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This paper proposes a unified approach for controlling the Cartesian compliance of multiple points assigned along the linkage chains of the fully actuated serial manipulator. With this method, a number of points (as much as the total number of moving linkages) and their desired compliances may be specified. Then, their motion to perform a particular operation are designated, of which the compatibility is not required. Rather, it will be accounted for automatically by the controller. The controller attempts to accomplish higher-priority tasks with the available control space while the lower-priority tasks might not be completely achieved due to task confliction or inadequate dimension of the control vector space. Additionally, with the use of generalized inverse, the method is capable of controlling the manipulator at the singularities seamlessly.