A novel contour error estimation in biaxial contouring control

The objective of the multi-axis coordinated control system is to minimize the contour error which is the minimal distance from the actual position to the desired trajectory. Contour error estimation is of importance during the contouring control. Conventional researches adopt a way that approximating the contour error by the distance from the actual position to the tangent line or plane at the desired position. However, it suffers from the case of overcutting and undercutting. In this paper, a novel contour error estimation approach, based on the geometric properties of the desired trajectory, is proposed. In this case, the contour error is evaluated in the way that taking the difference between the current radius and the radius of the curvature at the desired position. It is found that the proposed approach gives a better result in the evaluation of contour error when tracking trajectories with both constant curvature and nonconstant curvature. Moreover, the proposed approach gives a better tracking result when the cross-coupled control, based on the stable close loops of individual servo axis, is designed to achieve the contouring control.