A Study on the Nested Velocity Planning Method for NURBS Curves

To ensure that NURBS curve interpolation meets motion constraints during machining while maintaining low velocity fluctuations, this paper proposes a nested look-ahead velocity planning algorithm. Traditional methods require identifying feedrate-sensitive points and segmenting the curve, which may lead to local velocity exceeding the limits and can involve significant computational effort. The proposed method does not require sensitive-point detection and instead constructs the velocity profile in a globally consistent manner. The algorithm combines a backtracking S-curve acceleration/deceleration strategy to ensure compliance with motion constraints with the Gear prediction–correction method for parameter interpolation, achieving low velocity fluctuation. Through nested iterative refinement, the planned feedrate is continuously corrected until all segments satisfy the imposed constraints. Simulation results show that the method effectively prevents local velocity overshoot, significantly reduces velocity fluctuations compared with conventional second-order Taylor expansion methods, and generates feedrate profiles with continuous acceleration that minimize dynamic shocks during motion. Therefore, the proposed approach provides an effective solution for NURBS-based machining, fully meeting motion constraints while maintaining low velocity fluctuation.