Post on 18-Jan-2016
transcript
CSE-473 Project 2
Monte Carlo Localization
Localization as state estimation
Markov Localization as State Estimation (2)
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Motion:
Perception:
… is optimal under the Markov assumption
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Kalman filters, Hidden Markov Models, DBN
Markov!
Markov!
[Schiele et al. 94], [Weiß et al. 94], [Borenstein 96],
[Gutmann et al. 96, 98], [Arras 98]
Kalman Filters
[Burgard et al. 96,98], [Fox et al. 99], [Konolige et al. 99]
Piecewise constant
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
Converges to true density
Sample-based Density Representation
Importance Sampling
Weight samples: g
fw
Sample-based Density Representation
Sensor Information: Importance Sampling
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Robot Motion
Sensor Information: Importance Sampling
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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)
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Motion Model P(l | a, l’)
Model odometry error as Gaussian noise on and
Motion Model P(l | a, l’)
Start
Global Localization (sonar)
Using Ceiling Maps for Localization
[Dellaert et al. 99]
Vision-based Localization
P(z|x)
h(x)z
Vision-based Localization
[CVPR-99]
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
Condensation Tracking
Mixed-State Tracking
Tracking Multiple People