Model Adaptation in Monte Carlo Localization Omid Aghazadeh

1. Model Adaptation in Monte Carlo Localization Omid Aghazadeh

2. Outline • The localization problem & localization methods • The Particle Filter • Contribution: Model adaptation for Particle Filter • Conclusions

3. 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

4. Localization Problemcont'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

5. Multi modal distributions • global localization, (unknown) data association → Multi modal distribution

6. Multi modal distributions, cont’d • Multiple observations narrow down the hypothesis space, but does not solve multi modality

7. Localization Methods • Bayes Filter + 1st 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

8. Particle Filter • The particle filter’s elegant solution: use samples to represent the pdf Original Figure from Probabilistic Robotics, Thrun et Al, MIT Press

9. 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)

10. 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

11. 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

12. Model Adaptation • When do we need more diffusion? →(Process noise model) • When is it better to have sharp likelihood distribution? →(Measurement noise model)

13. 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

14. Experiments • Standard KLD vs Adaptive KLD in tracking problems(uni-modal). Process and Observation noise models adapted, sensor model altered.

15. Experiments, cont’d • Number of particles vs time

16. Experiments, cont’d • Scatter of Particles vs time

17. Experiments, cont’d • Error vs time

18. Experiments, cont’d • Adapted Model Parameters vs time(PWO)

19. 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)