ICRA 2012 talk

transcript

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

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

, 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 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

x1 x2 x3 x4x

Accuracy: example

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

x1 x2 x3 x4x

Accuracy: example

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

x1 x2 x3 x4x

Accuracy: example

Merging of all the local restrictions leads to reasanable approximation

x1 x2 x3 x4x

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

Some benchmarking

With a static field the coverage index always tends to one

0 200 400 600 800 1000

Coverage Index

Some benchmarking

Comparison between different approaches

LawnmowerProposedRandomDeployment0.5

200 400 600 800 1000 1200

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

ICRA 2012 talk

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