Algorithms for time-optimal control of CNC machines along curved tool paths

By Sebastian D. Timar, Rida T. Farouki, Tait S. Smith, Casey L. Boyadjieff. 2005

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Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds (2007, methodology): “The case in which all axes are in the ‘‘constant’’ regime is covered by our earlier study [9], but cases involving one or more of the axes in the ‘‘mixed’’ regime have not been previously addressed.”
Design of a real-time adaptive NURBS interpolator with axis acceleration limit (2010, methodology): “A time-optimal interpolator with constant axis acceleration bound was presented by Timar et al. [ 24 ].”
Feedrate optimization for smooth minimum-time trajectory generation with higher order constraints (2016, background): “There are a number of trajectory planning algorithms which generate trajectory to drive a manipulator or motion stage with constraints on joint torques or actuator forces along a given geometric path in minimum or near-minimum time [1–8].”