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SLAM with fleeting detections Fabrice LE BARS. SLAM with fleeting detections 30/04/2015- 2 Outline  Introduction  Problem formalization  CSP on tubes.

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Presentation on theme: "SLAM with fleeting detections Fabrice LE BARS. SLAM with fleeting detections 30/04/2015- 2 Outline  Introduction  Problem formalization  CSP on tubes."— Presentation transcript:

1 SLAM with fleeting detections Fabrice LE BARS

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

3 SLAM with fleeting detections 30/04/ 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/ Introduction  Experiments with Daurade and Redermor submarines with marks in the sea

5 SLAM with fleeting detections 30/04/ Problem formalization

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

7 SLAM with fleeting detections 30/04/ 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/ 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/ Problem formalization  Waterfall Example: lateral sonar image

10 SLAM with fleeting detections 30/04/ 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/ CSP on tubes

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

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

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

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

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

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

24 SLAM with fleeting detections 30/04/ Conclusion

25 SLAM with fleeting detections 30/04/ 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/ Questions?  Contacts


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