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Understanding Bayes Filter in Robotics: A Comprehensive Overview

Explore the core concepts of the Bayes Filter and related models, including state estimation, prediction and correction steps, motion and observation models, and different realizations. Learn about probabilistic motion models, odometry-based and velocity-based models, sensor models for laser scanners, and landmark perception using range-bearing sensors. This introduction covers the key principles and techniques essential for state estimation in robotic systems. Dive into this framework for recursive state estimation and its applications in mobile robotics.

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Understanding Bayes Filter in Robotics: A Comprehensive Overview

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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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