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G. Antonelli and S. Chiaverini and A. Marino, A coordination strategy for multi-robot sampling of dynamic fields, Proceedings 2012 IEEE International Conference on Robotics and Automation, St Paul, MN, pp. 1113--1118, 2012.
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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
antonelli@unicas.it
http://webuser.unicas.it/lai/robotica
ICRA 2012 - St. Paul
Antonelli Chiaverini Marino St Paul, 15 May 2012
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
Antonelli Chiaverini Marino St Paul, 15 May 2012
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. . .
Antonelli Chiaverini Marino St Paul, 15 May 2012
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
Antonelli Chiaverini Marino St Paul, 15 May 2012
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
Antonelli Chiaverini Marino St Paul, 15 May 2012
Voronoi partitions II
Spontaneous distribution of restaurants
Antonelli Chiaverini Marino St Paul, 15 May 2012
Voronoi partitions III
Voronoi in nature
Antonelli Chiaverini Marino St Paul, 15 May 2012
Voronoi partitions IV
Voronoi in art: Escher
Antonelli Chiaverini Marino St Paul, 15 May 2012
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
Antonelli Chiaverini Marino St Paul, 15 May 2012
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
Antonelli Chiaverini Marino St Paul, 15 May 2012
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.
Antonelli Chiaverini Marino St Paul, 15 May 2012
Accuracy: example
Global computation of ξ(x) for a given spatial variability τs
τs
x1 x2 x3 x4x
ξ(x)
Antonelli Chiaverini Marino St Paul, 15 May 2012
Accuracy: example
Computation made by x2 (it does not “see” x4)
τs
x1 x2 x3 x4x
ξ(x)
Antonelli Chiaverini Marino St Paul, 15 May 2012
Accuracy: example
Only the restriction to V or2 is needed for its movement computation
τs
x1 x2 x3 x4x
ξ(x)
V or2
Antonelli Chiaverini Marino St Paul, 15 May 2012
Accuracy: example
Merging of all the local restrictions leads to reasanable approximation
τs
x1 x2 x3 x4x
ξ(x)
V or2
Antonelli Chiaverini Marino St Paul, 15 May 2012
Accuracy
Based on:
communication bit-rate
computational capability
area dimension
Antonelli Chiaverini Marino St Paul, 15 May 2012
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
Antonelli Chiaverini Marino St Paul, 15 May 2012
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
Antonelli Chiaverini Marino St Paul, 15 May 2012
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
Antonelli Chiaverini Marino St Paul, 15 May 2012
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
Antonelli Chiaverini Marino St Paul, 15 May 2012
Challenge
reuse pieces of code for different setup
Antonelli Chiaverini Marino St Paul, 15 May 2012
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
Antonelli Chiaverini Marino St Paul, 15 May 2012
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