Smooth and Time Optimal Trajectory Planning for Industrial Robot Using a Single Polynomial

  • Minh-Tuan NguyenEmail author
  • Jin-Huang Huang
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 104)


This paper proposes a method for smoothing and optimizing trajectory in robotics. The trajectory in the joint space with the constraints of velocity, acceleration and jerk is interpolated by a single polynomial and the traveling time is then minimized by sequential quadratic programming algorithm. The proposed approach is performed on an industrial robot and results are compared with another planning method. The results show that the single polynomial makes the trajectory simple because only one interpolation polynomial is used while the continuity conditions of the trajectory, velocity, acceleration and jerk are simultaneously satisfied. Additionally, the optimized traveling time is also obtained.


Trajectory planning Single polynomial Time optimal trajectory Sequential quadratic programming 



This research was supported by the Ministry of Science and Technology of Taiwan under Contract Nos. MOST 107-2221-E-035-074-MY3 and MOST 107-2218-E-035-016.


  1. 1.
    Aribowo, W., Terashima, K.: Cubic spline trajectory planning and vibration suppression of semiconductor wafer transfer robot arm. Int. J. Autom. Technol. 8(2), 265–274 (2014)CrossRefGoogle Scholar
  2. 2.
    Zhang, J., Meng, Q., Feng, X., Shen, H.: A 6-DOF robot-time optimal trajectory planning based on an improved genetic algorithm. Robot. Biomim. 5(3), 1–7 (2018)Google Scholar
  3. 3.
    Williams II, R.L.: Simplified robotics joint-space trajectory generation with a via point using a single polynomial. J. Robot. 2013, 1–7 (2013)CrossRefGoogle Scholar
  4. 4.
    Chettibi, T.: Smooth point-to-point trajectory planning for robot manipulators by using radial basis functions. Robotica 37(3), 539–559 (2018)CrossRefGoogle Scholar
  5. 5.
    Huang, J., Hu, P., Wu, K., Zeng, M.: Optimal time-jerk trajectory planning for industrial robots. Mech. Mach. Theory 121, 530–544 (2018)CrossRefGoogle Scholar
  6. 6.
    Simon, D., Isik, C.: Optimal trigonometric robot joint trajectories. Robotica 9, 379–386 (1991)CrossRefGoogle Scholar
  7. 7.
    Egerstedt, M., Martin, C.F.: Optimal trajectory planning and smoothing splines. Automatica 37, 1057–1064 (2001)CrossRefGoogle Scholar
  8. 8.
    Lu, S., Zhao, J., Jiang, L., Liu, H.: Solving the time-jerk optimal trajectory planning problem of a robot using augmented lagrange constrained particle swarm optimization. Math. Probl. Eng. 2017, 1–10 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lu, S., Zhao, J., Jiang, L., Liu, H.: Time-jerk optimal trajectory planning of a 7-DOF redundant robot. Turk. J. Electr. Eng. Comput. Sci. 25, 4211–4222 (2017)CrossRefGoogle Scholar
  10. 10.
    Fang, Y., Hu, J., Liu, W., Shao, Q., Qi, J., Peng, Y.: Smooth and time-optimal S-curve trajectory planning for automated robots and machines. Mech. Mach. Theory 137, 127–153 (2019)CrossRefGoogle Scholar
  11. 11.

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Mechanical and Aeronautical EngineeringFeng Chia UniversityTaichungTaiwan, ROC
  2. 2.Department of Mechanical and Computer Aided EngineeringFeng Chia UniversityTaichungTaiwan, ROC
  3. 3.Faculty of Mechanical EngineeringHung Yen University of Technology and EducationHung YenVietnam

Personalised recommendations