ICRA 2012 talk

A coordination strategy for multi-robot

sampling of dynamic fields

Gianluca Antonelli, Stefano Chiaverini, Alessandro Marino

Universita degli Studi di Cassino e del Lazio Meridionale

[email protected]

http://webuser.unicas.it/lai/robotica

ICRA 2012 - St. Paul

Antonelli Chiaverini Marino St Paul, 15 May 2012

mailto:[email protected]

http://webuser.unicas.it/lai/robotica

Problem formulation

Coordinated multiple robots aimed at sampling a dynamic field

Mathematically strong overlap with (dynamic)

coveragedeploymentresource allocationpatrollingexplorationmonitoring

slight differences depending on assumptions and objective functions


The rules of the game

Totally decentralized

Robust to wide range of failures

communicationsvehicle lossvehicle still

Flexible/scalable to the number of vehicles add vehicles anytime

Possibility to tailor wrt communication capabilities

Not optimal but benchmarking required

Anonymity

To be implemented on a real set-up obstacles. . .


Proposed solution

Based on a proper merge of the Voronoi and Gaussian processesconcepts

Communication required only to exchange key data

Motion computed to increase information

Map-based

Framework to handle

Spatial variability regions with different interestTime-dependency forgetting factorAsynchronous spot visiting demand

Designed together with a patrolling strategy


Voronoi partitions I

The Voronoi partitions (tessellations/diagrams) are a subdivisions of aset S characterized by a metric with respect to a finite number ofpoints belonging to the set

union of the cells gives back the set

the intersection of the cells is null

computation of the cells is a

decentralized algorithm without

communication needed


Voronoi partitions II

Spontaneous distribution of restaurants


Voronoi partitions III

Voronoi in nature


Voronoi partitions IV

Voronoi in art: Escher


Background I

Variable of interest is a Gaussian processhow much do I trust that

a given point is safe?Given the points of measurements done. . .

Sa ={(xa1 , t

a1 ), (x

a2 , t

a2 ), . . . , (x

ana

, tana

)}

and one to do. . .

Sp = (xp, t)

Synthetic Gaussian representation of the condition distribution

{

µ = µ(xp, t) + c(xp, t)TΣ−1

Sa(ya − µa)

σ = K(f(xp, t), f(xp, t))− c(xp, t)TΣ−1

Sac(xp, t)

c represents the covariances of the acquired points vis new one


Description I

The variable to be sampled is a confidence map

Reducing the uncertainty means increasing the highlighted term

µ = µ(xp, t) + c(xp, t)TΣ−1

Sa(ya − µa)

σ = K(f(xp, t), f(xp, t)) − c(xp, t)TΣ−1

Sac(xp, t)︸︷︷︸

ξ

− > ξ example


Description II

Distribute the computation among the vehicleseach vehicle in its own Voronoi cell

Compute the optimal motion to reduce uncertainty

Several choices possible:

minimum, minimum over an

integrated path, etc.


Accuracy: example

Global computation of ξ(x) for a given spatial variability τs

τs

x1 x2 x3 x4x

ξ(x)


Accuracy: example

Computation made by x2 (it does not “see” x4)

τs

x1 x2 x3 x4x

ξ(x)


Accuracy: example

Only the restriction to V or2 is needed for its movement computation

τs

x1 x2 x3 x4x

ξ(x)

V or2


Accuracy: example

Merging of all the local restrictions leads to reasanable approximation

τs

x1 x2 x3 x4x

ξ(x)

V or2


Accuracy

Based on:

communication bit-rate

computational capability

area dimension


Numerical validation

Dozens of numerical simulations by changing the key parameters:

vehicles number

faults

obstacles

sensor noise

areashape/dimension

comm. bit-rate

space scale

time scale

2

3 4


Some benchmarking

With a static field the coverage index always tends to one

0 200 400 600 800 1000

0.2

0.4

0.6

0.8

1

step

[]

Coverage Index


Some benchmarking

Comparison between different approaches

00

LawnmowerProposedRandomDeployment0.5

1.5

2

200 400 600 800 1000 1200

1

[]

step

same parameters

lawnmower rigid wrtvehicle loss

deployment suffersfrom theoreticalflaws


Two marine patrolling experiments

3 ASVs july 2011

Instituto Superior Tecnico100× 100m1m/sGPS localiz.WiFi comm.switched off only for batteryresults under evaluation

2 AUVs february 2012

with GraalTech at NURC150× 150× 5m1.5m/slocaliz. asynch 5 time/mincomm. 32 byte/min33 minutespaper in preparation


Challenge

reuse pieces of code for different setup


CO3AUVs

fundings : FP7 - Cooperation - ICT - Challenge 2Cognitive Systems, Interaction, Robotics

kind : Collaborative Project (STREP)acronym : CO3AUVsduration : 3 yearsstart : Feb 2009 ended few weeks ago

budget : ≈ 2.5Me

http://www.Co3-AUVs.eu


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