Sliding mode control with third-order contour error estimation for free-form contour following

Abstract

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.