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Velocity control algorithm in glass polishing based on the cubic NURBS curve

To limit velocity fluctuations and to achieve a controllable jerk value in a glass polishing process, a new velocity control algorithm is proposed based on nonuniform rational B-splines (NURBS). The key of this algorithm is replacing the traditional linear acceleration–deceleration with flexible NURBS acceleration–deceleration. Based on the linear acceleration–deceleration algorithm, the control points of the NURBS curve are confirmed, and the final velocity of the polishing wheel center is solved using the Preston equation. With jerk continuity and limitations of the servo system, nonlinear equations are constructed, and the weighting factors corresponding to the control points are obtained. Cubic velocity control equations can be derived from the obtained feature parameters, which include the final velocity, control points, weighting factors and knot vectors. Based on the proposed NURBS acceleration–deceleration algorithm, a fourth-order Runge–Kutta formula was used to obtain the initial points, and the Milne–Hamming equation was used to predict and correct the next point. The predictor-corrector interpolation algorithm for parametric trajectory was implemented during the polishing process. The experimental results indicate that the proposed approach guarantees limited fluctuations of the relative velocity at contact points and ensure smoother velocity changes at dangerous points.