ISSN 0253-2778

CN 34-1054/N

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Dynamic BFGS method for uncalibrated visual servoing

  • 1.

    Department of Automation, University of Science and Technology of China, Hefei 230027, China

  • 2.

    Key Laboratory of Chinese Academy of Spatial Information Processing and Application System, Hefei 230027, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.01.001
  • Received Date: 25 December 2013
  • Accepted Date: 01 May 2014
  • Rev Recd Date: 01 May 2014
  • Publish Date: 30 January 2015
    Abstract

  • Abstract

    Based on the dynamic BFGS (Broyden-Fletcher-Goldfarb-Shanno) method, an uncalibrated visual servoing control approach was presented for the real time tracking of a moving targets. The method directly estimated, global Hessian matrix containing the residual (the Hessian matrix of an object function), thus reducing the cost of computation. Meanwhile, it solved the singularity problem of the Hessian matrix. According to the approximate affine model of the mapping relations between the joint variables map and the image plane, an estimation of the image Jacobian matrix was obtained, which increased the robustness in tracking a dynamic target. Based on the Matlab Robotools, a mechanical arm visual tracking system with three degrees of freedom was constructed. By means of simulation experiments, the presented method was compared with the direct computing method of the residual term and the D-DFP method. The results verify the good tracking performance of the D-BFGS method.

