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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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 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 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 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



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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