A. Marino and G. Antonelli and A.P. Aguiar and A. Pascoal, Multi-robot harbor patrolling: a probabilistic approach, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, Algarve, PT, pp. , 2012.

1. A new approach to multi-robot harbour patrolling:
theory and experiments
Alessandro Marino, Gianluca Antonelli,
A. Pedro Aguiar, Ant´nio Pascoal
o
Universit` di Salerno, Italy
a
Universit` di Cassino e del Lazio Meridionale, Italy
a
Universidade do Porto, Portugal
Instituto Superiore T´cnico, Portugal
e
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

2. Problem formulation
Multi-robot harbor patrolling
Mathematically strong overlap with (time varying)
coverage
deployment
resource allocation
sampling
exploration
monitoring
slight differences depending on assumptions and objective functions
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

3. The rules of the game
Totally decentralized
Robust to a wide range of failures
communications
vehicle loss
vehicle 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

4. 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 interest
Time-dependency forgetting factor
Asynchronous spot visiting demand
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

5. Voronoi partitions I
Voronoi partitions (tessellations/diagrams)
Subdivisions of a set S characterized by a metric with respect to a
finite 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

6. Voronoi partitions II
Spontaneous distribution of restaurants
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

7. Voronoi partitions III
Voronoi in nature
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

8. Voronoi partitions IV
Voronoi in art: Escher
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

9. Background I
how much do I trust that
Variable of interest is a Gaussian process
a given point is safe?
Given the points of measurements done. . .
Sa = (xa , ta ), (xa , ta ), . . . , (xaa , taa )
1 1 2 2 n n
and one to do. . .
Sp = (xp , t)
Synthetic Gaussian representation of the condition distribution
µ = µ(xp , t) + c(xp , t)T Σ Sa (y a − µa )
ˆ −1
σ = K(f (xp , t), f (xp , t)) − c(xp , t)T Σ −1 c(xp , t)
ˆ Sa
c represents the covariances of the acquired points vis new one
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

10. 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)T Σ Sa (y a − µa )
 ˆ
−1
σ = K(f (xp , t), f (xp , t)) − c(xp , t)T Σ −1 c(xp , t)
ˆ Sa


ξ
− > ξ example
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

11. Description II
Distribute the computation among the vehicles
each 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

12. Accuracy: example
Global computation of ξ(x) for a given spatial variability τs
τs
ξ(x)
x1 x2 x3 x4
x
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

13. Accuracy: example
Computation made by x2 (it does not “see” x4 )
τs
ξ(x)
x1 x2 x3 x4
x
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

14. Accuracy: example
Only the restriction to V or2 is needed for its movement computation
τs
ξ(x)
V or2
x1 x2 x3 x4
x
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

15. Accuracy: example
Merging of all the local restrictions leads to a reasonable approximation
τs
ξ(x)
V or2
x1 x2 x3 x4
x
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

16. Accuracy
Based on:
communication bit-rate
computational capability
area dimension
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

17. Numerical validation
Dozens of numerical simulations by changing the key parameters:
vehicles number
faults
obstacles 2
sensor noise
area shape/dimension 3 4
comm. bit-rate
space scale
time scale
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

18. Some benchmarking
With a static field the coverage index always tends to one
Coverage Index
1
0.8
0.6
[]
0.4
0.2
0 200 400 600 800 1000
step
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

19. Some benchmarking
Comparison between different approaches
2
same parameters
1.5 lawnmower rigid wrt
vehicle loss
[]
1 deployment suffers
Lawnmower from theoretical
Proposed
Random flaws
0.5 Deployment
00 200 400 600 800 1000 1200
step
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

20. Two marine patrolling experiments
3 ASVs july 2011 2 AUVs february 2012
Instituto Superior T´cnico
e with GraalTech at NURC
100 × 100 m 150 × 150 × 5 m
1 m/s 1.5 m/s
GPS localiz. localiz. asynch 5 time/min
WiFi comm. comm. 32 byte/min
duration as long as batteries on 33 minutes
results under evaluation
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012

21. CO3AUVs
Cooperative Cognitive Control of Autonomous Underwater Vehicles
fundings : FP7 - Cooperation - ICT - Challenge 2
Cognitive Systems, Interaction, Robotics
kind : Collaborative Project (STREP)
acronym : CO3 AUVs
duration : Feb 2009-Gen 2012
http://www.Co3-AUVs.eu
Marino, Antonelli, Aguiar, Pascoal Vila Moura, 8 October 2012