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In this paper we describe an online solution for avoiding the occurrence of both algorithmic and kinematic singularities in task-priority based kinematic controllers of robotic manipulators. The proposed approach uses a secondary task correction and a successive task projection in order to maintain the measure of manipulability of the correspondent space augmentation approach over a minimum value. It shows a gain in performance and a better task error especially when working in proximity of singular configurations. It is particularly suitable for autonomous systems where an offline trajectory control scheme is often not applicable.