Certified space curve fitting and trajectory planning for CNC machining with cubic B-splines. (January 2019) - Lin, Fengming; Shen, Li-Yong; Yuan, Chun-Ming; Mi, Zhenpeng
Abstract: In CNC machining, the tool path following G01 codes generally introduces large computations and inherent discontinuities. A common way to avoid these shortcomings is fitting the G01 polyline with a parametric curve and then scheduling the feedrate along the fitted curve. However, curve fitting with confined error in three dimensional space is nontrivial since the Hausdorff distance between a space G01 segment and a rational parametric curve segment is difficult to formulate. In this paper, we derive the explicit expression for the Hausdorff distance between a line segment and a curve segment, and then propose a curve fitting algorithm for G01 polylines. Instead of the traditional two-stage model, we present a combined trajectory planning model with error constraints as well as dynamic constraints. Moreover, an effective and efficient algorithm is designed to solve this model. Experimental results are provided to illustrate and clarify our methods. Highlights: An explicit Hausdorff distance is given for a line segment and a curve segment. A space curve fitting algorithm with confined error for space G01 polylines is given. A two-to-one trajectory planning model is proposed for space G01 polylines. An effective and efficient algorithm is designed to solve the two-to-one model.