Transformation-Domain Gaussian Smoothing for Translational Direct Visual Servoing

Abstract

Direct visual servoing (DVS) uses raw pixel intensities to control robot motion, yielding high accuracy at convergence. However, the associated photometric cost function is highly nonconvex, which leads to a narrow domain of convergence due to local minima. This work addresses that issue by adapting a Gaussian homotopy framework for cost function smoothing from cross-correlation to the sum of squared differences (SSD) objective used in DVS. The result is a spatially varying, transformation-domain kernel that depends on the motion model, producing smoother cost landscapes and enlarging the convergence basin. We first apply the smoothing to an SSD cost, derive its corresponding transformation kernel for the motion model in the camera domain, and then incorporate it into a DVS control law. The method is compared against uniform image domain blurring via Photometric Gaussian Mixtures. Experiments with an eye-in-hand robotic arm setup over three degrees of freedom translation and with different initial poses show that cost smoothing significantly increases the convergence domain while preserving the accuracy of DVS.