SLAM with fleeting detections
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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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Slam with fleeting detections

SLAM with fleeting detections

Fabrice LE BARS


Outline

Outline

  • Introduction

  • Problem formalization

  • CSP on tubes

  • Contraction of the visibility relation

  • Conclusion


Introduction

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


Introduction1

Introduction

Experiments with Daurade and Redermor submarines with marks in the sea


Problem formalization

Problem formalization


Problem formalization1

Problem formalization

Equations


Problem formalization2

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.


Problem formalization3

Problem formalization

Waterfall

is a function that associates to a time a subset

is called the waterfall (from the lateral sonar community).


Problem formalization4

Problem formalization

Waterfall

Example: lateral sonar image


Problem formalization5

Problem formalization

Waterfall

On a waterfall, we do not detect marks, we get areas where we are sure there are no marks


Csp on tubes

CSP on tubes


Csp on tubes1

CSP on tubes

  • CSP

    • Variables are trajectories (temporal functions) , and real vector

    • Domains are interval trajectories (tubes) , and box

    • Constraints are:


Csp on tubes2

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


Csp on tubes3

CSP on tubes

  • Tubes

    • The integral of a tube can be defined as:

    • We have also:


Csp on tubes4

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:


Csp on tubes5

CSP on tubes

  • Tubes

    • Contractions with tubes: e.g. increasing function constraint


Contraction of the visibility relation

Contraction of the visibility relation


Contraction of the visibility relation1

Contraction of the visibility relation

  • Problem: contract tubes , with respect to a relation:

  • 2 theorems: 1 to contract and the other for


Contraction of the visibility relation2

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


Contraction of the visibility relation3

Contraction of the visibility relation

  • Example 1

    • is at

    • Telemeter accuracy is , scope is

    • Visibility function and observation function are:


Contraction of the visibility relation4

Contraction of the visibility relation

  • Example 1

    • We have:

      which translates to:

      with:


Contraction of the visibility relation5

Contraction of the visibility relation

  • Example 1: contraction of

  • Example 1


Contraction of the visibility relation6

Contraction of the visibility relation

  • Example 2: contraction of


Conclusion

Conclusion


Conclusion1

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


Questions

Questions?

  • Contacts

    • [email protected]


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