An efficient method to compute the inverse Jacobian matrix in visual servoing

The work presents a method for estimating the inverse Jacobian matrix of a function, without computing the direct Jacobian matrix. The resulting inverse Jacobian matrix is shown to perform much better in modelling a relation /spl theta/ = f/sup -1/ (x) than the classical Moore-Penrose inverse J/sup +//sub f/. Theoretical insight as well as comparisons in the domain of visual servoing are provided to demonstrate this assertion.

[1]  Anthony A. Maciejewski,et al.  Computational modeling for the computer animation of legged figures , 1985, SIGGRAPH.

[2]  R. Paul.  Robot manipulators : mathematics, programming, and control : the computer control of robot manipulators , 1981 .

[3]  M. Iwatsuki,et al.  A new formulation of visual servoing based on cylindrical coordinate system with shiftable origin , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[4]  Peter I. Corke,et al.  A new partitioned approach to image-based visual servo control , 2001, IEEE Trans. Robotics Autom..

[5]  Harvey Lipkin,et al.  Uncalibrated Eye-in-Hand Visual Servoing , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[6]  Lee E. Weiss,et al.  Dynamic visual servo control of robots: An adaptive image-based approach , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

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

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

[9]  Michel Dhome,et al.  Hyperplane Approximation for Template Matching , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Koichiro Deguchi,et al.  A Direct Interpretation of Dynamic Images with Camera and Object Motions for Vision Guided Robot Control , 2000, International Journal of Computer Vision.

[11]  Franck Plestan,et al.  Sensor based robot control in the presence of uncertainties: bounding the task function tracking errors , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

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

[13]  Olac Fuentes,et al.  Experimental evaluation of uncalibrated visual servoing for precision manipulation , 1997, Proceedings of International Conference on Robotics and Automation.

[14]  Minoru Asada,et al.  Versatile visual servoing without knowledge of true Jacobian , 1994, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'94).

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

[16]  Peter I. Corke,et al.  A tutorial on visual servo control , 1996, IEEE Trans. Robotics Autom..

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

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

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

[20]  Carme Torras,et al.  Vision-based robot positioning using neural networks , 1996, Image Vis. Comput..