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Visual Servoing of Robot Manipulators Part I : Projective Kinematics

Andreas Ruf 1 Radu Horaud 1 
1 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : Visual servoing of robot manipulators is a key technique where video images, i.e. the visual appearance of an object is used to control the end-effector. Most such methods use robots and cameras that have been calibrated. In this report we suggest a non-metric formulation of visual servoing that works with an uncalibrated stereo rig, i.e. in the projective space associated with it. In consequence, the robot kinematics and the robot Jacobian have to defined projectively, as well. Elementary motions of robot joints are pure rotations and pure translations. Rather than representing them by Euclidean transformations, the uncalibrated stereo rig suggests to represent them by corresponding projective transformations (homographies). They are introduced as projective rotations and projective translations, their algebraic properties and special parameterizations are thoroughly investigated- . This gives raise to the definition of a projectiv kinematic map and a projective Jacobian matrix. Unlike the classical robot Jacobian, which relates joint-velocities to end-effector velocities, we establish a direct relationship between joint-velocities and image-velocities, i.e. the velocitie- s of those images points corresponding to end-effector features. Finally, we provide a practical method to establish the projective kinematics and describe preliminary simulated experiments of stereo-based visual servoing using the non-metric model. Nevertheless, in depth analysis of projective control will be the topic of a forthcoming paper.
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Reports (Research report)
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Submitted on : Wednesday, May 24, 2006 - 11:34:01 AM
Last modification on : Thursday, October 27, 2022 - 4:02:56 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:31:01 PM


  • HAL Id : inria-00073002, version 1


Andreas Ruf, Radu Horaud. Visual Servoing of Robot Manipulators Part I : Projective Kinematics. [Research Report] RR-3670, INRIA. 1999. ⟨inria-00073002⟩



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