To reduce the contour error in contour-following tasks, the most common method is to design a contour controller based on the contour error model. Therefore, how to estimate the contour error in real-time and with high accuracy plays an important role in contour-following control. It is difficult to guarantee real-time performance, high estimation accuracy and strong robustness against arbitrary trajectories at the same time. In this paper, a contour error estimation method based on the third-order osculating helix is proposed. The osculating helix can fully consider the geometric characteristics of the interpolation trajectory and is closer to the desired interpolation trajectory. On this basis, PD-type tracking error sliding mode surface and PD-type contour error sliding mode surface are redesigned to fully take into account the regulating effect of the velocity tracking error and velocity contour error. Experimental results demonstrate the effectiveness of the proposed contour control approach.

为了减少轮廓跟随任务中的轮廓误差，最常用的方法是基于轮廓误差模型设计轮廓控制器。因此，如何实时，高精度地估计轮廓误差在轮廓跟随控制中起着重要的作用。难以同时保证实时性能，高估计精度和针对任意轨迹的强大鲁棒性。提出了一种基于三阶逼近螺旋的轮廓误差估计方法。闭合螺旋线可以充分考虑插值轨迹的几何特性，并且更接近所需的插值轨迹。在此基础上，重新设计了PD型跟踪误差滑模曲面和PD型轮廓误差滑模曲面，以充分考虑到速度跟踪误差和速度轮廓误差的调节效果。实验结果证明了提出的轮廓控制方法的有效性。