| Volume 26 Issue 10 - Publication Date: 1 September 2007 |
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Towards a Unified Approach to Motion Planning for Dynamic
Underactuated Mechanical Systems with Non-holonomic Constraints |
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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 generalize our prior results in motion analysis to
design gaits for a more general family of underactuated mechanical
systems. In particular, we analyze and generate gaits for mixed mechanical
systems which are systems whose motion is simultaneously
governed by both a set of non-holonomic velocity constraints and a
notion of a generalized momentum being instantaneously conserved
along allowable directions of motion. Through proper recourse to
geometric mechanics, we are able to show that the resulting motion
from a gait has two portions: a geometric and a dynamic contribution.
The main challenge in motion planning for a mixed system is
understanding how to separate the geometric and dynamic contributions
of motion due to a general gait, thus simplifying gait analysis. In
this paper, we take the first step towards addressing this challenge in
a generalized framework. Finally, we verify the generality of our approach
by applying our techniques to novel mechanical systems which
we introduce in this paper as well as by verifying that seemingly different
prior motion planning results could actually be explained using
the gait analysis presented in this paper. |
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| Multimedia Key |
= Video |
 = Data |
= Code |
= Image |
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Extension |
Type |
Description |
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Example
1:Video showing the actual motion of the variable inertia snakeboard while performing the purely dynamic gait, PDVS
1 . The frames are
chosen to depict one complete gait where is the gait’s period. (1.5 MB) wmv |
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Example
2: Video Showing the actual motion of the variable inertia snakeboard while performing the purely dynamic gait, PDVS
2 . The frames are
chosen to depict one complete gait where is the gait’s period.(1.5 MB) wmv |
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3 |
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Example
3: Video Showing the actual motion of the variable inertia snakeboard while performing the kino-dynamic gait, KDVS
3 . The frames are
chosen to depict one complete gait where is the gait’s period. (1.5 MB) avi |
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