| Volume 23 Issue 7/8- Publication Date: 1 July-August 2004 |
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| Feedback Control Methods for
Distributed Manipulation Systems that Involve Mechanical Contacts |
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| T.D. Murphey and J.W.
Burdick Division of Engineering and Applied Science, California
Institute of Technology, Pasadena, CA, USA |
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In this paper we introduce
feedback control methods for distributed manipulation systems thatmove
objects via rolling and slipping point contacts. Because of the intermittent
nature of these mechanical contacts, the governing mechanics of these
systems are inherently nonsmooth. We first present a methodology to
model these non-smooth mechanical effects in a manner that is tractable
for non-smooth control analysis. Using these models, we show that when
considerations of these non-smooth effects are taken into account, a
class of traditional open-loop distributed manipulation control methods
cannot stabilize objects near an equilibrium. However, stability can
be achieved through the use of feedback, and we present non-smooth feedback
laws with guaranteed stability properties. We then describe an experimental
modular distributed manipulation test-bed upon which one can implement
a variety of control schemes. Experiments with this test-bed confirm
the validity of our control algorithms. Multimedia extensions include
videos of these experiments.
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| Multimedia Key |
= Video |
 = Data |
= Code |
= Image |
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Extension |
Type |
Description |
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1 |
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Example
One: This is a video of an experimental implementation of an
open-loop elliptic velocity field. Recall that the object being
manipulated is a clear piece of plexiglass with a white and black
piece of paper on top for feedback. As predicted, the x and y coordinates
are successfully stabilized and the ? dynamics are not stabilized.
(5.8MB) |
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2 |
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Example
Two: This is a video of an experimental implementation of the
underactuated system. Notice that despite the underactuation, the
plexiglass is stabilized to the origin at the desired orientation.
(17.1MB) |
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Example
Three: This is a video of an experimental implementation of
the fully actuated system. Here the advantage of full actuation
is clear. The trajectory to the desired equilibrium is quite smooth
and the wheels are all coordinated without any slipping. (9.8MB)
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Example
Four: This is a video of an experimental implementation of the
globally stabilizing controller that combines the open-loop techniques
with the closed-loop techniques. Outside the circle shown in the
video, the system is running open loop. However, as soon as the
center of mass of the plexiglass enters the circle, the closed-loop
control is turned on and the plexiglass is stabilized to the origin
at the correct orientation using the full actuation control laws.
(9.1MB) |
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