COORDINATION and NETWORKING of
GROUPS OF MOBILE AUTONOMOUS
AGENTS
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
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”
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.
We’ve 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.
Sensor Localization in Large Ad Hoc Communication Networks
Does there exist a unique
solution to the problem?
500m
sensors
Each Sensor:
1. is fixed in position.
2. can communicate
with neighbors.
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.
Sensor Localization in Large Ad Hoc Communication Networks
Does there exist a unique
solution to the problem?
Answer is central to:
1. 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.
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
s
s = speed
i
i= heading
Each agent’s heading is updated using a local rule based on the average
of its own current heading plus the headings of its “neighbors.”
Vicsek’s 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 agent’s 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.
Vicsek’s
Bifrucation
Leader’s Neighbors Yellow
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 i’s a sensing region is meant a closed disk of
radius r centered at agent i’s current position.
r
sensing region
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.
connected
disconnected
trapping
Concluding Remarks
New data structures, models, etc.are needed to represent large groups
of mobile autonomous agents at various degrees of granularity, for purposes 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.