Research on fast NURBS interpolation with arc length as parameter

Aiming at the high speed and precision machining of complex parts, a fast NURBS interpolation based on arc length is proposed. Since the NURBS curve parameters have no geometric meaning, there are nonlinearly mapped to the arc length S. The arc length is difficult to calculate directly with the analytical expression, and it is difficult to plan the speed of the curve without the arc length information. Based on this, this paper uses Gauss integral to calculate the arc length of the curve, and simultaneously performs five-degree polynomial modeling on the parameters u and arc length S to establish the mapping relationship between them. At the time of interpolation, speed planning can be performed, and the next interpolation point can be quickly calculated in real time to maintain small speed fluctuations. Simulation results verify the effectiveness of the algorithm.