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This paper presents the reverse priority impedance control of manipulators with reference to redundant robots of a given task. The reverse priority kinematic control of redundant manipulators is first expressed in detail. The motion in the joint space is derived following the opposite order compared with the classical task priority–based solution. Then the Cartesian impedance control is combined with the reverse priority impedance control to solve the reverse hierarchical impedance controlled, so that the Cartesian impedance behavior can be divided into the primary priority impedance control and the secondary priority impedance control. Furthermore, the secondary impedance control task will not disturb the primary impedance control task. The motion in the joint space is affected following the opposite order and working in the corresponding projection operators. The primary impedance control tasks are implemented at the end, so as to avoid the possible deformations caused by the singularities occurring in the secondary impedance control tasks. Hence, the proposed reverse priority impedance control of manipulator can achieve the desired impedance control tasks with proper hierarchy. In this paper, the simulation experiments of the manipulator will verify the proposed reverse priority control algorithm. [ABSTRACT FROM AUTHOR]