Probabilistic Methods in Mobile Robotics

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

Bayes Formula

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)

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:

Normalization

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.

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.

Where am I? + Mobile Robot Localization

Principle of Robot Localization

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)

Motion Model

Model for Proximity Sensors l 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)

Grid-based Markov Localization Three-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 ARobot BRobot C