Authors: Nicolas Andreff, Bernard Espiau, Radu Horaud
Organizations: Institut Français de Mécanique Avancée, BP 265, 63175 Aubière Cedex, France. · INRIA Rhône-Alpes and GRAVIR-IMAG, 655, av. de l’Europe, 38330 Montbonnot Saint Martin, France.
In this work, we present a fundamentally new approach to visual servoing using lines. It is based on a theoretical and geometrical study of the main line representations which allowed us to define a new representation, the so-called binormalized Plucker coordinates. They are particularly well suited to visual servoing. Indeed, they allow the definition of a proper image line alignment concept. The control law which realizes such an alignment has moreover several properties: partial decoupling between rotation and translation, analytical inversion of the motion equations and global asymptotic stability conditions. This control law was validated both in simulation and experimentally in the specific case of an orthogonal trihedron.
Figures & tables
Figure 1: Detail of a part to be welded.
Figure 2: Geometric interpretation of the normalized Plücker coordinates of a line.
Figure 3: The binormalized Plücker coordinates have a sequential interpretation: from image measurements to the estimation of 3 d components.
Figure 4: Geometrical objects generated by lines with fixed components of their binormalized Plücker coordinates
Figure 5: Two different choices for the definition interval of θ
Figure 6: The action of the translation control V=−μhu×(h−h∗) : in the case where u=u∗ (left) and in the general case (right).
Figure 7: A laser pointer is rigidly linked to the camera
Figure 8: Sequential activation of the control in rotation and then in translation: Rotation (left) and translation (right) control.
Figure 9: Sequential activation of the control in rotation and then in translation: Errors in orientation (solid line), on the image line projections (dotted line) and on the laser spot position (dashed line).
Figure 10: Sequential activation of the control in rotation and then in translation: Trajectory of the trihedron in the image (left) and in the 3 d space (right).
Figure 11: Simultaneous activation of the control in rotation and then in translation: Rotation (left) and translation (right) control.
Figure 12: Simultaneous activation of the control in rotation and then in translation: Errors in orientation (solid line), on the image line projections (dotted line) and on the laser spot position (dashed line).
Figure 13: Simultaneous activation of the control in rotation and then in translation: Trajectory of the trihedron in the image (left) and in the 3 d space (right).
Figure 14: Pure translation: Desired (left) and initial (right) positions of the robot.
Figure 15: Pure translation: coefficients of the vectors hi (left) and ui (right) along the control.
Figure 16: Pure translation: Rotation (left) and translation (right) control.
Figure 17: Pure translation: Errors (left) and image trajectory of the trihedron center (right).
Figure 18: Pure rotation: Rotation (left) and translation (right) control.
Figure 19: Pure rotation: Errors (left) and image trajectory of the trihedron center (right).
Sorbonne Universit´e, LIP6, Equipe PolSys, Paris, France · Centre national de la Recherche Scientifique (CNRS), Laboratoire des Sciences du Num´erique de Nantes (LS2N), UMR CNRS 6004, Nantes, France