Image Based Visual Servoing: Estimated Image Jacobian by Using Fundamental Matrix VS Analytic Jacobian

Abstract

Abstract. This paper describes a comparative study of performance between the estimated image Jacobian that come from taking into account the geometry epipolar of a system of two cameras, and the well known analytic image Jacobian that is utilized for most applications in visual servoing. Image Based Visual Servoing architecture is used for controlling a 3 d.o.f. articular system using two cameras in eye to hand configuration. Tests in static and dynamic cases were carried out, and showed that the performance of estimated Jacobian by using the properties of the epipolar geometry is such as good and robust against noise as the analytic Jacobian. This fact is considered as an advantage because the estimated Jacobian does not need laborious previous work prior the control task in contrast to the analytic Jacobian does.

Invisible Leash: Object-Following Robot

“…Multiple projects [3,7,8] have used image-based visual servoing, or a modi ication of the method. This method uses the image Jacobian to determine velocity vectors.…”

Survey of Visual and Force/Tactile Control of Robots for Physical Interaction in Spain

“…These papers include the epipolar constraint or fundamental matrix in the interaction matrix calculation. A comparison between this online estimated interaction matrix and the analytic interaction matrix is described in [ 34 ]. Echegoyen et al [ 35 ] develop the equations to obtain the interaction matrix for an Aibo ERS-7 robot.…”

“…The process of searching and tracking of the grasping points is also described, as well as the desired grasping pose, which is computed online. Sebastian, Pari et al take into account the epipolar geometry of two fixed cameras overlooking the scene for online estimation of the image Jacobian [ 32 - 34 ]. The stereo rig is used for obtaining the epipolar constraints or the fundamental matrix computation.…”

3D image-based dynamic visual servoing with uncalibrated stereo cameras

“…In general, the image Jacobian can be computed using direct depth information [4], [5], or by approximation via on-line estimation of depth of the features [2], [3], [6], or using depth-independent image Jacobian matrix [7], [8], [9]. Additionally, many papers directly estimate on-line the complete image Jacobian in different ways [10], [11], [12], [13]. However, all these methods use redundant image point coordinates to define (as a general rule) a non-square image Jacobian, which is a differentiable mapping from SE(3) to s ∈ R 2p (with p as the number of feature points).…”