model adaptation in monte carlo localization omid aghazadeh

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SWAR Sept 8, 2009 © 2009 Omid Aghazadeh

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)

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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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Scatter of Particles vs time

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Error vs time

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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)

model adaptation in monte carlo localization omid aghazadeh

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