Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Model Adaptation in Monte Carlo Localization Omid Aghazadeh

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Outline The localization problem & localization methods The Particle Filter Contribution: Model adaptation for Particle Filter Conclusions

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh 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

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Localization Problem cont'd Varying degrees of uncertainty due to measurement errors, model errors, unknown associations and etc make the localization problem challenging Localization 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

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Multi modal distributions global localization, (unknown) data association → Multi modal distribution

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Multi modal distributions, cont’d Multiple observations narrow down the hypothesis space, but does not solve multi modality

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Localization Methods Bayes Filter + 1 st order Markov assumption: Continuous EKF Localization cannot deal with multi modal distributions Discrete: can deal with multi modality Grid based Accuracy  Waste of resources Particle Filters

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Particle Filter The particle filter’s elegant solution: use samples to represent the pdf Original Figure from Probabilistic Robotics, Thrun et Al, MIT Press

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Particle Filter, cont’d Re-Sampling Survival of the particles with more weights Prediction Moving particle set using Diffusion → (Process Noise Model) Weighting Likelihood using Sensor Model Very high likelihood for a few particles leads to particle deprivation → (Measurement Noise Model)

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh 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

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh KLD Sampling The number of particles we need depends on how scattered the particles are Quantize 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

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Model Adaptation When do we need more diffusion? → (Process noise model) When is it better to have sharp likelihood distribution? → (Measurement noise model)

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh 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

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Experiments Standard KLD vs Adaptive KLD in tracking problems(uni-modal). Process and Observation noise models adapted, sensor model altered.

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Experiments, cont’d Number of particles vs time

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Experiments, cont’d Scatter of Particles vs time

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Experiments, cont’d Error vs time

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh Experiments, cont’d Adapted Model Parameters vs time(PWO)

Centre for Autonomous Systems SWAR Sept 8, 2009 © 2009 Omid Aghazadeh 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)