SLAM with fleeting detections

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# SLAM with fleeting detections - PowerPoint PPT Presentation

SLAM with fleeting detections. Fabrice LE BARS. Outline. Introduction Problem formalization CSP on tubes Contraction of the visibility relation Conclusion. Introduction. Context: Offline SLAM for submarine robots Fleeting detections of marks Static and punctual marks

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## SLAM with fleeting detections

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Presentation Transcript
1. SLAM with fleeting detections Fabrice LE BARS

2. Outline • Introduction • Problem formalization • CSP on tubes • Contraction of the visibility relation • Conclusion

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. Introduction Experiments with Daurade and Redermor submarines with marks in the sea

5. Problem formalization

6. Problem formalization Equations

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. Problem formalization Waterfall is a function that associates to a time a subset is called the waterfall (from the lateral sonar community).

9. Problem formalization Waterfall Example: lateral sonar image

10. Problem formalization Waterfall On a waterfall, we do not detect marks, we get areas where we are sure there are no marks

11. CSP on tubes

12. CSP on tubes • CSP • Variables are trajectories (temporal functions) , and real vector • Domains are interval trajectories (tubes) , and box • Constraints are:

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. CSP on tubes • Tubes • The integral of a tube can be defined as: • We have also:

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. CSP on tubes • Tubes • Contractions with tubes: e.g. increasing function constraint

17. Contraction of the visibility relation

18. Contraction of the visibility relation • Problem: contract tubes , with respect to a relation: • 2 theorems: 1 to contract and the other for

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. Contraction of the visibility relation • Example 1 • is at • Telemeter accuracy is , scope is • Visibility function and observation function are:

21. Contraction of the visibility relation • Example 1 • We have: which translates to: with:

22. Contraction of the visibility relation • Example 1: contraction of • Example 1

23. Contraction of the visibility relation • Example 2: contraction of

24. Conclusion

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. Questions? • Contacts • fabrice.le_bars@ensta-bretagne.fr