Robust Monte Carlo Localization for Mobile Robots

1
Robust Monte Carlo Localization for Mobile Robots

• Sebastian Thrun
• Dieter Fox
• Wolfram Burgard
• Frank Dellaert

2
Problem

• Localization of mobile robots with uncertain
  sensors
• Uncertain starting position
• Kidnapped robot
• We know the layout of the world

3
Problems Illustrated
4
Previous Work

• Kalman Filters
• Markov Localization

5
One Solution Monte Carlo

• Particle based solution
• Particles represent the distribution over our
  poses

6
How do we represent the distribution?

• Explicitly difficult at best
• Markov assumption
• Implicitly cloud of particles is the
  distribution

7
Predict and Correct
8
Algorithm Step 1

• Start off with a uniform distribution over the
  set of poses.

9
Algorithm Step 2

• Weight each of the particles according to
• Normalize weights so they sum to 1

10
Algorithm Step 3

• Select a particle according to the weighted
  distribution and generate a new particle based on
  p(xx,a). Do this n times.

11
Algorithm Conclusion

• After robot moves into room

12
Also for Object Localization
13
A Problem

• Sensors with very little noise can cause MCL to
  perform poorly or fail
• If particles not generated near actual position,
  robot may falsely localize in another position
  and never recover.

14
Another Problem

• MCL is unable to recover from the kidnapped robot
  problem
• Particle distribution has already localized
  elsewhere, and particles will never generate in
  new position.

15
What to do, what to do?

• To overcome this, add particles uniformly
• Or, assume that sensors have more noise than they
  really do

16
The Dual of MCL

• The techniques used to augment MCL are not
  mathematically sound. How can we fix MCL the
  Right Way?
• Base the distribution on the observations
• Base weights on the probability that a previous
  position distribution (x) and our observed
  action (a) brought us to the new distribution

17
Correct-Predict
18
Algorithm for Dual of MCL

• Generate random x according to p(xo)
• Generate random x according to p(xa, x)
• Assign weight w Bel(x) where Bel is the
  belief
• Add to the distribution particle x with weight w

19
Whats wrong with Dual?

• Doesnt include any knowledge of previous
  location.
• Degrades rapidly with poor sensor performance.

20
OK, so how do we fix THAT?

• Strength of Dual-MCL and MCL compliment each
  other mix them!
• Mixture MCL
• Assign a mixing ratio r, such that n(1-r) samples
  are generated by MCL and nr samples by Dual-MCL.
  
• r .1

21
What happens?
22
What happens?
23
How does it compare to hacks
24
Kidnapping Problem
25
Overview
26
Overview

• Modeled with MCL
• Improved (mathematically) with Dual
• Robust solution Mixture MCL
• Proven to work in Smithsonian with Minerva, CMUs
  tour guide robot.

27
Sequential Monte Carlo Animation