COORDINATION and NETWORKING of

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COORDINATION and NETWORKING of GROUPS OF
MOBILE AUTONOMOUS AGENTS
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COOPERATIVE CONTROL
Yale is the lead institution on a
cross-disciplinary NSF project with Harvard,
Princeton, U. of Washington aimed at
understanding how various animal groups such as
fish schools and bird flocks coordinate their
collective motions and how groups of mobile
autonomous agents such as AUVs might use these
biological principles to collectively perform
useful tasks such as data gathering, search and
rescue, in a safe, cooperative, and coordinated
manner.
A FISH WHORL
The Grouper
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ROADMAP
1. Rigid Graph Theory
Maintaining Vehicle Formations Using Rigid
GraphTheory
Sensor Localization in Large Ad Hoc
Communication Networks
2. Emergent Behavior
The Flocking Problem
The Multi-Agent Rendezvous Problem
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Maintaining Vehicle Formations Using Rigid Graph
Theory
By an n vehicle formation is meant collection of
n mobile autonomous agents i.e., robots moving
through real 2 or 3 space.
Maintaining a formation means making sure that
the distance between each pair of agents remains
nominally unchanged over time.
Formation maintenance is typically achieved by
requiring some, but not all agent pairs to
maintain fixed distances between them.
Weve developed a framework based on the theory
of rigid graphs from classical mechanics
Cayley, Maxwell, for devising provably
correct procedures for so maintaining very
large formations.
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Sensor Localization in Large Ad Hoc Communication
Networks
Each Sensor
Does there exist a unique solution to the
problem?
1. is fixed in position.
2. can communicate with neighbors.
500m
3. knows distance from each neighbor.
Some sensors know their positions in world
coordinates.
Localization problem is for each sensor to
determine its position in world coordinates by
communicating with its neighbors.
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Sensor Localization in Large Ad Hoc Communication
Networks
Does there exist a unique solution to the
problem?
Answer is central to

• determining required
• topology of the network.

2. the devising of provable correct
distributed localization algorithms.
We introduced rigid graph theory to the
networking community and settled the uniqueness
question.
Localization problem is for each sensor to
determine its position in world coordinates by
communicating with its neighbors.
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THE FLOCKING PROBLEM
In a recent Phy. Rev. Letters paper Vicsek et al.
simulated a flock of n agents particles all
moving in the plane at the same speed s, but
with different headings ?1, ?2, , ?n
Each agents heading is updated using a local
rule based on the average of its own current
heading plus the headings of its neighbors.
Vicseks simulations demonstrate that these
nearest neighbor rules can cause all agents to
eventually move in the same direction despite the
absence of centralized coordination and despite
the fact that each agents set of neighbors
changes with time.
Using graph theory and the theory of
non-homogeneous Markov chains we have provided a
complete theoretical explanation for this
observed behavior.
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Bifrucation
Vicseks
Leaders Neighbors Yellow
Following Red Leader
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The Multi-agent Rendezvous Problem
deals with set of n mobile autonomous agents
which can all move in the plane.
Each agent is able to continuously sense the
relative positions of all other agents in its
sensing region where by agent is a sensing
region is meant a closed disk of radius r
centered at agent is current position.
Problem Devise local control strategies, one
for each agent, which without active
communication between agents, cause all
members of the group to
eventually rendezvous at a single unspecified
point.
We have devised a provably correct solution to
this problem which provides a framework for the
development of a wide range of group maneuvers
e.g., forming Yale Marching Band formations
using decentralized control.
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connected
disconnected
trapping
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Concluding Remarks
New data structures, models, etc.are needed to
represent large groups of mobile autonomous
agents at various degrees of granularity, for
pur- poses of simulations, management, analysis,
communication and control.
Such representations will exploit tools from both
graph theory and from the theory of dynamical
systems
At least initially, individual agent descriptions
using simple kinematic and dynamic models will
suffice.
System complexity will stem more from the number
of agent models being studied than from the
detailed properties of the individual agent
models.
New concepts of robustness, stability, etc. are
needed to understand such systems to address
issues such as cascade failure,
security, reliability, coordination, etc.