Three-dimensional iterative contour error estimation based on an orthogonal cross-coupled control approach

This paper shows that the timed trajectory tracking in traditional cross-coupled control (CCC) methods would cause the foot point backstepping and discontinuity for iterative contour error estimation methods in the corner. To address the problems, we propose an orthogonal CCC (OCCC) method for three-dimensional smooth and discrete reference contours, where the feed direction depends on the real-time estimated foot point and is orthogonal to the contouring direction. The spatial velocity field composed of the feed-direction velocity commands would attract the actual point to travel the complete reference trajectory smoothly. Comparative experiments are conducted, and the results indicate that the proposed OCCC method can significantly reduce the number of iterations and obtain better convergence stability. Moreover, the curve parameter of the estimated foot point can increase continuously in the whole reference trajectory, and the contour error vector can smoothly sweep through the corner, resulting in better contouring control and measurement.