PhD graduated (ATER, )
Team : PolSys
    Sorbonne Université - LIP6
    Boîte courrier 169
    Couloir 26-00, Étage 3, Bureau 338
    4 place Jussieu
    75252 PARIS CEDEX 05

Tel: +33 1 44 27 71 30, Jorge.Garcia-Fontan (at)

Supervision : Mohab SAFEY EL DIN

Co-supervision : BRIOT Sébastien

Singularity and stability analysis of vision-based controllers

The objective of this PhD thesis is to explore the failure cases of Image-Based Visual Servoing (IBVS), a class of Robotics controllers based on computer vision data. The failure cases arise from two sources:

  • The singularities of the governing kinematic equations, leading to issues in the controllability of the system.
  • The existence of multiple equilibrium points of the system, as a consequence of which the convergence of IBVS is not guaranteed.
These issues and their effects on the performance of IBVS have been known for decades; however their study remains a challenge, largely due to the complexity of the systems of polynomial equations involved. The singularities are the rank-deficiency conditions of a so-called interaction matrix, and have been identified only for relatively simple cases, while the equilibrium points are the local minima of an error potential function.
In this thesis we approach the above problems using advanced tools from computer algebra and algebraic geometry, in particular Gröbner bases computations using state-of-the-art algorithms and software. Our main contributions are twofold:
  1. The singularity conditions related to the observation of N>3 lines in the image, extending previous results concerning the singularities for other image features.
  2. The computation of the equilibria of IBVS from the observation of N = 4 points in the image features. This is to our knowledge first result regarding the computation of the local minima of IBVS.

Defence : 01/24/2023 - 14h - Campus Pierre et Marie Curie, salle Jacques Pitrat (25-26/105)

Jury members :

Mr. Nicolas Andreff, Professeur, Université de Franche-Comté, FEMTO-ST [Rapporteur]
Mr. Josef Schicho, Professeur, Johannes Kepler University, RISC [Rapporteur]
Mr. Sébastien Briot, Directeur de recherche, CNRS, LS2N.
Mr. Laurent Busé, Directeur de recherche, INRIA Université Côte d’Azur.
Mr. François Chaumette, Directeur de recherche, INRIA Rennes-Bretagne Atlantique, IRISA
Mrs. Isabelle Fantoni, Directrice de recherche, CNRS, LS2N
Mr. Stef Graillat, Professeur, Sorbonne Université, LIP6
Mr. Mohab Safey El Din, Professeur, Sorbonne Université, LIP6
Mr. Philippe Martinet, Directeur de recherche, INRIA Sophia Antipolis

2022-2023 Publications