Abstract
This paper concerns the stability analysis of a new visual servoing approach which is invariant on camera intrinsic parameters. Contrarily to standard methods, the invariant visual servoing approach can be used with a zooming camera or when the reference image is learned with a camera different from that used for servoing. Even if the error computed in an invariant space does not depend on the camera intrinsic parameters, they are needed to estimate the interaction matrix which links the camera velocity to the displacements of the features in the invariant space. Thus, calibration errors can affect the stability of the control law. For this reason, it is important to study the robustness of the proposed vision-based control with respect to uncertainties on the parameters of the system.
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References
B. Barmish. New Tools for Robustness of Linear Systems. Macmilian, New York, 1994.
R. Basri, E. Rivlin, and I. Shimshoni. Visual homing: surfing on the epipole. International Journal of Computer Vision, 33(2):22–39, 1999.
D. Bellot and P. Danes. Towards an lmi approach to multicriteria visual servoing. In European Control Conference, Porto, Potugal, September 2001.
S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM, 1994.
F. Chaumette. Potential problems of stability and convergence in image-based and position-based visual servoing. In D. Kriegman, G. Hager, and A. Morse, editors, The confluence of vision and control, volume 237 of LNCIS Series, pages 66–78. Springer Verlag, 1998.
C. C. Cheah, S. Kawamura, and S. Arimoto. Feedback control for robotic manipulator with uncertain kinematics and dynamics. In IEEE Int. Conf. on Robotics and Automation, volume 4, pages 3607–3612, Leuven, Belgium, May 1998.
P. Corke and S. Hutchinson. A new partitioned approach to image-based visual servo control. IEEE Transactions on Robotics and Automation, 14(4):507–515, August 2001.
K. Deguchi. Optimal motion control for image-based visual servoing by decoupling translation and rotation. In IEEE Int. Conf. on Intelligent Robots and Systems, volume 2, pages 705–711, October 1998.
L. Deng, F. Janabi-Sharifi, and W. J. Wilson. Stability and robustness of visual servoing methods. In IEEE Int. Conf. on Robotics and Automation, volume 2, pages 1605–1609, Washington D.C., May 2002.
Y. Dufournaud, C. Schmid, and R. Horaud. Matching images with different resolutions. In IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 618–618, Hilton Head Island, South Carolina, USA, June 2000.
B. Espiau. Effect of camera calibration errors on visual servoing in robotics. In 3rd Int. Symposium on Experimental Robotics, Kyoto, Japan, October 1993.
B. Espiau, F. Chaumette, and P. Rives. A new approach to visual servoing in robotics. IEEE Trans. on Robotics and Automation, 8(3):313–326, June 1992.
O. Faugeras. Three-dimensionnal computer vision: a geometric viewpoint. MIT Press, Cambridge, MA, 1993.
G. D. Hager. Calibration-free visual control using projective invariance. In IEEE Int. Conf. on Computer Vision, pages 1009–1015, MIT, Cambridge (USA), June 1995.
R. Hartley and R. Kaucic. Sensitivity of calibration to principal point position. In European Conference on Computer Vision, volume 2, pages 433–446. Copenhagen, Denmark, May 2002.
K. Hashimoto. Visual Servoing: Real Time Control of Robot manipulators based on visual sensory feedback, volume 7 of World Scientific Series in Robotics and Automated Systems. World Scientific Press, Singapore, 1993.
K. Hashimoto and T. Noritsugu. Enlargement of stable region in visual servo. In IEEE Conference on Decision and Control, pages 3927–3932, Sydney, Australia, December 2000.
S. Hutchinson, G. D. Hager, and P. I. Corke. A tutorial on visual servo control. IEEE Trans. on Robotics and Automation, 12(5):651–670, October 1996.
R. Kelly, R. Carelli, O. Nasisi, B. Kuchen, and F. Reyes. Stable visual servoing of camera-in-hand robotic systems. IEEE Trans. on Mechatronics, 5(1):39–48, March 2000.
E. Malis. Vision-based control using different cameras for learning the reference image and for servoing. In IEEE/RSJ International Conference on Intelligent Robots Systems, volume 3, pages 1428–1433, Maui, Hawaii, November 2001.
E. Malis. Visual servoing invariant to changes in camera intrinsic parameters. In International Conference on Computer Vision, volume 1, pages 704–709, Vancouver, Canada, July 2001.
E. Malis. An unified approach to model-based and model-free visual servoing. In European Conference on Computer Vision, volume 4, pages 433–447, Copenhagen, Denmark, May 2002.
E. Malis. Vision-based control invariant to camera intrinsic parameters: stability analysis and path tracking. In IEEE International Conference on Robotics and Automation, volume 1, Washington, D.C., USA, May 2002.
E. Malis and F. Chaumette. Theoretical improvements in the stability analysis of a new class of model-free visual servoing methods. IEEE Transaction on Robotics and Automation, 18(2):176–186, April 2002.
E. Malis, F. Chaumette, and S. Boudet. 2 1/2 d visual servoing. IEEE Trans, on Robotics and Automation, 15(2):234–246, April 1999.
Y. Mezouar and F. Chaumette. Design and tracking of desirable trajectories in the image space by integrating mechanical and visibility constraints. In IEEE Int. Conference on Robotics and Automation, Seoul, South Korea, May 2001.
G. Morel, J. Szewczyk, S. Boudet, and J. Pot. Explicit incorporation of 2d constraints in vision based control of robot manipulators. In Proc. ISER’99: Experimental Robotics IV, pages 99–108, Sidney, Australia, April 1999.
J. G. P. Martinet. Position based visual servoing using a nonlinear approach. In IEEE/RSJ International Conference on Intelligent Robots and Systems, volume 1, pages 531–536, Kyongju, Korea, October 1999.
C. Samson, M. Le Borgne, and B. Espiau. Robot Control: the Task Function Approach, volume 22 of Oxford Engineering Science Series. Clarendon Press, Oxford, UK, 1990.
C. Samson, M. Le Borgne, and B. Espiau. Robot Control: the Task Function Approach, volume 22 of Oxford Engineering Science Series. Clarendon Press, Oxford, UK, 1991.
G. W. Stewart and J.-g. Sun. Matrix perturbation theory. Computer Science and Science Computing. Harcourt Brace Jovanovich, 1990.
M. Sznaier, B. Murphy, and O. Camps. An lpv approach to synthesizing robust active vision systems. In IEEE Conference on Decision and Control, pages 2545–2550, Sydney, Australia, December 2000.
S. Tarbouriech and P. Soueres. Advanced control strategies for the visual servoing scheme. In IFAC Symposium on Robot Control, SYROCO, volume 2, pages 457–462, September 2000.
M. Werman, S. Banerjee, S. Dutta Roy, and M. Qiu. Robot localization using uncalibrated camera invariants. In IEEE Int. Conference on Computer Vision and Pattern Recognition, volume II, pages 353–359, Fort Collins, CO, June 1999.
W. J. Wilson, C. C. W. Hulls, and G. S. Bell. Relative end-effector control using cartesian position-based visual servoing. IEEE Trans. on Robotics and Automation, 12(5):684–696, October 1996.
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Malis, E. (2003). Stability Analysis of Invariant Visual Servoing and Robustness to Parametric Uncertainties. In: Bicchi, A., Prattichizzo, D., Christensen, H.I. (eds) Control Problems in Robotics. Springer Tracts in Advanced Robotics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36224-X_17
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DOI: https://doi.org/10.1007/3-540-36224-X_17
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