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SLAM with fleeting detections Fabrice LE BARS

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SLAM with fleeting detections 30/04/2015- 2 Outline Introduction Problem formalization CSP on tubes Contraction of the visibility relation Conclusion

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SLAM with fleeting detections 30/04/2015- 3 Introduction Context: Offline SLAM for submarine robots Fleeting detections of marks Static and punctual marks Known data association Without outliers Tools: Interval arithmetic and constraint propagation on tubes

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SLAM with fleeting detections 30/04/2015- 4 Introduction Experiments with Daurade and Redermor submarines with marks in the sea

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SLAM with fleeting detections 30/04/2015- 5 Problem formalization

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SLAM with fleeting detections 30/04/2015- 6 Problem formalization Equations

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SLAM with fleeting detections 30/04/2015- 7 Problem formalization Fleeting data A fleeting point is a pair such that It is a measurement that is only significant when a given condition is satisfied, during a short and unknown time.

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SLAM with fleeting detections 30/04/2015- 8 Problem formalization Waterfall is a function that associates to a time a subset is called the waterfall (from the lateral sonar community).

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SLAM with fleeting detections 30/04/2015- 9 Problem formalization Waterfall Example: lateral sonar image

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SLAM with fleeting detections 30/04/2015- 10 Problem formalization Waterfall On a waterfall, we do not detect marks, we get areas where we are sure there are no marks

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SLAM with fleeting detections 30/04/2015- 11 CSP on tubes

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SLAM with fleeting detections 30/04/2015- 12 CSP on tubes CSP Variables are trajectories (temporal functions), and real vector Domains are interval trajectories (tubes), and box Constraints are:

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SLAM with fleeting detections 30/04/2015- 13 CSP on tubes Tubes The set of functions from to is a lattice so we can use interval of trajectories A tube, with a sampling time is a box-valued function constant on intervals The box, with is the slice of the tube and is denoted

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SLAM with fleeting detections 30/04/2015- 14 CSP on tubes Tubes The integral of a tube can be defined as: We have also:

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SLAM with fleeting detections 30/04/2015- 15 CSP on tubes Tubes However, we cannot define the derivative of a tube in the general case, even if in our case we will have analytic expressions of derivatives:

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SLAM with fleeting detections 30/04/2015- 16 CSP on tubes Tubes Contractions with tubes: e.g. increasing function constraint

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SLAM with fleeting detections 30/04/2015- 17 Contraction of the visibility relation

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SLAM with fleeting detections 30/04/2015- 18 Contraction of the visibility relation Problem: contract tubes, with respect to a relation: 2 theorems: 1 to contract and the other for

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SLAM with fleeting detections 30/04/2015- 19 Contraction of the visibility relation Example 1: Dynamic localization of a robot with a rotating telemeter in a plane environment with unknown moving objects hiding sometimes a punctual known mark

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SLAM with fleeting detections 30/04/2015- 20 Contraction of the visibility relation Example 1 is at Telemeter accuracy is, scope is Visibility function and observation function are:

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SLAM with fleeting detections 30/04/2015- 21 Contraction of the visibility relation Example 1 We have: which translates to: with:

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SLAM with fleeting detections 30/04/2015- 22 Contraction of the visibility relation Example 1 Example 1: contraction of

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SLAM with fleeting detections 30/04/2015- 23 Contraction of the visibility relation Example 2: contraction of

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SLAM with fleeting detections 30/04/2015- 24 Conclusion

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SLAM with fleeting detections 30/04/2015- 25 Conclusion In this talk, we presented a SLAM problem with fleeting detections The main problem is to use the visibility relation to contract positions We proposed a method based on tubes contractions

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SLAM with fleeting detections 30/04/2015- 26 Questions? Contacts fabrice.le_bars@ensta-bretagne.fr

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