[ From John Gardner (931129.1300 est)]
Bill Powers (931129.0900 MST)
I'd like to repeat what Avery said: in the Little Man Version 2,
which I THINK you have, the arm dynamics are included for the
three dimensions of control; the main missing df is roll about
the axis of the upper arm. The dynamical calculations are in the
module ARMDYNAM.C, which also contains the model of the stretch
and tendon reflexes. Also there are some details such as an
attempt to include the branches of the biceps and triceps which
span two joints, an addition that had the interesting effect of
reducing interactions between the arm segments.
I may have had Little Man V. 2 at one point, but I can't locate it now.
If you could send me a copy and the write-up, I'd be happy to take a
look at it. In particular, I'd be happy to investigate the fourth
DOF, it might not be too bad.
The secret seems to be in the fact that nature has provided
feedback loops for acceleration, velocity, and position using
tendon forces and muscle length (magnitude and rate). Joint angle
sensing provides an outer loop that gives good position control.
With all derivatives under explicit control, stabilization is
almost a freeby.
That's an interesting point about natural derivative feedback
inherent in the dynamics. As far as stabilization goes, it shouldn't
be all that surprising that you can stabilize it in this fashion. For
all the talk about 'inverse dynamics' computation in the robotic
community, real robots (industrial type) are NEVER controlled with
inverse dynamic computations. It's usually a pretty simple, local
level control loop, I think similar to the one you describe. After the
hardware people were using this technique for several years, the
mathematicians finally gave in and found a way to prove that, yes, it
is possible to stabilize a system like this with only local control
loops.
But I don't know how
to write out the detailed equations in 4 df that will produce the
required physical model of the arm, so I'm sort of stuck. It
would be nice to have a general 3-D vector disturbance term, too.
Hey, I can recognize a hint when I see one. Like I said, if you send
me the latest version, I'd be happy to take a look, maybe I can
make some headway over the holiday break.
>Optimal energy usage is clearly not a major consideration.
Agreed.
Well, I'm really going on my trip now, I'll be incommunicado for
the next week. Good luck to all.
John Gardner