On the efficient second order minimization and image-based visual servoing

This paper deals with the efficient second order minimization (ESM) and the image-based visual servoing schemes. In other word, it deals with the minimization based on the pseudo-inverses of the mean of the Jacobians or on the mean of Jacobian Pseudo-inverses. Chronologically, it has been noted by Tahri and Chaumette (2003) that the (ESM) improves generally the system behavior compared to the case where only the simple Jacobian Pseudo- inverses is used. Subsequently, a mathematical explanation has been given by Malis (2004). In this paper, the proofs given by Malis are considered to deal with their validity. It will be shown that there is a limitation to the the validity of this method and some precautions should be taken, for adequate application of it. In other words, we will show that the use of ESM does not necessary ensures a better system behavior, especially in the cases where large rotational motions are considered.

[1]  William J. Wilson,et al.  Relative end-effector control using Cartesian position based visual servoing , 1996, IEEE Trans. Robotics Autom..

[2]  E. Malis,et al.  2 1/2 D Visual Servoing , 1999 .

[3]  Selim Benhimane,et al.  Integration of Euclidean constraints in template based visual tracking of piecewise-planar scenes , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[4]  François Chaumette,et al.  Path planning for robust image-based control , 2002, IEEE Trans. Robotics Autom..

[5]  François Chaumette,et al.  Potential problems of stability and convergence in image-based and position-based visual servoing , 1997 .

[6]  P. Martinet,et al.  Path Planning for image based control with omnidirectional cameras , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[7]  François Chaumette,et al.  Application of moment invariants to visual servoing , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[8]  Daniel E. Koditschek,et al.  Visual servoing via navigation functions , 2002, IEEE Trans. Robotics Autom..

[9]  Francois Chaumette,et al.  Potential problems of unstability and divergence in image-based and position-based visual servoing , 1999, 1999 European Control Conference (ECC).

[10]  Selim Benhimane,et al.  Real-time image-based tracking of planes using efficient second-order minimization , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[11]  François Chaumette,et al.  Point-based and region-based image moments for visual servoing of planar objects , 2005, IEEE Transactions on Robotics.

[12]  François Chaumette,et al.  New decoupled visual servoing scheme based on invariants from projection onto a sphere , 2008, 2008 IEEE International Conference on Robotics and Automation.

[13]  François Chaumette,et al.  Image moments: a general and useful set of features for visual servoing , 2004, IEEE Transactions on Robotics.

[14]  Robert E. Mahony,et al.  Visual servoing of an under-actuated dynamic rigid-body system: an image-based approach , 2002, IEEE Trans. Robotics Autom..

[15]  Patrick Rives,et al.  A new approach to visual servoing in robotics , 1992, IEEE Trans. Robotics Autom..

[16]  Omar Tahri.  Utilisation des moments en asservissement visuel et en calcul de pose , 2004 .

[17]  Ezio Malis,et al.  Improving vision-based control using efficient second-order minimization techniques , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[18]  Larry S. Davis,et al.  Model-based object pose in 25 lines of code , 1992, International Journal of Computer Vision.

[19]  Jean-Thierry Lapresté,et al.  A Hessian approach to visual servoing , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[20]  Guillaume Morel,et al.  Calibration Free Image Point Path Planning Simultaneously Ensuring Visibility and Controlling Camera Path , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.