1. 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. 1 National Space Program Office, Hinchu, Taiwan, R.O.C 2 National Cheng Kung University, Tainan, Taiwan, R.O.C. 3 National Chiao-Tung University, Hsinchu, Taiwan, R.O.C

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

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

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

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

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

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)

16. The Homogeneous Transformation

17. (1)Earth-Centered-Earth-Fixed (ECEF), i.e., {e} (2)Camera coordinate,i.e., {c} (3)Body frame,i.e., {b} (4) [X C Y C Z C ] T : The target location expressed in {C} (5) b T C : Transformation between {b} and {c} (6) e T b : Transformation between {e} and {b} Note

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

19. UKF 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. Unscented Transformation (UT)

20. Nonlinear function The discrete time nonlinear transition equation

21. UT

22. Unscented Kalman Filter (UKF) 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.

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

24. UKF Time update equations (Prediction):

25. UKF Measurement update equations (Correction):

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

27. State Assignment Process (Dynamic) Model

28. Measurement (Sensor) Model

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

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

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

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

35. Outline  Introduction  Fundamental Concepts  Simulation Results  Conclusion

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

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

44. 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 1 Landmark 2 Landmark 3 Landmark 4

45. 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.

52. Case 3: UAV is moving. 282.843 m/s

53. Case 3: UAV is moving. 282.843 m/s At the beginning of the simulation, cluster-1 serves as landmarks.

54. Case 3: UAV is moving. 282.843 m/s Because the flight vehicle is gradually departing far away from the cluster-1, it will cause landmarks to displace out of the FOV, and even cause UKF to diverge;

55. Case 3: UAV is moving. 282.843 m/s so cluster-2 takes over after the 100 th iteration.

59. 150 m/s 20 m/s 0 m/s 200 m/s

60. 20 m/s 50 m/s 0 m/s

65. Outline  Introduction  Fundamental Concepts  Simulation Results  Conclusion

66. Conclusion A compact, unified formulation is made The use of UKF -- faster convergence rate, less dependent upon I.C., no linearization is ever needed Successful identification of larger angle maneuvering Target tracking can be implemented very easily

67. Thank you ！