Multicriteria Analysis of Visual Servos through Rational Systems, Biquadratic Lyapunov Functions, and LMIs

  • Patrick Danès
  • Daniel F. Coutinho
  • Sylvain Durola
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 401)


This chapter outlines a generic method to the analysis of eye-in-hand position-based or image-based visual servos. This analysis is said to be “multicriteria” as both the convergence and the fulfillment of important constraints can be assessed, including the target visibility, the avoidance of actuators’ saturations, and the exclusion of 3D areas. The field of nonlinear “rational” systems is first shown to constitute a sound and versatile framework to the problem. The fundamentals of a solution based on Lyapunov theory are overviewed next, together with the noteworthy difficulties raised by robotics. Constructive results are finally presented, on the basis of biquadratic or piecewise-biquadratic Lyapunov functions, leading to feasibility/ optimization programs subject to linear matrix inequalities (LMIs). A case study illustrates the approach.


Lyapunov Function Matrix Function Linear Matrix Inequality Visual Servo Actuator Saturation 
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Copyright information

© Springer London 2010

Authors and Affiliations

  • Patrick Danès
    • 1
  • Daniel F. Coutinho
    • 2
  • Sylvain Durola
    • 1
  1. 1.CNRS; LAAS; 7 avenue du colonel Roche, F-31077 Toulouse, France and Université de Toulouse; UPS, INSA, INP, ISAE; LAASToulouseFrance
  2. 2.Group of Automation and Control SystemsPUC-RSPorto AlegreBrazil

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