Smooth minimum time trajectory planning with minimal feed fluctuation

Smooth and effective feedrate profile is very important for high-speed and high-precision machining. In this paper, a two-stage feedrate scheduling scheme (TFSS) is proposed to efficiently generate the smooth feedrate profile. The minimum time trajectory planning (MTTP) is firstly employed to generate the initial feedrate profile considering constraints of both the kinematics and the chord error. To improve the computational efficiency, the MTTP is transformed into a problem of linear programming by applying direct transcription method. Then, all the sharp corners along the initial feedrate profile are identified, especially those that are interacted by each other. The jerk-limited method of eliminating interaction (JMEI) at sharp corners is applied to smooth the final feedrate profile. Finally, the improved feed correction polynomials are applied to reduce the fluctuations owing to non-arc-length parameterization. To illustrate the validity and rationality of the proposed scheme, two curves were employed to verify the proposed method. The simulation and experimental results demonstrate the efficiency of the proposed scheme for the nonuniform rational basis spline (NURBS) tool paths.