A novel scheme for flexible NURBS-based C2 PH Spline Curve contour following task using Neural Network

Abstract

In this paper, a novel scheme for approximation of complicated CNC tool paths, designed by non-uniform rational B-spline (NURBS) curves, is proposed. The idea of this approximation is based on introducing flexible NURBS-based C2 PH Spline Curves. Using the specifications of nodal points on a NURBS curve and introducing the coefficients for the velocity and acceleration vectors on these points, as well as defining flexible connection nodes, a new method is presented to design a tool path via C2 PH spline curves. Values of the velocity/acceleration vector coefficients corresponding to the flexible connection nodes on the original NURBS curve are computed by genetic algorithm and Neural Network. To this end, the normal distance between the tool path and its corresponding original NURBS curve is considered as the objective function. Using combination of the time-dependent feedrate and constant feedrate interpolations, the position commands of the designed curve are generated. Several contour following tasks were implemented with pseudo-derivative feedback feed forward (PDFF) controller. Experimental and simulation results confirm that the devised interpolator is not only feasible for machining the complicated tool path represented in the improved NURBS-based C2 PH spline form but also yields satisfactory contouring performance under variable feedrate.