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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benhimane, S., Malis, E.: Homography-based 2d visual tracking and servoing. International Journal of Robotic Research 26(7), 661–676 (2007)
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)
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)
Bonnabel, S., Martin, P., Rouchon, P.: Symmetry-preserving observers. IEEE Trans. on Automatic Control 53(11), 2514–2526 (2008)
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)
Chaumette, F., Hutchinson, S.: Visual servo control, part ii: Advanced approaches. IEEE Robotics and Automation Magazine 14(1), 109–118 (2007)
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)
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)
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)
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)
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)
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)
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)
Lageman, C., Mahony, R., Trumpf, J.: Gradient-like observers for invariant dynamics on a lie group. IEEE Trans. on Automatic Control (2009)
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)
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)
Malis, E., Chaumette, F., Boudet, S.: 2 1/2 D visual servoing. IEEE Trans. on Robotics and Automation 15(2), 234–246 (1999)
Malis, E., Vargas, M.: Deeper understanding of the homography decomposition for vision-based control. Research Report 6303, INRIA (2007)
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)
Martin, P., Salaün, E.: An invariant observer for earth-velocity-aided attitude heading reference systems. In: IFAC World Congress, pp. 9857–9864 (2008)
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)
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)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer London
About this chapter
Cite this chapter
Malis, E., Hamel, T., Mahony, R., Morin, P. (2010). Estimation of Homography Dynamics on the Special Linear Group. In: Chesi, G., Hashimoto, K. (eds) Visual Servoing via Advanced Numerical Methods. Lecture Notes in Control and Information Sciences, vol 401. Springer, London. https://doi.org/10.1007/978-1-84996-089-2_8
Download citation
DOI: https://doi.org/10.1007/978-1-84996-089-2_8
Publisher Name: Springer, London
Print ISBN: 978-1-84996-088-5
Online ISBN: 978-1-84996-089-2
eBook Packages: EngineeringEngineering (R0)