Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Analysis of the Formation Problem for Autonomous Robots   In the formation control problem for autonomous robots a distributed control
law steers the robots to the desired target formation. A local stability result
of the target formation can be derived by methods of linearization and center
manifold theory or via a Lyapunov-based approach. It is well known that there
are various other undesired invariant sets of the robots' closed-loop dynamics.
This paper addresses a global stability analysis by a differential geometric
approach considering invariant manifolds and their local stability properties.
The theoretical results are then applied to the well-known example of a cyclic
triangular formation and result in instability of all invariant sets other than
the target formation.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex