Chapter 2 Empirical Characterization of Convergence Properties for Kernel-based Visual Servoing

Abstract. Visual servoing typically involves separate feature tracking and control processes. Feature tracking remains an art, and is generally treated as independent of the underlying controller. Kernel-based visual servoing (KBVS) is a categorically different approach that eliminates explicit feature tracking. This chapter presents an experimental assessment of the convergence properties (domain of attraction and steady-state error) of the proposed approach. Using smooth weighting functions (the kernels) and Lyapunov theory, we analyze the controllers as they act on im-ages acquired in controlled environments. We ascertain the domain of attraction by finding the largest positive invariant set of the Lyapunov function, inside which its time derivative is negative definite. Our experiments show that KBVS attains a maximum pixel error of one pixel and is commonly on the order of one tenth of a pixel. 2.1 Featureless Visual Servoing Typically, visual servoing involves tracking image features and controlling a robot based on the motions of these image features. Usually this involves tuning the fea-ture tracking algorithm and controller independently, with no clear notion of how to co-optimize tracking and control. KBVS is distinguished from traditional visual servoing techniques in two respects, namely the lack of explicit feature tracking at each image frame and the inherent combination of tracking and control. Thes