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Aiming at the problem of servoing task failure caused by the manipulated object deviating from the camera field-of-view (FOV) during the robot manipulator visual servoing (VS) process, a new VS method based on an improved tracking learning detection (TLD) algorithm is proposed in this article, which allows the manipulated object to deviate from the camera FOV in several continuous frames and maintains the smoothness of the robot manipulator motion during VS. Firstly, to implement the robot manipulator visual object tracking task with strong robustness under the weak FOV constraints, an improved TLD algorithm is proposed. Then, the algorithm is used to extract the image features (object in the camera FOV) or predict image features (object out of the camera FOV) of the manipulated object in the current frame. And then, the position of the manipulated object in the current image is further estimated. Finally, the visual sliding mode control law is designed according to the image feature errors to control the motion of the robot manipulator so as to complete the visual tracking task of the robot manipulator to the manipulated object in complex natural scenes with high robustness. Several robot manipulator VS experiments were conducted on a six-degrees-of-freedom MOTOMANSV3 industrial manipulator under different natural scenes. The experimental results show that the proposed robot manipulator VS method can relax the FOV constraint requirements on real-time visibility of manipulated object and effectively solve the problem of servoing task failure caused by the object deviating from the camera FOV during the VS.