++ ++++++++ ++++++++
++++++++ ++++++++
The 123 gaits has the three legs 120deg out of phase:
++++++++ ++++++++ ++++++++ ++++++++ ++++++++ ++++++++
++++++++ ++++++++ ++++++++
++++ ++++++++ ++++++++ ++++++++ ++++++++ ++++++++
++++++++ ++++++++ ++++++++
++++++++ ++++++++ ++++++++ ++++++++ ++++++++ ++++++++
++++++++ ++++++++
That looks like a rotating "bowling along the ground" gait but it would be
nice if the "head" sensors always pointed forwards so we'll assume that the
body and hips don't rotate.
You could lengthen each of the "on the ground" segments of the 123 so that
sometimes three legs are on the ground. And you could shorten each of the
"on the ground" segments so that sometimes only one leg is on the ground.
But you would never change the phase relation of the legs. That's like a
bipedal gait. Humans have only one gait; the proportion of the time each
foot is on the ground changes between walk, trot, run but the phase
relation is always 180deg. Horses have several with different phase
relations for walk, trot, canter and gallop. And greyhounds and cheetahs
bound.
A tripod could walk and trot by changing the time each foot is on the
ground but retaining the 120deg phase. It could break into 2(13) bounding
(like a greyhound) for fast movement. Like a very speedy "one-legged-man on
crutches".
Let's assume that when walking (always two feet on the ground) the legs
swing in straight line so the footsteps show three separate parallel lines
(unlike humans whose footsteps are in a single line). The body will weave
from side to side so as to keep the centre of gravity over the line joining
the two on-the-ground feet. The line joining the two on-the-ground feet
will be at an angle to the direction of travel and (I think) will help the
body "fall" from side to side in time with the footsteps like an inverted
pendulum. Presumably, the speed of the gait will be tuned so that it
matches both the period of the inverted pendulum and the pendulum of the
legs.
Hmmm. I think this might be worth simulating or at least animating!
There are a lot of illustrations of tripods on
http://drzeus.best.vwh.net/wotw/timeline.html
many of which look plausible. But these are all "stills" of course.
Chris Dickinson once hoped to make / still hopes to make / is making a
movie:
http://members.iinet.net.au/~chrisdn/waroftheworlds/
so it will be interesting to see what gait the animators choose. Ray
Harryhausen also hoped one day to make a movie. Supposedly, another WOTW
movie is currently being made (maybe that's a euphemism for "trying to get
funding") but I can't find a web page.
Several companies have sold plastic kits of tripod robots including a
Bandai kit of a "Dark Nebula Tripod Tank" from the animated "Starblazers"
series. I've no idea what the the animated "Starblazers" series is or was.
The front cover of my copy of Larry Niven's "Neutron Star" (ISBN 0 7088
8011 8) shows a Pierson's Puppeteer (a three-legged alien) trotting. It is
clearly using the 123 gait but only one foot is on the ground. I suspect a
web search would turn up more pictures of Puppeteers and maybe even a
discussion group.
Don't forget kangaroos: they use a kind of 3-legged gait when grazing (the
front legs move together as leg-1, the back legs move together as leg-2 and
the tail is leg-3). And brittle-stars that have lost two legs can move very
well with the remaining three. Brittle-stars have weird locomotion that's
well worth studying. I think McNeil Alexanders classic book on animal
locomotion has pictures but I can't find my copy.
By coincidence, I saw a three-legged dog in the park today so I studied it
carefully. It had modified the usual dog bounding - front legs together,
back legs together, arched back - but the front legs were somewhat out of
phase.
And yes - I am rather a fan of War of the Worlds and Larry Niven,
Peter Balch
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