| Volume 26 Issue 10 - Publication Date: 1 September 2007 |
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| Geometric Motion Planning Analysis for Two Classes of Underactuated
Mechanical Systems |
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| E. A. Shammas, H. Choset, and A. A. Rizzi The Robotics Institute, Carnegie Mellon University
5000 Forbes Avenue, Pittsburgh, PA 15213, USA |
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| In this paper we generate gaits for two types of underactuated mechanical
systems: principally kinematic and purely mechanical systems.
Our goal is to specify inputs in the form of gaits, that is, a
sequence of controlled shape changes of a multi-bodied mechanical
system that when executed would produce a desired change in the
unactuated position or orientation variables of the entire mechanical
system. In other words, we want to indirectly control the unactuated
degrees of freedom of the mechanical system utilizing a controlled
“internal” shape change. More precisely, in this paper we develop a
gait evaluation tool which easily measures the change of position,
computed in a body-attached coordinate frame, due to any closed
curve in the shape space. This evaluation tool is simple enough that
we can use it to generate gaits or to design curves that move the
mechanical system along a desired direction. Finally, we verify that
this gait analysis technique applies to two seemingly different classes
of mechanical systems, purely mechanical and principally kinematic
systems, and unify the gait generation problem for both classes. |
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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
1:Video showing the actual planer pivoting dynamic model while performing the square gait, GPPDM
1 . The frames are
chosen to depict one complete gait where
is the gait’s period. Note the slight overall clockwise rotation of the model. (0.9 MB) wmv |
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2 |
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Example
2: Video Showing the actual kinematic snake while performing a figure-eight type curve. The frames are chosen
to depict one complete gait where
is the gait’s period. Note the small translation of the robot in the x direction.(0.7 MB) wmv |
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3 |
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Example
3: Video Showing the actual kinematic snake while performing a singular figure-eight type curve. The frames are
chosen to depict one complete gait where
is the gait’s period. Note the relatively large translation of the robot in the x direction. (0.7 MB) avi |
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4 |
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Example
4: Video Showing the actual kinematic snake while performing a singular figure-eight type curve. The frames are
chosen to depict one complete gait where
is the gait’s period. Note the relatively large rotation of the kinematic snake. (1.7 MB) avi |
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