A curve fitting method, apparatus and device based on a drawing tool for improving the accuracy of curve fitting. The method includes: determining a fitting area containing the original curve, in the fitting area, performing at least one sub-fitting operation on the original curve until the end condition of the curve fitting is satisfied, and generating a fitting curve corresponding to the original curve based on the fitting curve corresponding to each sub-fitting operation. This method can fit the original curve segments in the fitting area, which improves the accuracy of the obtained fitting curve.

This invention, a feedrate scheduling method for five-axis dual-spline curve interpolation, belongs to multi-axis NC (Numerical Control) machining filed, featured a feedrate scheduling method with constant speed at feedrate-sensitive regions under axial drive constraints for five-axis dual-spline interpolation. This method first discretizes the tool-tip spline with equal arc length, thus getting the relation between the axial motion and the toolpath by computing the first, second, and third order derivatives of the axial positions with respect to the tool-tip motion arc length. After that, determine the feedrate-sensitive regions with the constraints of axial drive limitations and the objective of balanced machining quality and efficiency. Finally, determine the acceleration/deceleration-start-point curve parameters by bi-directional scanning. The invented method can effectively make a balance between the feed motion stability and efficiency in five-axis machining, and possesses a high computational efficiency and a good real-time capability.

A numerical controller that creates a tool path from a plurality of command points includes: a command point sequence acquisition unit that acquires an existing command point sequence; a command point creating unit that creates at least one additional command point, based on the existing command point sequence; and an interpolation processing unit that interpolates the existing command point sequence and the additional command point to create the tool path. The command point creating unit outputs, as the additional command point, an intersection point Q1 between an arc C1 passing through consecutive three command points, P0, P1 and P2, in the existing command point sequence and a perpendicular bisector of a line segment whose end points are P1 and P2.

A method for minimizing tracking errors in dynamic systems including obtaining desired trajectory data of the dynamic system, obtaining a set of constraints on at least one of the desired and actual trajectories of the dynamic system, obtaining a set of uniform or non-uniform rational B-splines having known original B-spline basis functions but unknown B-spline coefficients, applying a trajectory optimization process to the desired trajectory data including applying forward filtering to B-spline basis functions and utilizing the original and filtered B-spline basis functions to select optimal coefficients of the B-splines, and outputting an optimal motion command signal in response to the trajectory optimization process to the dynamic system such that a resultant actual trajectory is substantially equal to the desired trajectory while satisfying the set of constraints on the at least one of the desired and actual trajectories.

This invention, a feedrate scheduling method for five-axis dual-spline curve interpolation, belongs to multi-axis NC (Numerical Control) machining filed, featured a feedrate scheduling method with constant speed at feedrate-sensitive regions under axial drive constraints for five-axis dual-spline interpolation. This method first discretizes the tool-tip spline with equal arc length, thus getting the relation between the axial motion and the toolpath by computing the first, second, and third order derivatives of the axial positions with respect to the tool-tip motion arc length. After that, determine the feedrate-sensitive regions with the constraints of axial drive limitations and the objective of balanced machining quality and efficiency. Finally, determine the acceleration/deceleration-start-point curve parameters by bi-directional scanning. The invented method can effectively make a balance between the feed motion stability and efficiency in five-axis machining, and possesses a high computational efficiency and a good real-time capability.

A numerical controller that creates a tool path from a plurality of command points includes: a command point sequence acquisition unit that acquires an existing command point sequence; a command point creating unit that creates at least one additional command point, based on the existing command point sequence; and an interpolation processing unit that interpolates the existing command point sequence and the additional command point to create the tool path. The command point creating unit outputs, as the additional command point, an intersection point Q1 between an arc C1 passing through consecutive three command points, P0, P1 and P2, in the existing command point sequence and a perpendicular bisector of a line segment whose end points are P1 and P2.

A method for minimizing tracking errors in dynamic systems including obtaining desired trajectory data of the dynamic system, obtaining a set of constraints on at least one of the desired and actual trajectories of the dynamic system, obtaining a set of uniform or non-uniform rational B-splines having known original B-spline basis functions but unknown B-spline coefficients, applying a trajectory optimization process to the desired trajectory data including applying forward filtering to B-spline basis functions and utilizing the original and filtered B-spline basis functions to select optimal coefficients of the B-splines, and outputting an optimal motion command signal in response to the trajectory optimization process to the dynamic system such that a resultant actual trajectory is substantially equal to the desired trajectory while satisfying the set of constraints on the at least one of the desired and actual trajectories.