Aiming at the problems of low data registration success rate and insufficient pose control accuracy in traditional assembly methods for workpiece assembly tasks with planar weak geometric contour structures, an assembly method for industrial parts based on planar point cloud registration and relative pose control is proposed. First, the workpiece point cloud information is reconstructed by the binocular structured light sensor, and the obtained results are registered using the RANSAC-ICP algorithm. Then, the relationship between the plane normal vector feature and the maximum distance is corrected to achieve accurate point cloud registration. The relative pose relationship-based manipulator control method is proposed, which omits the calibration of the tool coordinate system and directly controls the manipulator movement by relative pose. Then, it takes the relative pose error as the evaluation standard of the control system error to realize the reliability assembly. Finally, experiments are conducted using a large industrial manipulator in a real test scenario. The results show that the registration success rate of the proposed method is improved by 85 percentage points compared to the traditional assembly method, and the automatic assembly accuracy is better than 0.5 mm, which means that the method can effectively solve the problem of planar workpiece assembly.