Spline-Based Time-Optimal Control for Smooth Trajectory Generation of CNC Machines with Geometric Constraints

High demands in a modern industry require computerized numerical control machines to accurately track the desired workpiece contour in a minimum motion time for productivity. Generally, minimum motion time and accuracy are contradictory; therefore, the machine slows down tracking in the workpieces with strict geometric constraints. This study presents time optimal trajectory generation of the workpieces, focusing on straight-line, circle, and spline contour segments by considering fitting errors as geometric constraints. For machining purposes, the given workpiece is divided into several G-code segments represented by the piecewise continuous functions for trajectory generation. In this study, the cubic B-spline function represents each segment trajectory, and the optimal control problem is formulated. The effectiveness is investigated considering different geometric constraints, and the motion time of the resulting trajectories are compared and discussed.