1. Particle filters for Robot Localization
An implementation of Bayes Filtering
Markov Localization

2. Monte Carlo Localization
Repeated
Random
Sampling

3. Particle Filters Idea: Represent belief by random samples
Estimation of non-Gaussian, nonlinear processes
Monte Carlo filter, Survival of the fittest, Condensation, Bootstrap filter, Particle filter

4. MC Localization Start with lots of random samples (aka particles)
Weight each with probability based on sensor reading.

5. MC Localization Given an action a,
Use importance weighting to select from the old particles
Probabilistically create new particle given action and motion model

6. Adaptive Monte Carlo Localization
often abbreviated AMCL

7. Particle Filters

8. Sensor Information: Importance Sampling

9. Robot Motion

10. Sensor Information: Importance Sampling

11. Robot Motion

12. Particle Filter Algorithm
Sample the next generation for particles using the proposal distribution
Compute the importance weights :
weight = target distribution / proposal distribution
Resampling: "Replace unlikely samples by more likely ones"

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

15. 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’.

16. Resampling Stochastic universal sampling Systematic resamplingw2 w3 w1 wn
Wn-1 w2 w3 w1 wn
Wn-1
Stochastic universal sampling
Systematic resampling
Linear time complexity
Easy to implement, low variance
Roulette wheel
Binary search, n log n

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

19. Motion Model Reminder
Start

20. Proximity Sensor Model Reminder
Sonar sensor
Laser sensor

37. Sample-based Localization (sonar)

38. Initial Distribution

39. After Incorporating Ten Ultrasound Scans

40. After Incorporating 65 Ultrasound Scans

41. Estimated Path

42. Mobile Robot Localization
Each particle is a potential pose of the robot
Proposal distribution is the motion model of the robot (prediction step)
The observation model is used to compute the importance weight (correction step)