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Task-space regulation of robot manipulators can be classified into two fundamental approaches, namely, transpose Jacobian regulation and inverse Jacobian regulation. In this paper, two inverse Jacobian regulators with gravity compensations are presented, and the stability problems are formulated and solved. It is shown that the inverse Jacobian systems can be stabilized, and there exists a region of attraction such that the system remains stable. Our results show that the two fundamental approaches are two dual controllers, in the sense that the transpose Jacobian matrix can be replaced by the inverse Jacobian matrix and vice versa. The theoretical results are verified experimentally by implementing the inverse Jacobian regulators on an industrial robot, PUMA560.