Adaptive visual servoing using common image features with unknown geometric parameters

This paper generalizes the concept of the depth-independent interaction matrix, developed for point and line features in our early work, to generalized image features. We derive the conditions under which the depth-independent interaction matrix can be linearly parameterized by the geometric parameters of the generalized image features, and propose an adaptive visual servo controller for robot manipulators using the generalized image features whose geometric parameters are unknown. To estimate the unknown parameters on-line, we propose new error functions that are linear to estimation errors of the parameters and an algorithm that minimizes the error functions using multiple images. The Lyapunov theory is used to prove asymptotic stability of the proposed controller based on the nonlinear dynamics of the manipulator. It is also shown that in addition to points and lines, other common image features like distances, angles, areas, and centroids all satisfy the conditions for the linear parameterization. Experiments have been conducted to validate the proposed control method.