Robots used in machining processes are more prone to inaccurate motion due to low location accuracy and asymmetrical structure. In this paper, a new method for improving robot motion precision was proposed to correct machining trajectory and improve stability of the robotic system on machining welding groove of complex integral impeller. First, the flange curves are extracted and equidistantly discretized; the corresponding discrete points on the central axis are obtained according to impeller 3D model. Then, according to the central point and symmetrical mapping theory, the corresponding discrete points of the central axis and the cover tray curve are obtained in turn, and the discrete points of the cover tray curve are smoothly connected to form the cover curve, which is the theoretical curve after processing. The distance between the cover curve and the flange curve is the machining allowance. Second, a unification of different coordinates of platform system is obtained based on coordinates transformation, and gravity compensation is accomplished to obtain the contact force. Third, the cutter tool keeps close contact with the flange curve along the feed motion and reads the actual position of the flange curve by in situ force/position control. The actual trajectory of the flange curve and the deviation between theoretical and actual trajectory was achieved. Finally, the actual cover tray curve is achieved by offsetting the machining allowance along the cutting depth with the actual trajectory. In this way, the positioning accuracy of the robot can be controlled by controlling the repetitive positioning accuracy, and the subsequent variable depth cutting can be realized. Experiments were performed to verify the benefits of correcting machining trajectory to achieve the machining of variable cutting depth on welding groove of blade and improve machining accuracy. © 2019, Springer-Verlag London Ltd., part of Springer Nature.