Advertisement

Estimation of Homography Dynamics on the Special Linear Group

  • Ezio Malis
  • Tarek Hamel
  • Robert Mahony
  • Pascal Morin
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 401)

Abstract

During the last decade, a number of highly successful visual servo control and real-time image processing algorithms have been proposed that use the homography between images of a planar scene as the primary measurement. The performance of the algorithms depends directly on the quality of the homography estimates obtained, and these estimates must be computed in real-time. In this chapter, we exploit the special linear Lie group structure of the set of all homographies to develop an on-line dynamic observer that provides smoothed estimates of a sequence of homographies and their relative velocities. The proposed observer is easy to implement and computationally undemanding. Furthermore, it is straightforward to tune the observer gains and excellent results are obtained for test sequences of simulation and real-world data.

Keywords

Visual Tracking Visual Servo Special Linear Group Nonlinear Observer Homography Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Benhimane, S., Malis, E.: Homography-based 2d visual tracking and servoing. International Journal of Robotic Research 26(7), 661–676 (2007)CrossRefGoogle Scholar
  2. 2.
    Benhimane, S., Malis, E., Rives, P., Azinheira, J.R.: Vision-based control for car platooning using homography decomposition. In: IEEE Conf. on Robotics and Automation, pp. 2173–2178 (2005)Google Scholar
  3. 3.
    Bonnabel, S., Martin, P., Rouchon, P.: Non-linear observer on lie groups for left-invariant dynamics with right-left equivariant output. In: IFAC World Congress, pp. 8594–8598 (2008)Google Scholar
  4. 4.
    Bonnabel, S., Martin, P., Rouchon, P.: Symmetry-preserving observers. IEEE Trans. on Automatic Control 53(11), 2514–2526 (2008)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Bonnabel, S., Rouchon, P.: Invariant Observers. In: Bonnabel, S., Rouchon, P. (eds.) Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems. LNCIS, pp. 53–67. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Chaumette, F., Hutchinson, S.: Visual servo control, part ii: Advanced approaches. IEEE Robotics and Automation Magazine 14(1), 109–118 (2007)CrossRefGoogle Scholar
  7. 7.
    Deguchi, K.: Optimal motion control for image-based visual servoing by decoupling translation and rotation. In: IEEE/RSJ Conf. on Intelligent Robots and Systems, pp. 705–711 (1998)Google Scholar
  8. 8.
    Fang, Y., Dixon, W., Dawson, D., Chawda, P.: Homography-based visual servoing of wheeled mobile robots. IEEE Trans. on Systems, Man, and Cybernetics - Part B 35(5), 1041–1050 (2005)CrossRefGoogle Scholar
  9. 9.
    Faugeras, O., Lustman, F.: Motion and structure from motion in a piecewise planar environment. International Journal of Pattern Recognition and Artificial Intelligence 2(3), 485–508 (1988)CrossRefGoogle Scholar
  10. 10.
    Hamel, T., Mahony, R.: Attitude estimation on SO(3) based on direct inertial measurements. In: IEEE Conf. on Robotics and Automation, pp. 2170–2175 (2006)Google Scholar
  11. 11.
    Hashimoto, K.: Visual Servoing: Real Time Control of Robot manipulators based on visual sensory feedback. World Scientific Series in Robotics and Automated Systems, vol. 7. World Scientific Press, Singapore (1993)Google Scholar
  12. 12.
    Hutchinson, S., Hager, G.D., Corke, P.I.: A tutorial on visual servo control. IEEE Trans. on Robotics and Automation 12(5), 651–670 (1996)CrossRefGoogle Scholar
  13. 13.
    Lageman, C., Mahony, R., Trumpf, J.: State observers for invariant dynamics on a lie group. In: Conf. on the Mathematical Theory of Networks and Systems (2008)Google Scholar
  14. 14.
    Lageman, C., Mahony, R., Trumpf, J.: Gradient-like observers for invariant dynamics on a lie group. IEEE Trans. on Automatic Control (2009)Google Scholar
  15. 15.
    Mahony, R., Hamel, T., Pflimlin, J.M.: Non-linear complementary filters on the special orthogonal group. IEEE Trans. on Automatic Control 53(5), 1203–1218 (2008)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Malis, E., Chaumette, F.: Theoretical improvements in the stability analysis of a new class of model-free visual servoing methods. IEEE Trans. on Robotics and Automation 18(2), 176–186 (2002)CrossRefGoogle Scholar
  17. 17.
    Malis, E., Chaumette, F., Boudet, S.: 2 1/2 D visual servoing. IEEE Trans. on Robotics and Automation 15(2), 234–246 (1999)CrossRefGoogle Scholar
  18. 18.
    Malis, E., Vargas, M.: Deeper understanding of the homography decomposition for vision-based control. Research Report 6303, INRIA (2007)Google Scholar
  19. 19.
    Martin, P., Salaün, E.: Invariant observers for attitude and heading estimation from low-cost inertial and magnetic sensors. In: IEEE Conf. on Decision and Control, pp. 1039–1045 (2007)Google Scholar
  20. 20.
    Martin, P., Salaün, E.: An invariant observer for earth-velocity-aided attitude heading reference systems. In: IFAC World Congress, pp. 9857–9864 (2008)Google Scholar
  21. 21.
    Samson, C., Le Borgne, M., Espiau, B.: Robot Control: the Task Function Approach. Oxford Engineering Science Series, vol. 22. World Scientific Press, Clarendon Press (1991)Google Scholar
  22. 22.
    Suter, D., Hamel, T., Mahony, R.: Visual servo control using homography estimation for the stabilization of an x4-flyer. In: IEEE Conference on Decision and Control, pp. 2872–2877 (2002)Google Scholar
  23. 23.
    Thienel, J., Sanner, R.M.: A coupled nonlinear spacecraft attitude controller and observer with an unknow constant gyro bias and gyro noise. IEEE Trans. on Automatic Control 48(11), 2011–2015 (2003)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Vargas, M., Malis, E.: Visual servoing based on an analytical homography decomposition. In: IEEE Conf. on Decision and Control and European Control Conf., pp. 5379–5384 (2005)Google Scholar
  25. 25.
    Wilson, W.J., Hulls, C.C.W., Bell, G.S.: Relative end-effector control using cartesian position-based visual servoing. IEEE Trans. on Robotics and Automation 12(5), 684–696 (1996)CrossRefGoogle Scholar

Copyright information

© Springer London 2010

Authors and Affiliations

  • Ezio Malis
    • 1
  • Tarek Hamel
    • 2
  • Robert Mahony
    • 3
  • Pascal Morin
    • 1
  1. 1.INRIASophia AntipolisFrance
  2. 2.I3S-CNRSSophia AntipolisFrance
  3. 3.Department of EngineeringAustralian National UniversityActonAustralia

Personalised recommendations