On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Computer Control of Manufacturing Systems
Computer Control of Manufacturing Systems
Numerical Methods
International Journal of Robotics and Automation
Contour error reduction for free-form contour following tasks of biaxial motion control systems
Robotics and Computer-Integrated Manufacturing
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Algorithms are developed to compute the feedrate variation along a curved path, that ensures minimum traversal time for a 3-axis CNC machine subject to both fixed and speed-dependent axis acceleration bounds arising from the output-torque characteristics of the axis drive motors. For a path specified by a polynomial parametric curve, the time-optimal feedrate is determined as a piecewise-analytic function of the curve parameter, with segments that correspond to saturation of the acceleration along one axis under constant or speed-dependent limits. Break points between the feedrate segments may be computed by numerical root-solving methods. For segments that correspond to fixed acceleration bounds, the (squared) optimal feedrate is rational in the curve parameter. For speed-dependent acceleration bounds, the optimal feedrate admits a closed-form expression in terms of a novel transcendental function whose values may be efficiently computed, for use in real-time control, by a special algorithm. The optimal feedrate admits a real-time interpolator algorithm, that can drive the machine directly from the analytic path description. Experimental results from an implementation of the time-optimal feedrate on a 3-axis CNC mill driven by an open-architecture software controller are presented. The algorithm is a significant improvement over that proposed in [Farouki RT, Rajan VT. Algorithms for polynomials in Bernstein form. Comput Aided Geometric Des 1988;5:1-26], since the addition of motor voltage constraints precludes the possibility of arbitrarily high speeds along linear or near-linear path segments.