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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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Presentation Transcript
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
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