Model Adaptation in Monte Carlo Localization Omid Aghazadeh
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Model Adaptation in Monte Carlo Localization
Omid Aghazadeh
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OutlineThe localization problem & localization methodsThe Particle FilterContribution: Model adaptation for Particle FilterConclusions
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Localization Problem
Determining the pose of the robot relative to a given map of the environment using sensory information → pdf
Original Figure from Probabilistic Robotics, Thrun et Al, MIT Press
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Localization Problemcont'd
Varying degrees of uncertainty due to measurement errors, model errors, unknown associations and etc make the localization problem challengingLocalization
Local(Position Tracking): We know the pose of the robot at the very first step Global: We just turned on the system and need to find where we are
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Multi modal distributions
global localization, (unknown) data association → Multi modal distribution
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Multi modal distributions, cont’d
Multiple observations narrow down the hypothesis space, but does not solve multi modality
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Localization Methods
Bayes Filter + 1st order Markov assumption:
ContinuousEKF Localization
cannot deal with multi modal distributions
Discrete: can deal with multi modalityGrid based
Accuracy Waste of resources
Particle Filters
dxmzuxxpmuxxpmxzpmzuxxp ttttttttttttt ),,,|(),,|(),|(),,,|( 112111
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Particle Filter
The particle filter’s elegant solution: use samples to represent the pdf
NiwxzpwxS it
itt
it
itt ,...,1},)|(,{ 1
Original Figure from Probabilistic Robotics, Thrun et Al, MIT Press
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Particle Filter, cont’d
Re-SamplingSurvival of the particles with more weights
PredictionMoving particle set using Diffusion →(Process Noise Model)
WeightingLikelihood using Sensor ModelVery high likelihood for a few particles leads to particle deprivation →(Measurement Noise Model)
tu
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Problems with the standard particle filter
How many samples(particles) to use? → KLD Sampling(Fox 2006)How to define process and measurement noise models?
Constant: can be too low (→ divergence) or too high( → loss of accuracy)Adaptive: contribution of this presentation
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KLD Sampling
The number of particles we need depends on how scattered the particles areQuantize the state-space and count the bins which contain at least one particle (k)The optimal number of particles follows a chi squared distribution with k-1 degrees of freedom
21,12
1
kn
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Model Adaptation
When do we need more diffusion? →(Process noise model)When is it better to have sharp likelihood distribution? →(Measurement noise model)
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Model Adaptation , cont’d
We need to have sharper likelihoods if the distribution is compact
We need weaker diffusion when the particles are accurately representing the desired distribution
Sensor model alteration/adaptation
))(()( tft qQ
))(),(()( tktnft rR
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Experiments
Standard KLD vs Adaptive KLD in tracking problems(uni-modal). Process and Observation noise models adapted, sensor model altered.
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Experiments, cont’d
Number of particles vs time
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Experiments, cont’d
Scatter of Particles vs time
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Experiments, cont’d
Error vs time
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Experiments, cont’d
Adapted Model Parameters vs time(PWO)
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Conclusions
Model adaptation can improve KLD sampling method in terms of
Accuracy(mean of the distribution)Certainty(spread of the distribution)Required resources(memory)Computations(run time)Particle Deprivation(multi hypothesis)