© sebastian thrun, CMU, 2000 1

CS226 Statistical Techniques In Robotics

Sebastian Thrun (Instructor) and Josh Bao (TA)

http://robots.stanford.edu/cs226Office: Gates 154, Office hours: Monday 1:30-3pm

© sebastian thrun, CMU, 2000 2

Warm-Up Assignment: Localization,Due Sept 23

© sebastian thrun, CMU, 2000 3

Warm-Up Assignment: Localization

© sebastian thrun, CMU, 2000 4

Warm-Up Assignment: Localization

© sebastian thrun, CMU, 2000 5

© sebastian thrun, CMU, 2000 6

Bayes Filtersx = stated = datam = mapt = timez = observationu = control),|( 0 mdxp tt

[Kalman 60, Rabiner 85]

1011011 ),,,|(),,,,|(),|( tttttttt dxmzuxpmzuxxpmxzp

),,,,|(),,,,,|( 011011 mzzuxpmzzuxzp ttttttt Bayes

),,,,|(),|( 011 mzzuxpmxzp ttttt Markov

110111 ),|(),|(),|( tttttttt dxmdxpuxxpmxzp

Markov1021111 ),,,|(),|(),|( ttttttttt dxmzuzxpuxxpmxzp

),,,,,|( 011 mzzuzxp tttt

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Nature of Odometry Data

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Probabilistic Kinematics

map m

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Nature of Sensor Data

© sebastian thrun, CMU, 2000 10

laser data p(o|s,m)

Probabilistic Range Sensing

© sebastian thrun, CMU, 2000 11

Posterior Probability (Single Scan)

p(o|s,m)observation o

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Grid Approximations

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Markov Localizationin Grid Map

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Monte Carlo Localization

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Sample Approximations

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Monte Carlo Localization, cont’d