    Abstract

    Based on the dynamic BFGS (Broyden-Fletcher-Goldfarb-Shanno) method, an uncalibrated visual servoing control approach was presented for the real time tracking of a moving targets. The method directly estimated, global Hessian matrix containing the residual (the Hessian matrix of an object function), thus reducing the cost of computation. Meanwhile, it solved the singularity problem of the Hessian matrix. According to the approximate affine model of the mapping relations between the joint variables map and the image plane, an estimation of the image Jacobian matrix was obtained, which increased the robustness in tracking a dynamic target. Based on the Matlab Robotools, a mechanical arm visual tracking system with three degrees of freedom was constructed. By means of simulation experiments, the presented method was compared with the direct computing method of the residual term and the D-DFP method. The results verify the good tracking performance of the D-BFGS method.
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    • References(18)
  • [1]
    Sanderson A C, Weiss L E. Image-based visual servo control using relational graph error signals [C]// Proceedings of the IEEE International Conference on Cybernetics and Society. 1980: 1 074-1 077.
    [2]
    Chaumette F, Hutchinson S. Visual servo control, Part I: Basic approaches [J]. IEEE Robotics & Automation Magazine, 2006, 13(4): 82-90.
    [3]
    Chaumette F, Hutchinson S. Visual servo control, Part II: Advanced approaches [J]. IEEE Robotics and Automation Magazine, 2007, 14(1): 109-118.
    [4]
    Piepmeier J A, McMurray G V, Lipkin H. Tracking a moving target with model independent visual servoing: A predictive estimation approach[C]// Proceedings of the IEEE International Conference on Robotics and Automation. Leuven, Belgium: IEEE Press, 1998, 3: 2 652-2 657.
    [5]
    Hosoda K, Asada M. Versatile visual servoing without knowledge of true Jacobian [C]// Proceedings of the IEEE/RSJ/GI International Conference on Intelligent Robots and Systems. Munich, Germany: IEEE Press, 1994, 1: 186-193.
    [6]
    Jagersand M, Fuentes O, Nelson R. Experimental evaluation of uncalibrated visual servoing for precision manipulation[C]// Proceedings of the IEEE International Conference on Robotics and Automation. Albuquerque, USA: IEEE Press, 1997, 4: 2 874-2 880.
    [7]
    徐德, 谭民, 李原. 机器人视觉测量与控制[M]. 北京: 国防工业出版社, 2008.
    [8]
    Piepmeier J A, Lipkin H, McMurray G V. A predictive estimation approach to model independent visual servoing[C]. ASCE, 1998.
    [9]
    Piepmeier J A, McMurray G V, Lipkin H. Uncalibrated dynamic visual servoing [J]. EEE Transactions on Robotics and Automation, 2004, 20(1): 143-147.
    [10]
    Kim G W, Lee B H, Kim M S. Uncalibrated visual servoing technique using large residual[C]// Proceedings of the IEEE International Conference on Robotics and Automation. Taiwn, China: IEEE Press, 2003, 3: 3 315-3 320.
    [11]
    赵杰, 李牧, 李戈, 等. 一种无标定视觉伺服控制技术的研究[J]. 控制与决策, 2006, 21(9): 1 015-1 019.
    [12]
    Kim G W. Uncalibrated visual servoing through the efficient estimation of the image Jacobian for large residual[J]. Journal of Electrical Engineering & Technology, 2013, 8(2): 385-392.
    [13]
    Janabi-Sharifi F, Deng L F, Wilson W J. Comparison of basic visual servoing methods[J]. IEEE/ASME Transactions on Mechatronics, 2011, 16(5): 967-983.
    [14]
    Sebastin J M, Pari L, Gonzlez C, et al. A new method for the estimation of the image Jacobian for the control of an uncalibrated joint system[C]// Proceedings of the 3rd International Conference on Image Analysis and Recognition. Póvoa de Varzim, Portugal: Springer, 2005: 631-638.
    [15]
    Munnae J. Uncalibrated robotic visual servo tracking for large residual problems[D]. Mechanical Engineering, Georgia Institute of Technology, 2010.
    [16]
    Dennis J E, Schnabel R B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations [M]. Philadelphia: SIAM Press, 1983.
    [17]
    Fu Q S, Zhang Z S, Shi J F. Uncalibrated visual servoing using more precise model[C]// IEEE Conference on Robotics, Automation and Mechatronics. Chengdu, China: IEEE Press, 2008: 916-921.
    [18]
    Dennis J E, Moré J J. Quasi-Newton methods, motivation and theory [J]. SIAM review, 1977, 19(1): 46-89.
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    [1]
    Sanderson A C, Weiss L E. Image-based visual servo control using relational graph error signals [C]// Proceedings of the IEEE International Conference on Cybernetics and Society. 1980: 1 074-1 077.
    [2]
    Chaumette F, Hutchinson S. Visual servo control, Part I: Basic approaches [J]. IEEE Robotics & Automation Magazine, 2006, 13(4): 82-90.
    [3]
    Chaumette F, Hutchinson S. Visual servo control, Part II: Advanced approaches [J]. IEEE Robotics and Automation Magazine, 2007, 14(1): 109-118.
    [4]
    Piepmeier J A, McMurray G V, Lipkin H. Tracking a moving target with model independent visual servoing: A predictive estimation approach[C]// Proceedings of the IEEE International Conference on Robotics and Automation. Leuven, Belgium: IEEE Press, 1998, 3: 2 652-2 657.
    [5]
    Hosoda K, Asada M. Versatile visual servoing without knowledge of true Jacobian [C]// Proceedings of the IEEE/RSJ/GI International Conference on Intelligent Robots and Systems. Munich, Germany: IEEE Press, 1994, 1: 186-193.
    [6]
    Jagersand M, Fuentes O, Nelson R. Experimental evaluation of uncalibrated visual servoing for precision manipulation[C]// Proceedings of the IEEE International Conference on Robotics and Automation. Albuquerque, USA: IEEE Press, 1997, 4: 2 874-2 880.
    [7]
    徐德, 谭民, 李原. 机器人视觉测量与控制[M]. 北京: 国防工业出版社, 2008.
    [8]
    Piepmeier J A, Lipkin H, McMurray G V. A predictive estimation approach to model independent visual servoing[C]. ASCE, 1998.
    [9]
    Piepmeier J A, McMurray G V, Lipkin H. Uncalibrated dynamic visual servoing [J]. EEE Transactions on Robotics and Automation, 2004, 20(1): 143-147.
    [10]
    Kim G W, Lee B H, Kim M S. Uncalibrated visual servoing technique using large residual[C]// Proceedings of the IEEE International Conference on Robotics and Automation. Taiwn, China: IEEE Press, 2003, 3: 3 315-3 320.
    [11]
    赵杰, 李牧, 李戈, 等. 一种无标定视觉伺服控制技术的研究[J]. 控制与决策, 2006, 21(9): 1 015-1 019.
    [12]
    Kim G W. Uncalibrated visual servoing through the efficient estimation of the image Jacobian for large residual[J]. Journal of Electrical Engineering & Technology, 2013, 8(2): 385-392.
    [13]
    Janabi-Sharifi F, Deng L F, Wilson W J. Comparison of basic visual servoing methods[J]. IEEE/ASME Transactions on Mechatronics, 2011, 16(5): 967-983.
    [14]
    Sebastin J M, Pari L, Gonzlez C, et al. A new method for the estimation of the image Jacobian for the control of an uncalibrated joint system[C]// Proceedings of the 3rd International Conference on Image Analysis and Recognition. Póvoa de Varzim, Portugal: Springer, 2005: 631-638.
    [15]
    Munnae J. Uncalibrated robotic visual servo tracking for large residual problems[D]. Mechanical Engineering, Georgia Institute of Technology, 2010.
    [16]
    Dennis J E, Schnabel R B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations [M]. Philadelphia: SIAM Press, 1983.
    [17]
    Fu Q S, Zhang Z S, Shi J F. Uncalibrated visual servoing using more precise model[C]// IEEE Conference on Robotics, Automation and Mechatronics. Chengdu, China: IEEE Press, 2008: 916-921.
    [18]
    Dennis J E, Moré J J. Quasi-Newton methods, motivation and theory [J]. SIAM review, 1977, 19(1): 46-89.
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