A complete S-shaped feedrate scheduling algorithm with variable acceleration limits

Abstract The conventional S-shaped feedrate scheduling method requires zero starting and ending acceleration to achieve smooth acceleration, which may result in frequent acceleration oscillations in CNC machines, particularly when processing G codes with numerous short length segments. To address this problem, we propose a novel S-shaped algorithm that allows for non-zero starting and ending acceleration, while also accounting for maximum acceleration and maximum velocity constraints. By incorporating this approach along with a bidirectional scanning strategy across all segments, we effectively group them into larger blocks suitable for planning the acceleration from 0 to 0. Subsequently, within each block, a bisection search algorithm is employed to determine the maximum velocity, thereby optimizing the scheduling process. This methodology offers enhanced flexibility by considering varying acceleration limits as well as starting and ending point accelerations across segments within a block, making it more applicable to practical scenarios compared to traditional methods. Simulation and experimental results further validate the effectiveness of our algorithm in reducing machining time without compromising accuracy.