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SLAM with Fleeting Detections by Fabrice Le Bars: Contraction of Visibility Relation

Explore offline SLAM for submarine robots with fleeting detections of marks, problem formalization using CSP on tubes, contracting visibility relation. Learn about experiments, equations, and examples. Discover how to use tubes and intervals efficiently in solving the SLAM problem.

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SLAM with Fleeting Detections by Fabrice Le Bars: Contraction of Visibility Relation

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  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

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