This paper proposes a unified approach for controlling the Cartesian compliance of multiple points assigned along the linkage chains of the manipulator. The method applies two key frameworks. Task-priority based control is used to synergistically plan the tasks of the advanced manipulation according to their relative priority. Then, the impedance control scheme is employed for implementing the controller. Additionally, with the use of generalized inverse theory throughout the development, the method is capable of controlling the manipulator at the singularities seamlessly. This low-level control system may be integrated with the high-level manipulation planning algorithm, which generates the online dynamical tasks based on the desired behavior and the sensor information, to accomplish the demanding operation.

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