1 / 61

Probabilistic Robotics

Probabilistic Robotics. Bayes Filter Implementations Particle filters. Sample-based Localization (sonar). Importance Sampling. Weight samples: w = f / g. Distributions. Distributions. Wanted: samples distributed according to p(x| z 1 , z 2 , z 3 ). This is Easy!.

osbourne-olsen
Download Presentation

Probabilistic Robotics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Probabilistic Robotics Bayes Filter Implementations Particle filters

  2. Sample-based Localization (sonar)

  3. Importance Sampling Weight samples: w = f / g

  4. Distributions

  5. Distributions Wanted: samples distributed according to p(x| z1, z2, z3)

  6. This is Easy! We can draw samples from p(x|zl) by adding noise to the detection parameters.

  7. Importance Sampling with Resampling

  8. Importance Sampling with Resampling Weighted samples After resampling

  9. Particle Filters

  10. Sensor Information: Importance Sampling

  11. Robot Motion

  12. Sensor Information: Importance Sampling

  13. Robot Motion

  14. Particle Filter Algorithm • Algorithm particle_filter( St-1, ut-1 zt): • For Generate new samples • Sample index j(i) from the discrete distribution given by wt-1 • Sample from using and • Compute importance weight • Update normalization factor • Insert • For • Normalize weights

  15. draw xit-1from Bel(xt-1) draw xitfrom p(xt | xit-1,ut-1) Importance factor for xit: Particle Filter Algorithm

  16. Resampling • Given: Set S of weighted samples. • Wanted : Random sample, where the probability of drawing xi is given by wi. • Typically done n times with replacement to generate new sample set S’.

  17. w1 wn w2 Wn-1 w1 wn w2 Wn-1 w3 w3 Resampling Implementation • Stochastic universal sampling • Systematic resampling • Linear time complexity • Easy to implement, low variance • Roulette wheel • Binary search, n log n

  18. Resampling Algorithm • Algorithm systematic_resampling(S,n): • For Generate cdf • Initialize threshold • For Draw samples … • While ( ) Skip until next threshold reached • Insert • Increment threshold • ReturnS’ Also called stochastic universal sampling

  19. Motion Model Reminder Start

  20. Proximity Sensor Model Reminder Sonar sensor Laser sensor

  21. Sample-based Localization (sonar)

  22. Initial Distribution

  23. After Incorporating Ten Ultrasound Scans

  24. After Incorporating 65 Ultrasound Scans

  25. Estimated Path

  26. Using Ceiling Maps for Localization

  27. P(z|x) z h(x) Vision-based Localization

  28. Under a Light Measurement z: P(z|x):

  29. Next to a Light Measurement z: P(z|x):

  30. Elsewhere Measurement z: P(z|x):

  31. Global Localization Using Vision

  32. Application: Rhino and Albert Synchronized in Munich and Bonn [Robotics And Automation Magazine, to appear]

More Related