Positioning error compensation on two-dimensional manifold for robotic machining

•A new method is proposed to improve the efficiency of error compensation for robots in aircraft industry.•The two-dimensional manifolds reduce the workspace's dimensionality from 6 to 2 to avoid the curse of dimensionality.•The continuity of robot's kinematic parameters and positioning errors in the new workspace are mathematically proved.•The feasibility of proposed method is validated by experiments conducted on a typical industrial robot.•The whole process of error compensation can be performed with the help of the integrated controlling system quickly.