Probabilistic Methods in Mobile Robotics
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Transcript of Probabilistic Methods in Mobile Robotics
Probabilistic Methods inMobile Robotics
Stereo cameras
Infra-red
Sonar
Laser range-finder
Sonar
Tactiles
Bayes Formula
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Bp
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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:
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openpopenspsopenp
Normalization
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Example
p(s|open) = 0.6 p(s|open) = 0.3 p(open) = p(open) = 0.5
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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
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s2 lowers the probability, that the door is open.
Where am I?
+
Mobile Robot Localization
Principle of Robot Localization
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
Markov Localization as State Estimation (1)
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Motion Model )',|( 11 lLaAlLP ttt
Model for Proximity Sensors
The sensor is reflected either by a known or by an unknown obstacle:
Laser sensor Sonar sensor
Motion:
Perception:
… is optimal under the Markov assumption
Kalman filters, Hidden Markov Models, DBN
Markov Localization as State Estimation (2)
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Grid-based Markov LocalizationThree-dimensional grid over the sate space of the robot:
Localization Example (1)
Localization Example
Sample-based Density Representation
D. Fox, Univ. of Washington
Global Localization (sonar)
Example Run Sonar
Example Run Laser
Localization for AIBO robots
D. Fox, Univ. of Washington
Localization for AIBO robots
D. Fox, Univ. of Washington
Mobile Robot Mapping
Mapping the Allen Center: Raw Data
Mapping the Allen Center
Multi-robot Mapping
Robot A Robot B Robot C