0
TECHNICAL PAPERS

# Decentralized Policies for Geometric Pattern Formation and Path Coverage

[+] Author and Article Information
Marco Pavone

Laboratory for Information and Decision Systems, Department of Aeronautics and Astronautics,  Massachusetts Institute of Technology, Cambridge, Massachusetts 02139pavone@mit.edu

Emilio Frazzoli

Laboratory for Information and Decision Systems, Department of Aeronautics and Astronautics,  Massachusetts Institute of Technology, Cambridge, Massachusetts 02139frazzoli@mit.edu

J. Dyn. Sys., Meas., Control 129(5), 633-643 (Oct 10, 2006) (11 pages) doi:10.1115/1.2767658 History: Received April 02, 2006; Revised October 10, 2006

## Abstract

This paper presents a decentralized control policy for symmetric formations in multiagent systems. It is shown that $n$ agents, each one pursuing its leading neighbor along the line of sight rotated by a common offset angle $α$, eventually converge to a single point, a circle or a logarithmic spiral pattern, depending on the value of $α$. In the final part of the paper, we present a strategy to make the agents totally anonymous, and we discuss a potential application to coverage path planning.

<>

## Figures

Figure 1

Eigenvalue placement for various α and n=6. On the most external circle there are just two eigenvalues. (a) α=0; (b) α=π∕6; (c) α=π∕6+π∕12; (d) α=2π∕6+π∕12.

Figure 2

Rendezvous to a point for n=6 agents and α=π∕6−π∕12

Figure 3

Circle formation for n=6 agents (α=π∕6)

Figure 4

Spiral formation for n=6 agents and α=π∕6+π∕12

Figure 5

Nonholonomic differentially driven mobile robot (adapted from Ref. 14)

Figure 6

Formations of n=8 nonholonomic agents (a) Circle formation for n=8 nonholonomic agents-detail; (b) circle formation for n=8 nonholonomic agents.

Figure 7

Circle formation for n=20 anonymous agents

Figure 8

Critical case for the anonymous approach. (a) Critical case: if α>0, ϕ̇ for agents 2 and 6 is negative while φ=0; (b) α=0: no agent leaves the convex hull; (c) α=π∕8: agents 2 and 6 leave the convex hull.

Figure 9

Archimedes spiral trajectories for n=12 agents with a footprint radius d=0.2

Figure 10

Archimedes spiral trajectories for n=16 agents that undergo six losses (agents with cross). The covered area is also shown.

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections