icra 2013 talk 2

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Coverage of a given area by means of coordinated autonomous robots is a mission required in several applications such as, for example, patrolling, monitoring or environmental sampling. From a mathematical perspective, this can often be modeled as the need to estimate a scalar field, eventually time varying as in the security applications. In this paper, the problem is addressed for the challenging underwater scenario, where localization and communication pose additional constraints. The solution exploits the appealing properties of the Voronoi partition of a convex set within a probabilistic framework. In addition, the algorithm is totally distributed and characterized by a strong engineering perspective allowing the handling of asynchronous communication or possible loss or adjunct of vehicles. Beyond the test in dozen of numerical case studies, the algorithm has been validated by a challenging underwater test in 3 dimension involving two Autonomous Underwater Vehicles (AUVs). The experiments were run in the La Spezia harbor, in Italy, in February 2012 as demo of the European project \co3auvs.

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  • 1. Experimental Results of Coordinated Coverage byAutonomous Underwater VehiclesAlessandro Marino, Gianluca AntonelliUniversit`a di Salerno, ItalyUniversit`a di Cassino & ISME (Integrated Systems for Marine Environment), Italyantonelli@unicas.ithttp://webuser.unicas.it/lai/roboticahttp://www.isme.unige.it/Marino, Antonelli Karlsruhe, 9 May 2013
  • 2. CO3AUVsCooperative Cognitive Control of Autonomous Underwater Vehiclesfundings : European FP7, Cognitive Systems, Interaction, Roboticskind : Collaborative Project (STREP)duration : 3 years, 2009-2012partners : Jacobs University, DE;ISME, I;Instituto Superior Tecnico, P;GraalTech, Ihttp://www.Co3-AUVs.euMarino, Antonelli Karlsruhe, 9 May 2013
  • 3. Problem formulationMulti-robot harbor patrollingTotally decentralizedRobust to a wide range of failurescommunicationsvehicle lossvehicle stillFlexible/scalable to the number of vehicles add vehicles anytimePossibility to tailor wrt communication capabilitiesNot optimal but benchmarking requiredAnonymityTo be implemented on a real set-up obstacles. . .Marino, Antonelli Karlsruhe, 9 May 2013
  • 4. Proposed solutionProper merge of the Voronoi and Gaussian processes conceptsMotion computed to increase informationFramework to handleSpatial variability regions with different interestTime-dependency forgetting factorAsynchronous spot visiting demandMathematically strong overlap with (time varying) coverage,deployment, resource allocation, sampling, exploration, monitoring, etc.slight differences depending on assumptions and objective functionsMarino, Antonelli Karlsruhe, 9 May 2013
  • 5. Proposed solutionProper merge of the Voronoi and Gaussian processes conceptsMotion computed to increase informationFramework to handleSpatial variability regions with different interestTime-dependency forgetting factorAsynchronous spot visiting demandMathematically strong overlap with (time varying) coverage,deployment, resource allocation, sampling, exploration, monitoring, etc.slight differences depending on assumptions and objective functionsMarino, Antonelli Karlsruhe, 9 May 2013
  • 6. Backgroundtheoretical detailsAntonelli, Chiaverini, Marino, A coordination strategy for multi-robotsampling of dynamic elds, ICRA 2012experimental validation with surface vehiclesMarino, Antonelli, Aguiar, Pascoal, Multi-robot harbor patrolling: aprobabilistic approach, IROS 2012Marino, Antonelli Karlsruhe, 9 May 2013
  • 7. Voronoi partitions IVoronoi partitions (tessellations/diagrams)Subdivisions of a set S characterized by a metric with respect to anite number of points belonging to the setunion of the cells gives back the setthe intersection of the cells is nullcomputation of the cells is adecentralized algorithm withoutcommunication neededMarino, Antonelli Karlsruhe, 9 May 2013
