Empirical Characterization of Convergence Properties for Kernel-based Visual Servoing - Visual Servoing via Advanced Numerical Methods - page 20

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

John P. Swensen, Vinutha Kallem, and Noah J. Cowan

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
apixel.

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. These