- ...based
- Terminology
accoring to Weiss' [Weiss and Sanderson, 1987]
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- ...eighties
- To be precise there was actually a parallel thread
on direct visual control used in the various autonomous vehicle projects,
but they were only controlling one variable; i.e. the steering angle.
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- ...pairs
- Note that they assume exact
problems, i.e. the same number of features as the number of controlled
variables. In fact they
even claim that is a necessary condition.
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- ...place
- Another problem not addressed
in Weiss and Sanderson's paper is how to make the initial feature assignment
without knowing the Jacobian.
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- ...
- We use capital letters to indicate
matrices, bold face for vectors, and plain for scalars and functions.
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- ...
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Updating formulas of rank 1 and 2 are most common. The motivation of
popular rank 2 formulas, such as the Davidson, Fletcher, Powell
(DFP) [Fletcher, 1987], is that they preserve symmetry
(
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positive definiteness of
, and
thus guarantee that the search direction
of a
quasi-Newton type controller is
a descent direction for
. The downside is we know
no strong convergence results of the DFP method in combination
with inexact line searches (which are used in our trust region
controller, described in Section 5.1).
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- ...method
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Trust region methods have wide use in optimization and data fitting,
(where they were pioneered by Levenberg and Marquart)
but we have not seen them combined with a quasi-Newton method with
estimated Jacobian before.
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- ...
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Electronic m-peg videos of the experiments in this
section are accessible through the Internet WWW. Use the menu in:
http://www.cs.rochester.edu/u/jag/PercAct/videos.html.
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- ...appearance
- A sparse representation,
based on hand picked features would work also. In fact that is what
we use when we do the inverse problem, visual
servoing (Chapter 5),
which is
the problem of: given a pose described in image space, control the
physical agent so
it attains that pose (again, without any prior calibration or models,
but by learning enough about the visual-motor transfer function on-line ).
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- ...motor
- We use motor state in a general sense, which can
be the joint frame of the articulated agent, but can also be a related
frame (e.g. Cartesian world).
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- ...camera
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Part of the training sequence is in
Video 4.
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- ...HREF="ftp://ftp.cs.rochester.edu/pub/u/jag/simrobot/">ftp
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A sample set of routines for 2D off line view syntgesis is availible
from:
ftp://ftp.cs.rochester.edu/pub/u/jag/simrobot/
Corke's toolbox is available from:
ftp://ftp.mathworks.com/pub/contrib/
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- ...space
- Think camera
space, although more general visual features are also used.
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