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Robot Mapping

Robot Mapping. A Short Introduction to the B a y es Filter and R ela t ed M od els. Cyrill Stachniss. 1. State Estimation.  Estimate the state of a system given observations and controls  Goal:. 2. R ecursive B a y es Filter 1. Definition of the belief. 3.

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Robot Mapping

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  1. RobotMapping A Short Introduction to the Bayes Filter and Related Models CyrillStachniss 1

  2. StateEstimation Estimatethe state of a systemgiven observations andcontrols Goal: 2

  3. Recursive Bayes Filter 1 Definition of thebelief 3

  4. Recursive Bayes Filter 2 Bayes’rule 4

  5. Recursive Bayes Filter 3 Markovassumption 5

  6. Recursive Bayes Filter 4 Law of totalprobability 6

  7. Recursive Bayes Filter 5 Markovassumption 7

  8. Recursive Bayes Filter 6 Markovassumption 8

  9. Recursive Bayes Filter 7 Recursiveterm 9

  10. Definition of Belief

  11. More Definitions

  12. Prediction and Correction Step Bayesfiltercan bewritten as atwo stepprocess Prediction step Correctionstep

  13. Motion and Observation Model Prediction step motionmodel Correction step sensor or observationmodel

  14. DifferentRealizations The Bayes filter is a framework for recursive stateestimation There are differentrealizations Differentproperties Linear vs. non-linear models for motion and observationmodels Gaussian distributionsonly? Parametric vs. non-parametricfilters …

  15. In thisCourse Kalmanfilter & friends Gaussians Linear or linearizedmodels Particlefilter Non-parametric Arbitrary models (samplingrequired)

  16. MotionModel

  17. Robot MotionModels Robotmotion is inherentlyuncertain Howcan we model thisuncertainty?

  18. Probabilistic Motion Models Specifies a posterior probability that actionu carries the robotfrom x to x’.

  19. TypicalMotion Models In practice, one often finds two types ofmotion models: Odometry-based Velocity-based Odometry-based models for systems thatare equippedwithwheel encoders Velocity-basedwhen no wheel encodersare available

  20. OdometryModel Robot movesfrom Odometryinformation to .

  21. Probability Distribution Noise in odometry Example: Gaussian noise

  22. Examples(Odometry-Based)

  23. Velocity-Based Model -90

  24. Motion Equation Robot movesfrom Velocityinformation to .

  25. Problem of theVelocity-Based Model Robot moves on a circle The circle constrains the finalorientation Fix: introduce an additional noise term on the final orientation

  26. Motion Including 3rdParameter Term to account for the finalrotation

  27. Examples (Velocity-Based)

  28. SensorModel

  29. Model for Laser Scanners Scanz consistsofK measurements. Individual measurements are independentgiven the robotposition

  30. Beam-EndpointModel

  31. Beam-EndpointModel map likelihoodfield

  32. Ray-castModel Ray-cast model considers the first obstacle longthe line ofsight Mixture of four models

  33. Model for Perceiving Landmarks with Range-Bearing Sensors Range-bearing Robot’s pose Observation of feature j at location

  34. Summary Bayes filter is a framework for state estimation Motion and sensormodel are the central modelsin the Bayesfilter Standardmodels for robotmotion and laser-based rangesensing

  35. Literature On the Bayesfilter Thrun et al. “Probabilistic Robotics”, Chapter 2 Course: Introduction to Mobile Robotics, Chapter 5 On motion and observationmodels Thrun et al. “Probabilistic Robotics”, Chapters 5 &6 Course: Introduction to Mobile Robotics, Chapters 6 &7

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