2.5D visual servoing with a fixed camera

In this paper, we investigate the translational and rotational motion of the end-effector of a robot under visual feedback from a fixed camera. We achieve an exponential stability result for the regulation of the end-effector to a desired location and orientation. Specifically, by utilizing visual information from one fixed camera, we capture the motion of 4 points located in a fictitious plane attached to the end-effector in Cartesian space. By assuming knowledge of the camera intrinsic parameters, we obtain the rotational motion of the end-effector through a homography decomposition while utilizing the pixel motion of one of the four points to obtain the translation information. The stability of the controller is proven through a Lyapunov-based stability analysis.

[1]  Zhong-Ping Jiang,et al.  Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties , 1998, Autom..

[2]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .

[3]  Ezio Malis.  Contributions a la modelisation et a la commande en asservissement visuel , 1998 .

[4]  Warren E. Dixon,et al.  Adaptive 2.5D visual servoing of kinematically redundant robot manipulators , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[5]  François Chaumette,et al.  2 1/2 D Visual Servoing with Respect to Unknown Objects Through a New Estimation Scheme of Camera Displacement , 2000, International Journal of Computer Vision.

[6]  Jie Huang,et al.  Global Robust Servomechanism Problem of Lower-Triangular Systems in the General Case1 , 2003, 2003 4th International Conference on Control and Automation Proceedings.

[7]  Benedetto Allotta,et al.  Nonlinear controllability and stability analysis of adaptive image-based systems , 2001, IEEE Trans. Robotics Autom..

[8]  A. Hanson,et al.  Scaled Euclidean 3D reconstruction based on externally uncalibrated cameras , 1995, Proceedings of International Symposium on Computer Vision - ISCV.

[9]  François Chaumette,et al.  2d 1/2 visual servoing with respect to a planar object , 1997 .

[10]  Jie Huang,et al.  Global robust stabilization of cascaded polynomial systems , 2002, Syst. Control. Lett..

[11]  Eduardo Sontag,et al.  Changing supply functions in input/state stable systems , 1995, IEEE Trans. Autom. Control..

[12]  Olivier Faugeras,et al.  Motion and Structure from Motion in a piecewise Planar Environment , 1988, Int. J. Pattern Recognit. Artif. Intell..

[13]  S. Hutchinson,et al.  A new hybrid image-based visual servo control scheme , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[14]  Zhong-Ping Jiang,et al.  A small-gain control method for nonlinear cascaded systems with dynamic uncertainties , 1997, IEEE Trans. Autom. Control..

[15]  François Chaumette,et al.  2 1/2 D visual servoing: a possible solution to improve image-based and position-based visual servoings , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[16]  François Chaumette,et al.  2½D visual servoing , 1999, IEEE Trans. Robotics Autom..

[17]  Eduardo D. Sontag,et al.  Input-Output-to-State Stability , 2001, SIAM J. Control. Optim..

[18]  Koichiro Deguchi,et al.  Optimal motion control for image-based visual servoing by decoupling translation and rotation , 1998, Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications (Cat. No.98CH36190).