A second-order conic optimization-based method for visual servoing

Abstract This work presents a novel method for the visual servoing control problem based on second-order conic optimization. Special cases of the proposed method provide similar results as those obtained by the position-based and image-based visual servoing methods. The goal in our approach is to minimize both the end-effector trajectory in the Cartesian space and image feature trajectories simultaneously. For this purpose, a series of second-order conic optimization problems is solved. Each problem starts from the current camera pose and finds the camera velocity as well as the next camera pose such that (1) the next camera pose is as close as possible to the line connecting the initial and desired camera poses, and (2) the next feature points are as close as possible to the corresponding lines connecting the initial and desired feature points. To validate our approach, we provide simulations and experimental results for several different camera configurations.

[1]  Moslem Kazemi,et al.  Path-Planning for Visual Servoing: A Review and Issues , 2010 .

[2]  Gerald Sommer,et al.  Models and Control Strategies for Visual Servoing , 2010 .

[3]  Gregory D. Hager,et al.  Robust Image Processing and PositionBased Visual Servoing , 2000 .

[4]  Danica Kragic,et al.  New shortest-path approaches to visual servoing , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[5]  Farrokh Janabi-Sharifi,et al.  Generalizations to Control Laws of Image-Based Visual Servoing , 2009 .

[6]  Yeung Sam Hung,et al.  Global Path-Planning for Constrained and Optimal Visual Servoing , 2007, IEEE Transactions on Robotics.

[7]  François Chaumette,et al.  Optimal Camera Trajectory with Image-Based Control , 2003, Int. J. Robotics Res..

[8]  Hidenori Kimura,et al.  Visual servoing with hand-eye manipulator-optimal control approach , 1996, IEEE Trans. Robotics Autom..

[9]  Maurizio Ficocelli,et al.  Formulation of radiometric feasibility measures for feature selection and planning in visual servoing , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[10]  Kim-Chuan Toh,et al.  SDPT3 — a Matlab software package for semidefinite-quadratic-linear programming, version 3.0 , 2001 .

[11]  C. V. Jawahar,et al.  Path planning approach to visual servoing with feature visibility constraints: A convex optimization based solution , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[12]  C. V. Jawahar,et al.  Visual Servoing by Optimization of a 2D/3D Hybrid Objective Function , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

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

[14]  François Chaumette,et al.  Analysis of classical and new visual servoing control laws , 2008, 2008 IEEE International Conference on Robotics and Automation.

[15]  François Chaumette,et al.  Visual servo control. I. Basic approaches , 2006, IEEE Robotics & Automation Magazine.

[16]  Olivier D. Faugeras,et al.  Determination of Camera Location from 2-D to 3-D Line and Point Correspondences , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

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

[18]  Farrokh Janabi-Sharifi,et al.  Visual Servoing: Theory and Applications , 2002 .

[19]  Radu Horaud,et al.  An analytic solution for the perspective 4-point problem , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

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

[21]  Seth Hutchinson,et al.  Visual Servo Control Part I: Basic Approaches , 2006 .

[22]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

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

[24]  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.

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

[26]  Joseph S.-C. Yuan.  A general photogrammetric method for determining object position and orientation , 1989, IEEE Trans. Robotics Autom..

[27]  Donald Goldfarb,et al.  Second-order cone programming , 2003, Math. Program..

[28]  Rafael Murrieta-Cid,et al.  Optimal Paths for Landmark-Based Navigation by Differential-Drive Vehicles With Field-of-View Constraints , 2007, IEEE Transactions on Robotics.

[29]  Nicholas R. Gans,et al.  Stable Visual Servoing Through Hybrid Switched-System Control , 2007, IEEE Transactions on Robotics.

[30]  Graziano Chesi,et al.  Visual Servoing Path Planning via Homogeneous Forms and LMI Optimizations , 2009, IEEE Transactions on Robotics.

[31]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[32]  William J. Wilson,et al.  Hybrid motion control and planning strategies for visual servoing , 2005, IEEE Transactions on Industrial Electronics.

[33]  Maurizio Ficocelli,et al.  Adaptive filtering for pose estimation in visual servoing , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[34]  William J. Wilson,et al.  Automatic selection of image features for visual servoing , 1997, IEEE Trans. Robotics Autom..

[35]  Antonio Bicchi,et al.  Optimal paths in a constrained image plane for purely image-based parking , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[36]  François Chaumette,et al.  Predictive Control for Constrained Image-Based Visual Servoing , 2010, IEEE Transactions on Robotics.

[37]  William J. Wilson,et al.  Stability and robustness of visual servoing methods , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).