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This paper presents a novel adaptive controller for image-based visual servoing using generalized image features. The key idea lies in the development of the depth-independent interaction matrix and the proposal of an adaptive algorithm for estimating the unknown geometric parameters of the features in the 3D space. Furthermore, we derive the conditions for the asymptotic stability of the proposed controller and demonstrate that the conditions are satisfied for six types of common image features: points, lines, distances, angles, areas, and centroids. Experiments have been conducted to validate the proposed controller.