  • 8. Voronoi partitions IIMarino, Antonelli Karlsruhe, 9 May 2013
  • 9. Background IVariable of interest is a Gaussian processhow much do I trust thata given point is safe?Given the points of measurements done. . .Sa = (xa1 , ta1 ), (xa2 , ta2 ), . . . , (xana, tana)and one to do. . .Sp = (xp, t)Synthetic Gaussian representation of the condition distribution = (xp, t) + c(xp, t)T1Sa(ya a) = K(f(xp, t), f(xp, t)) c(xp, t)T1Sac(xp, t)c represents the covariances of the acquired points vis new oneMarino, Antonelli Karlsruhe, 9 May 2013
  • 10. Description IThe variable to be sampled is a condence mapReducing the uncertainty means increasing the highlighted term = (xp, t) + c(xp, t)T1Sa(ya a) = K(f(xp, t), f(xp, t)) c(xp, t)T1Sac(xp, t) > exampleMarino, Antonelli Karlsruhe, 9 May 2013
  • 11. Description IIDistribute the computation among the vehicleseach vehicle in its own Voronoi cellCompute the optimal motion to reduce uncertaintySeveral choices possible:minimum, minimum over anintegrated path, etc.Marino, Antonelli Karlsruhe, 9 May 2013
  • 12. Accuracy: exampleGlobal computation of (x) for a given spatial variability ssx1 x2 x3 x4x(x)Marino, Antonelli Karlsruhe, 9 May 2013
  • 13. Accuracy: exampleComputation made by x2 (it does not see x4)sx1 x2 x3 x4x(x)Marino, Antonelli Karlsruhe, 9 May 2013
  • 14. Accuracy: exampleOnly the restriction to V or2 is needed for its movement computationsx1 x2 x3 x4x(x)V or2Marino, Antonelli Karlsruhe, 9 May 2013
  • 15. Accuracy: exampleMerging of all the local restrictions leads to a reasonable approximationsx1 x2 x3 x4x(x)V or2Marino, Antonelli Karlsruhe, 9 May 2013
  • 16. AccuracyBased on:communication bit-ratecomputational capabilityarea dimensionMarino, Antonelli Karlsruhe, 9 May 2013
  • 17. Numerical validationDozens of numerical simulations by changing the key parameters:vehicles numberfaultsobstaclessensor noisearea shape/dimensioncomm. bit-ratespace scaletime scale23 4Marino, Antonelli Karlsruhe, 9 May 2013
  • 18. Some benchmarkingWith a static eld the coverage index always tends to one0 200 400 600 800 10000.20.40.60.81step[]Coverage IndexMarino, Antonelli Karlsruhe, 9 May 2013
  • 19. Some benchmarkingComparison between dierent approaches00LawnmowerProposedRandomDeployment0.51.52200 400 600 800 1000 12001[]stepsame parameterslawnmower rigid wrtvehicle lossdeployment suffersfrom theoreticalflawsMarino, Antonelli Karlsruhe, 9 May 2013
  • 20. Vehicle characteristicsinternal diameter .125 mexternal diameter .14 mlength 2 mmass 30 kgmass variation range .5 kg(at water density 1.031 kg/m3)moving mass max displacement 0.050 mLead acid batteries 12 V 72 Ahautonomy at full propulsion 8 hdiving scope 050 mbreak point in depth 100 mspeed with jet pump propeller 1.01 m/s 2 knotsspeed with blade propeller 2.02 m/s 4 knotscpu 1GHz, VIA EDENdram 1GB, DDR2Marino, Antonelli Karlsruhe, 9 May 2013
  • 21. Experimental validationjoint experiment with Graaltech NURC (NATO Undersea ResearchCenter) facilities, La Spezia, ItalyMarino, Antonelli Karlsruhe, 9 May 2013
  • 22. Experimental validation2 F`olaga, 4 acoustic transponders, 1 gateway buoy110 80 4 m1.5 m/s33 minutesWHOI micromodem 80 bpsTime Division Multiple Accesslocalization: every 8 suser comm: 31 byte/min with 14 s delayMarino, Antonelli Karlsruhe, 9 May 2013
  • 23. Experimental validationDue to poor communication, the algorithm runs by predicting themovement of the other# elds size (bytes)1) vehicle ID 22) localization time 43) vehicle latitude 44) vehicle longitude 45) vehicle depth 46) target latitude 47) target longitude 48) target depth 4Marino, Antonelli Karlsruhe, 9 May 2013
  • 24. Experimental validation - videoCoverage index200 400 600 800 1000 1200 1400 16000.10.20.30.4[]0.500time [s] 1800Marino, Antonelli Karlsruhe, 9 May 2013