Image Based Visual Servoing: A New Method for the Estimation of the Image Jacobian in Dynamic Environments

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

“…Different approaches have been proposed to obtain a better behaviour than interaction matrix offline computation. Pari et al present an online interaction matrix estimator based on the previous movements of the camera [ 32 , 33 ]. These papers include the epipolar constraint or fundamental matrix in the interaction matrix calculation.…”

A comparative study between analytic and estimated image Jacobian by using a stereoscopic system of cameras

“…In previous work [16], we carried out experiments comparing the results obtained using one of the cameras and those obtained using two cameras: our results showed that using two cameras instead of one improved the behaviour of the all methods we tested. In many applications, improvement on the performance justifies the [18] gathers diverse methods to estimate the image Jacobian, Two of them are described in this section, the first method was designed by the authors and is based on incorporating the epipolar constraint of the system [16], the second method is based on the recursive updating of the Jacobian considering a covariance matrix with a forgetting factor [14], due to its good results in past works [13] [16] [17] this method is included into the tests and is described below. It is worth also mentioning the Kalman method where the system is modelled by its state variables which are updated using Kalman filter equations [15], the Broyden method that recursively update the Jacobian by using the last movement and the previous Jacobian [5].…”

“…In past papers [13] [16] [17] we presented a method to estimate image Jacobian by integrating epipolar geometry of the system [3], and compared with other existing algorithms from the literature by means of tests that consider static [13] and dynamic [16] cases.…”

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

“…Analytic Image Jacobian is widely used by the most researchers in Visual Servoing, it is well known that it require a thorough knowledge of the involved systems: calibration of the joint system, kinematic calibration of the visión system, and 3D reconstruction of features positions; they all are common sources of possible errors. In past papers [12] [15] we have presented a method to estimated image Jacobian by integrating epipolar geometry of the system [3], and compared with other existing algorithms from the literature with tests that consider static [12] and dynamic [15] cases.…”

“…This fact is considered as an advantage, because the estimated method reaches good performance without the need of a laborious previous work to the task. In order to diversify the study, tests were extended to the recursive last square method which gave good results in past works [12] [15]. This paper is organized as follows: after the present introduction, section 2 details the terminology and theoretical concepts used in the paper.…”