Download - CSE-473 Project 2 Monte Carlo Localization
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CSE-473 Project 2
Monte Carlo Localization
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Localization as state estimation
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Markov Localization as State Estimation (2)
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Motion:
Perception:
… is optimal under the Markov assumption
)()|()( lBelloPlBel
')'()',|()( dllBellalPlBel
Kalman filters, Hidden Markov Models, DBN
Markov!
Markov!
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[Schiele et al. 94], [Weiß et al. 94], [Borenstein 96],
[Gutmann et al. 96, 98], [Arras 98]
Kalman Filters
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[Burgard et al. 96,98], [Fox et al. 99], [Konolige et al. 99]
Piecewise constant
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Represent density by random samples Estimation of non-Gaussian, nonlinear processes
Monte Carlo filter, Survival of the fittest, Condensation, Bootstrap filter, Particle filter
Filtering: [Handschin, 70], [Gordon et al., 93], [Kitagawa 96]
Computer vision: [Isard et al. 96, 98] DBN: [Kanazawa et al., 95]
Particle Filters
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Converges to true density
Sample-based Density Representation
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Importance Sampling
Weight samples: g
fw
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Sample-based Density Representation
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Sensor Information: Importance Sampling
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loPlBel
lBelloPw
lBelloPlBel
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'd)'()'|()( , llBellalPlBel
Robot Motion
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Sensor Information: Importance Sampling
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)()|(
)()|()(
loPlBel
lBelloPw
lBelloPlBel
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Robot Motion 'd)'()'|()( , llBellalPlBel
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Set of samples St = {<l1, p1>, … <lN, pN>} described by position l and weight p
Initialize sample set S0 according to prior knowledge
For each motion do: Sampling: Generate from each sample in St-1 a new sample according to
motion model
For each observation s do: Importance sampling: Re-weight each sample with the likelihood
Resampling: Draw N samples from sample set St according to their
likelihood
Monte Carlo Localization (SIR)
' ii ll
)|( ii lsPp
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Motion Model P(l | a, l’)
Model odometry error as Gaussian noise on and
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Motion Model P(l | a, l’)
Start
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Global Localization (sonar)
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Using Ceiling Maps for Localization
[Dellaert et al. 99]
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Vision-based Localization
P(z|x)
h(x)z
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Vision-based Localization
[CVPR-99]
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Comparison to Grid-based Markov Localization (2)
Office environment: 20,000 samples versus 150
million states
NMAH: Global localization in 15 seconds instead
of 4 minutes
Vision-based: Can track the position in situations
in which grid-based approach fails
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Condensation Tracking
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Mixed-State Tracking
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Tracking Multiple People