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Complete Pose Determination for Low Altitude Unmanned Aerial Vehicle Using Stereo Vision

Complete Pose Determination for Low Altitude Unmanned Aerial Vehicle Using Stereo Vision. Luke K. Wang, Shan-Chih Hsieh, Eden C.-W. Hsueh 1 Fei-Bin Hsaio 2 , Kou-Yuan Huang 3. National Kaohsiung Univ. of Applied Sciences, Kaohsiung Taiwan, R.O.C.

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Complete Pose Determination for Low Altitude Unmanned Aerial Vehicle Using Stereo Vision

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  1. Complete Pose Determination for Low Altitude Unmanned Aerial Vehicle Using Stereo Vision Luke K. Wang, Shan-Chih Hsieh, Eden C.-W. Hsueh1 Fei-Bin Hsaio2, Kou-Yuan Huang3 National Kaohsiung Univ. of Applied Sciences, Kaohsiung Taiwan, R.O.C. 1National Space Program Office, Hinchu, Taiwan, R.O.C 2National Cheng Kung University, Tainan, Taiwan, R.O.C. 3National Chiao-Tung University, Hsinchu, Taiwan, R.O.C

  2. Outline • Introduction • Fundamental Concepts • Simulation Results • Conclusion

  3. Outline • Introduction • Fundamental Concepts • Simulation Results • Conclusion

  4. Introduction • Pose Estimation • Visual Motion Estimation • Kalman Filtering Technique • Unscented Kalman Filter vs. Extended Kalman Filter

  5. The schematics illustration of image-based navigation system

  6. CAMER (Right) CAMER (Left) IMAGE Feature Extraction Measurement & Process Error Initial State & Error Covariance UKF Estimated States

  7. What is needed ? Outline • Introduction • Fundamental Concepts • Simulation Results • Conclusion

  8. Fundamental Concepts • Quaternion • GPS Observation Equation • Perspective Projection • Coordinate Transformation • Unscented Kalman Filter (UKF)

  9. Quaternion The unit quaternion is defined by In matrix form the derivative of a quaternion may be written:

  10. If angular velocity is constant, equation is a system of first order linear time invariant differential equation with a closed-form solution where

  11. Fundamental Concepts • Quaternion • Perspective Projection • Coordinate Transformation • Unscented Kalman Filter (UKF)

  12. 3-D to 2-D Perspective Projection

  13. Fundamental Concepts • Quaternion • GPS Observation Equation • Perspective Projection • Coordinate Transformation • Unscented Kalman Filter (UKF)

  14. The Homogeneous Transformation

  15. The Homogeneous Transformation Note • (1)Earth-Centered-Earth-Fixed (ECEF), i.e., {e} • (2)Camera coordinate ,i.e., {c} • (3)Body frame ,i.e., {b} • (4) [XCYCZC]T : The target location expressed in {C} • (5) bTC : Transformation between {b} and {c} • (6) eTb : Transformation between {e} and {b}

  16. Fundamental Concepts • Quaternion • GPS Observation Equation • Perspective Projection • Coordinate Transformation • Unscented Kalman Filter (UKF)

  17. UKF Unscented Transformation (UT) • The UT is a method for calculating the statistics of a random variable which undergoes a nonlinear transformation [Julier et al., 1995]. • A L dimensional random vector having mean and covariance , and propagates through an arbitrary nonlinear function. • The unscented transform creates 2L+1 sigma vectors and weights W.

  18. Nonlinear function The discrete time nonlinear transition equation

  19. UT

  20. UKF Unscented Kalman Filter (UKF) • The UKF is an extension of UT to the Kalman Filter frame, and it uses the UT to implement the transformations for both TU and MU [Julier et al., 1995]. • None of any linearization procedure is taken. • Drawback of UKF -- computational complexity, same order as the EKF.

  21. UKF Time update equations (Prediction): Measurement update equations (Correction):

  22. UKF Time update equations (Prediction):

  23. UKF Measurement update equations (Correction):

  24. State Assignment Process (Dynamic) Model Measurement (Sensor) Model

  25. State Assignment Process (Dynamic) Model

  26. Measurement (Sensor) Model

  27. Measurement (Sensor) Model

  28. Standard UKF Quaternion prediction block diagram MU: Measurement Update

  29. ? Modified UKF Quaternion prediction block diagram MU: Measurement Update

  30. When the instantaneous angular rate is assumed constant, the quaternion differential equation has a closed- form solution

  31. Modified UKF ok Quaternion prediction block diagram MU: Measurement Update

  32. Outline • Introduction • Fundamental Concepts • Simulation Results • Conclusion

  33. Case 1: Four image marks are distributed evenly around the optical axis. Landmark 3 Landmark 4 Landmark 2 Landmark 1

  34. Notice that a rotation of at sampling instant 32.

  35. Notice that a rotation of at sampling instant 32.

  36. Notice that a rotation of at sampling instant 32.

  37. Notice that a rotation of at sampling instant 32.

  38. Notice that a rotation of at sampling instant 32.

  39. Notice that a rotation of at sampling instant 32.

  40. Case 2:Four image marks are initially distributed around the optical axis, but after 100 iterations, an image mark among them is gradually traveling away from the optical axis. Landmark 3 Landmark 4 Landmark 2 Landmark 1

  41. Case 2:Four image marks are initially distributed around the optical axis, but after 100 iterations, an image mark among them is gradually traveling far away from the optical axis.

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