A new approach to multi-robot harbour patrolling:theory and experiments
Alessandro Marino, Gianluca Antonelli,A. Pedro Aguiar, Antonio Pascoal
Universita di Salerno, Italy
Universita di Cassino e del Lazio Meridionale, Italy
Universidade do Porto, Portugal
Instituto Superiore Tecnico, Portugal
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Problem formulation
Multi-robot harbor patrolling
Mathematically strong overlap with (time varying)
coveragedeploymentresource allocationsamplingexplorationmonitoring
slight differences depending on assumptions and objective functions
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
The rules of the game
Totally decentralized
Robust to a 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. . .
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Proposed solution
Proper merge of the Voronoi and Gaussian processes concepts
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
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Voronoi partitions I
Voronoi partitions (tessellations/diagrams)
Subdivisions of a set S characterized by a metric with respect to afinite number of points 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
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Voronoi partitions II
Spontaneous distribution of restaurants
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Voronoi partitions III
Voronoi in nature
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Voronoi partitions IV
Voronoi in art: Escher
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 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
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 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
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 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.
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Accuracy: example
Global computation of ξ(x) for a given spatial variability τs
τs
x1 x2 x3 x4x
ξ(x)
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Accuracy: example
Computation made by x2 (it does not “see” x4)
τs
x1 x2 x3 x4x
ξ(x)
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Accuracy: example
Only the restriction to V or2 is needed for its movement computation
τs
x1 x2 x3 x4x
ξ(x)
V or2
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Accuracy: example
Merging of all the local restrictions leads to a reasonable approximation
τs
x1 x2 x3 x4x
ξ(x)
V or2
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Accuracy
Based on:
communication bit-rate
computational capability
area dimension
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Numerical validation
Dozens of numerical simulations by changing the key parameters:
vehicles number
faults
obstacles
sensor noise
area shape/dimension
comm. bit-rate
space scale
time scale
2
3 4
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 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
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 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
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
Two marine patrolling experiments
3 ASVs july 2011
Instituto Superior Tecnico100× 100m1m/sGPS localiz.WiFi comm.duration as long as batteries on
2 AUVs february 2012
with GraalTech at NURC150× 150× 5m1.5m/slocaliz. asynch 5 time/mincomm. 32 byte/min33 minutesresults under evaluation
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012
CO3AUVs
Cooperative Cognitive Control of Autonomous Underwater Vehicles
fundings : FP7 - Cooperation - ICT - Challenge 2Cognitive Systems, Interaction, Robotics
kind : Collaborative Project (STREP)acronym : CO3AUVsduration : Feb 2009-Gen 2012
http://www.Co3-AUVs.eu
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012