Gradient Projection Methods for Constrained Image-based Visual Servo

  • Wenzhuo Ma
  • Seth Hutchinson
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 401)


This chapter describes redundancy-based solutions to visual servo problems that require honoring constraints on camera motion that are imposed either by the environment or by physical limits on the robot system. The task function approach provides a formalism by which a secondary task can be achieved without disturbing the execution of the primary task. For problems considered here, secondary tasks correspond to enforcing various constraints. With gradient projection methods, the secondary task corresponds to the gradient of a cost function, and this gradient is projected onto the null space of the primary task to yield motions that will honor the constraints without interfering with the performance of the primary task. The chapter reprises the development of gradient projection methods in the context of constrained visual servo control, and presents simulation results to illustrate performance of the approach.


Primary Task Null Space Secondary Task Camera Motion Gradient Projection 
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  1. 1.
    Bertsekas, D.P.: Nonlinear Programming. Athena Scientific, Belmont (1995)zbMATHGoogle Scholar
  2. 2.
    Chaumette, F., Hutchinson, S.: Visual servo control, part I: Basic approaches. IEEE Robotics and Automation Magazine 13(4), 82–90 (2006)CrossRefGoogle Scholar
  3. 3.
    Chaumette, F., Hutchinson, S.: Visual servo control, part II: Advanced approaches. IEEE Robotics and Automation Magazine 14(1), 109–118 (2007)CrossRefGoogle Scholar
  4. 4.
    Chaumette, F., Marchand, E.: A redundancy-based iterative approach for avoiding joint limits: application to visual servoing. IEEE Trans. on Robotics and Automation 17(5), 719–730 (2001)CrossRefGoogle Scholar
  5. 5.
    Chiacchio, P., Chiaverini, S.: Closed-loop inverse kinematics schemes for constrained redundant manipulators with task space augmentation and task priority strategy. Int. J. Robot. Res. 10, 410–425 (1991)CrossRefGoogle Scholar
  6. 6.
    Corke, P.: A robotics toolbox for MATLAB. IEEE Robotics and Automation Magazine 3(1), 24–32 (1996)CrossRefGoogle Scholar
  7. 7.
    Corke, P.: Machine vision toolbox. IEEE Robotics and Automation Magazine 12(4), 16–25 (2005)CrossRefGoogle Scholar
  8. 8.
    Espiau, B., Chaumette, F., Rives, P.: A New Approach to Visual Servoing in Robotics. IEEE Trans. on Robotics and Automation 8, 313–326 (1992)CrossRefGoogle Scholar
  9. 9.
    Mansard, N., Chaumette, F.: Task sequencing for high-level sensor-based control. IEEE Trans. on Robotics 23(1), 60–72 (2007)CrossRefGoogle Scholar
  10. 10.
    Marchand, E., Hager, G.: Dynamic sensor planning in visual servoing. In: IEEE Int. Conf. on Robotics and Automation (ICRA 1998), Leuven, Belgium, pp. 1988–1993 (1998)Google Scholar
  11. 11.
    Mezouar, Y., Chaumette, F.: Path planning for robust image-based control. IEEE Trans. on Robotics and Automation 18(4), 534–549 (2002)CrossRefGoogle Scholar
  12. 12.
    Nakamura, Y.: Advanced robotics: redundancy and optimization. Addison-Wesley publishing company, Reading (1991)Google Scholar
  13. 13.
    Rosen, J.B.: The gradient projection method for nonlinear programming. part 1: Linear constraints. J. SIAM 8, 181–217 (1960)zbMATHGoogle Scholar
  14. 14.
    Samson, C., Le Borgne, M., Espiau, B.: Robot Control: The Task Function Approach. Clarendon Press, Oxford (1992)Google Scholar
  15. 15.
    Siciliano, B.: Kinematic control of redundant manipulators: A tutorial. Journal of Intelligent and Robotic Systems 3, 201–212 (1990)CrossRefGoogle Scholar
  16. 16.
    Yoshikawa, T.: Foundations of robotics: analysis and control. MIT Press, Cambridge (1990)Google Scholar

Copyright information

© Springer London 2010

Authors and Affiliations

  • Wenzhuo Ma
    • 1
  • Seth Hutchinson
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of IllinoisUrbanaUSA

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