1. SLAM with fleeting detections Fabrice LE BARS

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

3. 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

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

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

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

7. 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.

8. 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).

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

10. 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

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

12. 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:

13. 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

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

15. 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:

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

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

18. 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

19. 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

20. 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:

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

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

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

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

25. 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

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