Visual Servo Control Part II : Advanced Approaches

his article is the second of a two-part tutorial on visual servo control. In Part I (IEEE Robotics and Automation Magazine, vol. 13, no. 4), we introduced fundamental concepts and descr ibed basic approaches. Here we discuss more advanced concepts , and present a number of recent approaches. As described in Part I of the tutorial, visual servo schemes rely on the relationship ˙ s = L s v c (1) in which s is a set of geometrical features whose time derivative ˙ s is linearly related to the spatial velocity v c of the camera through the interaction matrix L s. Using this relationship, control schemes are designed to minimize the error e between the current value of the visual feature s and its desired value s * : e = s − s *. A classical proportional control scheme is given by: v c = −λ L + e e, (2) where L e is defined by ˙ e = L e v c , (3) and L + e is an approximation of the pseudo-inverse of L e. An approximation must be used because visual servo schemes require the values of three-dimensional (3-D) parameters that are not available directly from the image measurements. Recall that for position-based visual servo (PBVS) schemes 3-D parameters appear both in the error e and in the interaction matrix, while for basic image-based visual servo (IBVS), the depth of each point considered appears in the coefficients of the interaction matrix related to the transla-tional motions. This is the case even when L + e = L e * + is used in the control scheme, although in this case only the depth Z * of each point for the desired pose is needed, which is generally not difficult to obtain in practice. In all other cases, an estimation of the current depth must be made at each iteration of the control scheme. We begin Part II of the tutorial by describing two approaches to estimating the interaction matrix. First we describe how epipolar geometry can be used to estimate the 3-D parameters, which can then be used to construct the interaction matrix. We then describe how it is possible to estimate directly the numerical value of L + e. With these methods in hand, we then present more advanced techniques in visual servo control. These techniques aim to compensate for the …