Smooth minimum time trajectory planning with minimal feed fluctuation

  • Kai ZhaoEmail author
  • Shurong Li
  • Zhongjian Kang


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.


Minimum time Trajectory planning Linear programming NURBS interpolation Feedrate planning 


Funding information

This work is supported by the National Natural Science Foundation of China (grant number 61573378). This work is also partially supported by the Key Technologies R&D Program of Henan province (grant number 182102210197).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information and Control EngineeringChina University of Petroleum (East China)QingdaoChina
  2. 2.College of Computer Science and Information EngineeringAnyang Institute of TechnologyAnyangChina
  3. 3.School of AutomationBeijing University of Posts and TelecommunicationsBeijingChina

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