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Kalman filter and SLAM problem

Kalman filter and SLAM problem. 2005. 8. 5 Young Ki Baik Computer Vision Lab. Seoul National University. Contents. References Kalman filter SLAM problem Example (2D circular motion) Demo Conclusion and future work. References. An Introduction to the Kalman Filter

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Kalman filter and SLAM problem

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  1. Kalman filter and SLAM problem 2005. 8. 5 Young Ki Baik Computer Vision Lab. Seoul National University

  2. Contents • References • Kalman filter • SLAM problem • Example (2D circular motion) • Demo • Conclusion and future work

  3. References • An Introduction to the Kalman Filter • G. Welch and G. Bishop (SIGGRAPH 2001) • A Solution to the Simultaneous Localization and Map Building (SLAM) problem • Gamini Dissanayake. Et. Al. (IEEE Trans. Robotics and Automation 2001) • Lessons in Estimation Theory for Signal Processing, Communications and Control • Jerry M. Mendel (1995)

  4. Kalman filter • What is a Kalman filter? • Mathematical power tool • Optimal recursive data processing algorithm • Noise effect minimization • Applications • Tracking (head, hands etc.) • Lip motion from video sequences of speakers • Fitting spline • Navigation • Lot’s of computer vision problem

  5. Kalman filter • Example Sensor noise Measurement error Landmark Kalman filter How can we obtain optimal pose of robot and landmark simultaneously? Real location Robot Location with error Refined location Movement noise Localizing error (Processing error)

  6. Kalman filter • Example (Simple Gaussian form) • Assumption • All error form Gaussian noise • Estimated value • Measurement value

  7. Kalman filter • Example (Simple Gaussian form) • Optimal variance • Optimal mean Innovation Kalman gain

  8. Kalman filter • Example (Overall process) • Prediction • Update

  9. SLAM • What is SLAM problem? • Can we do localization and mapping simultaneously? • If we have the solution to the SLAM problem… • Allow robots to operate in an environment without a priori knowledge of a map • Open up a vast range of potential application for autonomous vehicles and robot • Kalman filter based approach • Research over the last decade has shown that SLAM is indeed possible

  10. SLAM • Kalman filter and SLAM problem • Extended Kalman filter form for SLAM • Prediction • Observation • Update : Previous value : Input and measure : Function : Computed value

  11. Implementation • Example (2D circular motion) • x, z, L • x : Position and direction of robot and L • z : Distance and angle from robot point of view • L : Landmark position • Setting of x and P

  12. Implementation • Example (2D circular motion) • Initial x and P • Setting of x and P with landmark 3x1 3x3 5x1 5x5

  13. Implementation • Example (2D circular motion) • Control input : 2d position and direction : Velocity and angular velocity : time (constant) : Circular motion with radius 25

  14. Implementation • Example (2D circular motion) • Real motion : Zero mean unit variance Gaussian random value : Control error for velocity : Control error for angular velocity White line : Control input motion Pink line : Real motion Large circle : robot

  15. Implementation • Example (2D circular motion) • Predicted and measured information of land mark • Prediction • Measurement : Position of i-th landmark (x,y) : Distance and angle (d, ) from a robot point of view r Range r = 20.0 sensor

  16. Implementation • Example (2D circular motion) • Jacobian matrix for F

  17. Implementation • Example (2D circular motion) • Jacobian matrix for H

  18. Implementation • Example (2D circular motion) • Error covariant matrix • Covariant matrix of control error • Covariant matrix of measurement error : Control error for velocity : Control error for angular velocity : measurement error for distance : Measurement error for angle

  19. Implementation • Kalman filter and SLAM problem • Extended Kalman filter form for SLAM • Prediction • Observation • Update : Previous value : Input and measure : Function : Computed value

  20. Implementation • Demo Large Circle(white, pink, yellow) : robot White line : control input path Pink line : real path Small white circle : Real landmark Yellow line : Estimated path (EKF) Large light blue circle : Detected (and estimated) landmark Blue ellipse : Uncertainty boundary

  21. Conclusion • Conclusion • Simple example and demo • Possibility of solution for SLAM problem using EKF • In the limit of successive observations, the error in estimated position of landmarks become fully correlated. • Future work • Considering closing loop and kidnapping problem • Applying EKF to general structure (robot) using vision sensor

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