Alt-BEAM Archive
Message #05347
To: "'beam@sgiblab.sgi.com'" beam@sgiblab.sgi.com
From: Wilf Rigter Wilf.Rigter@powertech.bc.ca
Date: Wed, 21 Jul 1999 19:11:14 -0700
Subject: [alt-beam] Re: Hoverbot & balancing acts ( was: LEGO lawnmower)
Nice topic Zoz!
Try a 2DOF balancing act with a 4 foot rod on the tip of your finger. Note
that your eyes, focused on the position of the tip (top) of the rod, are the
feedback sensors. Maintaining the tip of the rod in a fixed location with
reference to a bright point in the background worked best for me and I
found horizontal lines but not vertical lines in the background quite
distracting. At first I experienced some wild excursions of the bottom of
the rod while the tip moved relatively little but after some practice, the
correction signals (bottom swings) became smaller while the tip (error
signal) was almost stationary.
Aside from the 2DOF and the more or less fixed frame of reference, the
"finger/arm" actuator is different from the cart primarily because it has
less mass. The inertia of the rod is much lower than the inertia of the cart
if the mass of the rod is small compared to the cart and controlling the
energy required for accelerating and decelerating the mass of the cart
becomes the problem. In a kind of twist on "the tail wagging the dog", this
obscures the primary objective of finding a solution to "the balancing act".
To separate the balancing act from the dynamic control of cart
mass/acceleration this can be dealt with in two different methods :
1. add mass to the tip of the rod
2. lower the mass of the "cart".
While it maybe possible address method 1 by attaching a brick (or the cart's
gell cell battery) to the tip of the rod, I would rather not have to lock up
the cats and wear a hardhat and steel toes around this experiment for fear
of getting "hammered" while fine-tuning the system.
In some sense, method 1 is used in the MIT "Pogobot" since it's high inertia
body position is controlled by rapidly hopping and repositioning the single
low mass leg (rod). The pogobot has a strong periodic vertical motion like
a perpetual bouncing ball ( hey! there's a thought) even while maintaining a
fixed horizontal position. The balance error/correction signal would seem to
normally be a small component of that periodic motion. To cause a
horizontal motion a small but cumulative error signal is added to the
balance loop which causes the displacement in the desired direction (like a
bicore head). The energy required for the periodic vertical motion of the
massive body is returned by a spring suspension with a timeconstant which
gives the pogobot it's characteristic hopping frequency.
An alternative to the pogobot would be to keep the vertical displacement of
the heavy body to a minimum. In such a design, the mass of the body could
and should be as low as possible in a conical skirt around the central leg.
Sort of a pogo leg inside a Dalek body (Dabot). The leg is connected to top
of the body at maximum height above the center of gravity of the body.
In a static, rest or start position the skirt may be lowered to the ground
(by contracting the leg) and in the process the Dabot can graciously recover
from a failure to balance. Horizontal motion is produce by extending the leg
and by "shifting" center of gravity of the body relative to the top of the
leg (rod) augmented by an aperiodic hopping motion when the leg exceeds the
range of static "shifting". Contrary to pogobot's "hopping with shifting"
algorithm, Dabot's "shifting with hopping" design minimizes vertical
displacement and is easily integrated with a 3 leg or "bouncing ball drive"
design (let you chew on that for a bit).
Back to the "rod on a base" balancing act: perhaps method 2 could use the
simple approach of eliminating the cart altogether by attaching the bottom
of the rod to a linear actuator operating in a 1DOF horizontal plane. ie a
thin steel band attached to a wheel on a motor shaft and looped around an
idler wheel similar to a floppy drive or printer head positioner. Now comes
the interesting part of defining the problem in terms of the relationship
between the error signal (tip displacement) and the correction signal
(bottom displacement. Next the design of the sensors and a control loop
function which approximates the correct error correction response. Then with
a bit of luck and some fine tuning of the damping factor the rod may be kept
in balance (unless John posed a trick question and this is an intractable
problem). So who's gonna try this out? Speaking of which, balancing a ball
on a shifting incline plane would be a similar problem, yes?
enjoy!
Wilf Rigter mailto:wilf.rigter@powertech.bc.ca
tel: (604)590-7493
fax: (604)590-3411
> -----Original Message-----
> From: John A. deVries II [SMTP:zozzles@lanl.gov]
> Sent: Wednesday, July 21, 1999 9:55 AM
> To: beam@sgiblab.sgi.com
> Subject: Hoverbot & balancing acts ( was: RE: LEGO lawnmower)
>
> At 12:34 AM 07/21/1999 , Van Zoelen, Bram AA SSI-TSEA-352 wrote:
>
> >> Does this robot really require wheels?
> >>
> > You can also let it hover and the propellor can cut the grass in one
> go.
> > Bram
>
> Well, you could if you had enough energy (i.e. external power source,
> gas-powered, or -very- light batteries, etc.) I don't think that it could
> be made to work given typical BEAM technology (i.e. solar powered, biggish
> capacitors, or batteries that weigh a lot.)
>
> An interesting question comes up: given a sufficient energy source, let's
> say that one was designing a ground-effect style machine (i.e. a
> hovercraft
> & not a helicopter). How does one usually control which direction the
> craft is going? Would one gimbal the 'engine' or would one have
> controllable louvers or what?
>
> A similar question: an old problem in control theory is the "balancing
> rod". In its most simple form, you've got a cart that can only move (back
> or forth) along a line. Attached by a hinge is a rod that you want to
> keep
> pointing upwards. If no control is applied, the rod will fall. The
> problem is to move the cart forwards or backwards to keep the rod upright.
>
> Given a potentiometer (variable resistance) connected to the hinge, how
> would it be possible to construct a nervous net controller for such a
> cart?
> Is it really just another version of a "head"? Would you need something
> like a Unicore controller? Is some yet-unknown nervous net controller
> feasible? Would there be some angle/velocity sensing system that would be
> more appropriate for nervous net use?
>
> Just more food for thought...
>
>
> Zoz
>
> p.s. more complicated problems include a rod-on-top-of-a-rod and a rod
> that
> is gimbaled by a ball-and-socket joint so that it could fall in a
> two-dimensional manner.
>
>
> ---------------------------------------------------------------
>
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>
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