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[DPRG] Walking robot

Subject: [DPRG] Walking robot
From: David P. Anderson dpa at io.isem.smu.edu
Date: Wed Sep 24 13:34:01 CDT 2003


Chuck wrote:

> > >People don't "fall up" stairs.
> >I'm not sure that is true.  Can you elucidate?
> A stair climbing gait depends on a balanced vertical ascent. It becomes 
> more of a crawl the farther forward you lean up until you get to the 
> classic "kid running up stairs" gait using the hands/arms for stablizing 
> the torso.

I'm trying to square that with what I've learned about dynamic balance from
the two-wheel balancing robot.

The two-wheel balancing robot and the two-legged balancing human seem to me
to be doing basically the same thing, as far as the physics is concerned.

Both maintain balance by keeping the base underneath the center of gravity.
Both move forward by allowing the center of gravity to fall forward, and
using that falling force to counter-balance the torque required for
acceleration and locomotion.  

That is, the forward falling weight of the upper part of the body is
required to keep the torque required for forward movement from flipping
the body/robot over backwards.

In this way the human and the robot are both always falling forward when
in forward motion.  

Here is a video of the robot balancing while standing still (well, I'm
pushing it around) 


and here is one of it driving, and leaning forward to accelerate and
maintain constant velocity:


where you can see that it must lean forward slightly in order to overcome the
friction of the carpet, even when it is not accelerating.

Now if the robot were to drive from a smooth low friction surface like hardwood
to a higher friction surface like heavy pile carpet, more torque will be required
to maintain the same velocity, and the robot will have to lean further forward
in order for the "falling" force to counteract the increased torque.

In the same way, if the robot (or human) drives from a smooth level surface onto
an inclined ramp, more torque is required to go up the ramp, and the robot must
lean over further to counter-act (provide for) the increased torque.

Here is a video of the robot going up and down a ramp: 


Well, it got going too fast and fell down on the first try, but thereafter
you can see that it has to lean further forward to handle the increased
torque required to lift it's body weight when it goes up the ramp.

Now, it seems that you can make that ramp as steep as you want, as long as the
robot has sufficient batteries/motor/torque to climb the slope, it will just
lean further and further forward, and it is still, and must be, falling forward,
falling "up the slope,"  in order to go forward.

At some point the amount of forward tilt required will run into the increasing
steepness of the slope, the robot will assume the classic "kid running up the
stairs" posture.

Stairs are just an inclined slope that is customized for feet instead of wheels,
so your foot has a nice flat place to support it, but the human like the robot
must have a falling center of gravity in order to counteract the torque required
to ascend.  So the human walking gait (or two-legged robot walking gait), in my
understanding, does and in fact must, fall up the stairs.  

Stairs are just a special case of an inclined plane, and an inclined plane is just
a special case of a level plane, and the same walking and balancing principles would
appear to apply to all three, both for dynamically balancing two-wheel robots and
for dynamically balancing two-legged humans.


As an aside to the wheels vs. legs discussion, I'd be interested to see how one 
of the two-legged industrial walking robots, dynamic or static or any combination,
might handle something like this:



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