1. Probabilistic Methods in Mobile Robotics

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

3. Bayes Formula

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

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

6. Normalization

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

8. Integrating a second Measurement... u New measurement s 2 u p(s 2 |open) = 0.5p(s 2 |  open) = 0.6 s 2 lowers the probability, that the door is open.

9. Where am I? + Mobile Robot Localization

10. Principle of Robot Localization

11. l L t : position of the robot at time t l Given: l Map and sensor model: l Motion model: l Initial state of the robot: l Data  Sensor information (sonar, laser range-finder, camera) o i  Odometry information a i Markov Localization as State Estimation (1)

12. Motion Model

13. Model for Proximity Sensors l The sensor is reflected either by a known or by an unknown obstacle : Laser sensor Sonar sensor

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

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 ARobot BRobot C