Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Geometric Structure of Externally Actuated Planar Locomoting Systems
  in Ambient Media   Robots often interact with the world via attached parts such as wheels,
joints, or appendages. In many systems, these interactions, and the manner in
which they lead to locomotion, can be understood using the machinery of
geometric mechanics, explaining how inputs in the shape space of a robot affect
motion in its configuration space and the configuration space of its
environment. In this paper we consider an opposite type of locomotion, wherein
robots are influenced actively by interactions with an externally forced
ambient medium. We investigate two examples of externally actuated systems; one
for which locomotion is governed by a principal connection, and is usually
considered to possess no drift dynamics, and another for which no such
connection exists, with drift inherent in its locomotion. For the driftless
system, we develop geometric tools based on previously understood internally
actuated versions of the system and demonstrate their use for motion planning
under external actuation. For the system possessing drift, we employ
nonholonomic reduction to obtain a reduced representation of the system
dynamics, illustrate geometric features conducive to studying locomotion, and
derive strategies for external actuation.

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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex