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Probabilistic Methods in Mobile Robotics

Probabilistic Methods in Mobile Robotics. Stereo cameras. Sonar. Tactiles. Infra-red. Laser range-finder. Sonar. Bayes Formula. A Simple Example: Estimating the state of a door. Suppose a robot obtaines measurement s What is p(Door=open|SensorMeasurement=s) ? Short form: p(open|s).

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Probabilistic Methods in Mobile Robotics

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  1. Probabilistic Methods in Mobile Robotics

  2. Stereo cameras Sonar Tactiles Infra-red Laser range-finder Sonar

  3. Bayes Formula

  4. A Simple Example: Estimating the state of a door • Suppose a robot obtaines measurement s • What is p(Door=open|SensorMeasurement=s)? • Short form: p(open|s)

  5. Causal vs. Diagnostic Reasoning • We’re interested in p(open|s) (called diagnostic reasoning) • Often causal knowledge like p(s|open) is easier to obtain. • From causal to diagnostic: Apply Bayes rule:

  6. Normalization

  7. Example • p(s|open) = 0.6 p(s|open) = 0.3 • p(open) = p(open) = 0.5 s raises the probability, that the door is open.

  8. Integrating a second Measurement ... • New measurement s2 • p(s2|open) = 0.5 p(s2|open) = 0.6 s2lowers the probability, that the door is open.

  9. Mobile Robot Localization + Where am I?

  10. Principle of Robot Localization

  11. Markov Localization as State Estimation (1) • Lt: position of the robot at time t • Given: • Map and sensor model: • Motion model: • Initial state of the robot: • Data • Sensor information (sonar, laser range-finder, camera) oi • Odometry information ai

  12. Motion Model

  13. Model for Proximity Sensors • The sensor is reflected either by a knownor by an unknown obstacle: Sonar sensor Laser sensor

  14. Markov Localization as State Estimation (2) Motion: Perception:… is optimal under the Markov assumption Kalman filters, Hidden Markov Models, DBN

  15. Grid-based Markov Localization Three-dimensional grid over the sate space of the robot:

  16. Localization Example (1)

  17. Localization Example

  18. Sample-based Density Representation D. Fox, Univ. of Washington

  19. Global Localization (sonar)

  20. Example Run Sonar

  21. Example Run Laser

  22. Localization for AIBO robots D. Fox, Univ. of Washington

  23. Localization for AIBO robots D. Fox, Univ. of Washington

  24. Mobile Robot Mapping

  25. Mapping the Allen Center: Raw Data

  26. Mapping the Allen Center

  27. Multi-robot Mapping Robot A Robot B Robot C

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