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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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**Probabilistic Methods in**Mobile Robotics**Stereo cameras**Sonar Tactiles Infra-red Laser range-finder Sonar**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)**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:**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.**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.**Mobile Robot Localization**+ Where am I?**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**Model for Proximity Sensors**• The sensor is reflected either by a knownor by an unknown obstacle: Sonar sensor Laser sensor**Markov Localization as State Estimation (2)**Motion: Perception:… is optimal under the Markov assumption Kalman filters, Hidden Markov Models, DBN**Grid-based Markov Localization**Three-dimensional grid over the sate space of the robot:**Sample-based Density Representation**D. Fox, Univ. of Washington**Localization for AIBO robots**D. Fox, Univ. of Washington**Localization for AIBO robots**D. Fox, Univ. of Washington**Multi-robot Mapping**Robot A Robot B Robot C

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