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This note addresses the problem of position control of robotic manipulators both nonredundant and redundant in the task space. A computationally simple class of task space regulators consisting of a transpose adaptive Jacobian controller plus an adaptive term estimating generalized gravity forces is proposed. The Lyapunov stability theory is used to derive the control scheme. The conditions on controller gains ensuring asymptotic stability are obtained herein in a form of simple inequalities including some information extracted from both robot kinematic and dynamic equations. The performance of the proposed control strategy is illustrated through computer simulations for a direct-drive arm of a SCARA type redundant manipulator with the three revolute kinematic pairs operating in a two-dimensional task space.