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Continuity of Varying-Feature-Set Control Laws

Classical sensor-based control laws are based on the regulation of a set of features to a desired reference value. In this paper, we focus on the study of control laws whose feature set varies during the servo. In that case, we first show that the classical control laws that use an iterative least-square minimization are discontinuous. We then show that these discontinuities are due to the pseudo-inverse operator, which is not continuous at matrix rank change. To solve this problem, we propose a new inversion operator. This operator is equal to the classical pseudo-inverse operator in the continuous cases, and ensures the continuity everywhere. This operator is then used to build a new control law. This general control scheme is applied to visual servoing, in order to ensure the continuity of the control law when some visual features leave the camera field of view. The experiments prove the interest and the validity of our approach.