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Singularity issue has been a long standing problem in task-space control of robot. It is commonly assumed in the theoretical analysis of task-space control system that the robot is operating in a finite task space such that singularity problem can be avoided. This limits the potential workspace of the robot when task-space control is employed. In this paper, a singularity-robust task-space controller is proposed for tracking control of robot manipulator. The proposed controller consists of a joint-space position controller that is activated when the robot is near singular configurations, and a task-space tracking controller that is used when the robot leaves the singular region. Therefore, the robot can start from the singular regions and transit smoothly from joint space to task space. It can also enter the singular region during the course of movement. The stability of the closed-loop system is analyzed with consideration of the singularity issue. Experimental results are presented to illustrate the performance of the proposed controller.