Robust Jacobian estimation for uncalibrated visual servoing

Abstract

This paper addresses robust estimation of the uncalibrated visual-motor Jacobian for an image-based visual servoing (IBVS) system. The proposed method does not require knowledge of model or system parameters and is robust to outliers caused by various visual tracking errors, such as occlusion or mis-tracking. Previous uncalibrated methods are not robust to outliers and assume that the visual-motor data belong to the underlying model. In unstructured environments, this assumption may not hold. Outliers to the visual-motor model may deteriorate the Jacobian, which can make the system unstable or drive the arm in the wrong direction. We propose to apply a statistically robust M-estimator to reject the outliers. We compare the quality of the robust Jacobian estimation with the least squares-based estimation. The effect of outliers on the estimation quality is studied through MATLAB simulations and eye-in-hand visual servoing experiments using a WAM arm. Experimental results show that the Jacobian estimated by robust M-estimation is robust when up to 40% of the visualmotor data are outliers.

On the similarities between control based and behavior based visual servoing

“…Furthermore, calibration of the camera with respect to the end-effector is required. Hence, as observed by Shademan et al [20], classical IBVS (and certainly also PBVS) are model-based approaches.…”

Acquiring visual servoing reaching and grasping skills using neural reinforcement learning

“…Like our system, Piepmeier et al [19] have used an uncalibrated camera, while Shademan et al [20] estimated the visual-motor Jacobian without knowledge of the system, though hand-crafted control laws were used.…”

Uncalibrated image-based visual servoing

“…This is done for instance, using Gauss-Newton to minimize squared image error and nonlinear least squares optimization for the image Jacobian [9], [10]; using weighted recursive least squares (RLS), not to obtain the true parameters, but instead an approximation that still guarantees asymptotic stability of the control law in the sense of Lyaponov [11]; or using k-nearest neighbor regression to store previously estimated local models or previous movements, and estimating the Jacobian using local least squares (LLS) [12]. To provide robustness to outliers in the computation of the Jacobian, [13] proposes the use of an M-estimator. This paper presents a new approach to image-based visual servo in which the computation of the image Jacobian makes mild assumptions about the camera parameters.…”