Skip to main content
SpringerLink
Log in

Trajectory Planning of Rail Inspection Robot Based on an Improved Penalty Function Simulated Annealing Particle Swarm Algorithm

  • Regular Papers
  • Robot and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

To ensure the smooth operation of each joint and shorten the joint movement time of a rail inspection robot, a trajectory planning method based on time optimization with a penalty function is proposed. According to the Denavit-Hartenberg (D-H) model of the inspection robot, a kinematic solution is found, and the trajectory of each joint is generated using a mixed polynomial interpolation algorithm. Taking time optimization as the standard, the traditional particle swarm algorithm cannot handle complex constraints, easily falls to local optimum solutions, and has a slow convergence speed. An improved simulated annealing particle swarm algorithm with a penalty function (IPF-SA-PSO) is proposed to optimize the trajectory generated by the mixed polynomial interpolation algorithm. The simulation results show that the proposed algorithm, compared with the mixed polynomial interpolation method, can limit the angular velocity and reduce the running time of each manipulator joint. The two algorithms are experimentally verified based on a rail inspection robot, and the results show that after adopting the optimization algorithm, the angular velocity of each joint is within the angular velocity limit, the run time is shorter, and the operation is smoother, which indicates the effectiveness of the proposed algorithm. The proposed algorithm can optimize the robot running time, improve the smoothness, and be applied to the fields of the automatic tracking of abnormal targets and video acquisition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. N. Zhang, J. Y. Tian, and J. Long, “Research on multi-source and multi-period grey-evidential fusion evaluation model of porcine abnormal behaviors,” Heilongjiang Animal Science and Veterinary, no. 12, pp. 37–41, 2021.

    Google Scholar 

  2. K. B. Shi, J. Wang, Y. Y. Tang, and S. M. Zhong, “Reliable asynchronous sampled-data filtering of T–S fuzzy uncertain delayed neural networks with stochastic switched topologies,” Fuzzy Sets and Systems, vol. 381, pp. 1–25, 2020.

    Article  MathSciNet  MATH  Google Scholar 

  3. L. F. Hua, H. Zhu, K. B. Shi, S. M. Zhong, Y. Q. Tang, and Y. J. Liu, “Novel finite-time reliable control design for memristor-based inertial neural networks with mixed time-varying delays,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 68, no. 4, pp. 1599–1609, 2021.

    Article  MathSciNet  Google Scholar 

  4. X. Cai, K. B. Shi, S. M. Zhong, J. Wang, and Y. Q. Tang, “Dissipative analysis for high speed train systems via looped-functional and relaxed condition methods,” Applied Mathematical Modelling, vol. 96, pp. 570–583, 2021.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Y. Zhang, A. M. Zanchettin, and R. Villa, “Real-time trajectory planning based on joint-decoupled optimization in human-robot interaction,” Mechanism and Machine Theory, vol. 144, pp. 1–22, 2020.

    Article  Google Scholar 

  6. H. Wang, H. Wang, and J. H. Huang, “Smooth point-to-point trajectory planning for industrial robots with kine-matical constraints based on high-order polynomial curve,” Mechanism and Machine Theory, vol. 139, pp. 284–293, 2019.

    Article  Google Scholar 

  7. W. F. Xu, C. Li, and X. Q. Wang, “Study on non-holonomic Cartesian path planning of a free-floating space robotic system,” Advanced Robotics, vol. 23, no. 1, pp. 113–143, 2012.

    Google Scholar 

  8. W. J. Wang, T. Qing, and Y. T. Cao, “Robot time-optimal trajectory planning based on improved cuckoo search algorithm,” IEEE Access, vol. 8, pp. 86923–86933, 2020.

    Article  Google Scholar 

  9. M. M. Wang, J. J. Luo, and U. Walter, “Trajectory planning of free-floating space robot using particle swarm optimization (PSO),” Acta Astronautica, vol. 112, pp. 77–88, 2015.

    Article  Google Scholar 

  10. G. H. Yang, H. Lee, and Y. S. Ryuh, Development of a 3-DOF Fish Robot ‘ICHTHUS V5’, 2013.

  11. X. R. Xu, X. G. Wang, and F. Qin, “Trajectory planning of robot manipulators by using spline function approach,” Proc. of 3rd World Congress on Intelligent Control and Automation, pp. 1215–1219, 2000.

  12. C. K. Xiong, D. F. Chen, and D. Lu, “Path planning of multiple autonomous marine vehicles for adaptive sampling using Voronoi-based ant colony optimization,” Robotics and Autonomous Systems, vol. 15, pp. 90–103, 2019.

    Article  Google Scholar 

  13. B. A. Shafaat and T. Bertrand, “Robot time-optimal trajectory planning based on improved cuckoo search algorithm,” Proc. of IEEE International Symposium on Assembly and Task Planning (ISATP’97) - Towards Flexible and Agile Assembly and Manufacturing, pp. 1–6, 1997.

  14. A. Abraham, L. Jain, and R. Goldberg, Evolutionary Multiobjective Optimization, Springer London, 2005.

    Book  MATH  Google Scholar 

  15. X. Li, D. Wu, and J. J. He, “An improved method of particle swarm optimization for path planning of mobile robot,” Journal of Control Science and Engineering, vol. 2020, pp. 1–12, 2020.

    Article  MATH  Google Scholar 

  16. S. Paulo, I. Getúlio, and A. Paulo, “Hybrid PSO-cubic spline for autonomous robots optimal trajectory planning,” Proc. of 21st International Conference on Intelligent Engineering Systems Larnaca, pp. 131–136, 2017.

  17. A. Khare and S. Rangnekar, “A review of particle swarm optimization and its applications in solar photovoltaic system,” Applied Soft Computing, vol. 144, no. 5, pp. 2997–3006, 2013.

    Article  Google Scholar 

  18. P. I. Adamu, H. I. Okagbue, and P. E. Oguntunde, “Fast and optimal path planning algorithm (FAOPPA) for a mobile robot,” Wireless Personal Communications, vol. 106, no. 2, pp. 577–592, 2019.

    Article  Google Scholar 

  19. B. Song, Z. Wang, and L. Zou, “A new approach to smooth global path planning of mobile robots with kinematic constraints,” International Journal of Machine Learning and Cybernetics, vol. 10, no. 1, pp. 107–119, 2017.

    Article  Google Scholar 

  20. J. J. Kim and J. J. Lee, “Trajectory optimization with particle swarm optimization for manipulator motion planning,” IEEE Transactions on Industrial Informatics, vol. 11, no. 3, pp. 620–631, 2015.

    Article  Google Scholar 

  21. C. Liu, G. H. Cao, and Y. Y. Qu, “An improved PSO algorithm for time-optimal trajectory planning of delta robot in intelligent packaging,” International Journal of Advanced Manufacturing Technology, vol. 107, no. 3, pp. 1091–1099, 2019.

    Google Scholar 

  22. M. M. Wang, J. J. Luo, and J. P. Yuan, “Coordinated trajectory planning of dual-arm space robot using constrained particle swarm optimization,” Acta Astronautica, vol. 146, pp. 259–272, 2018.

    Article  Google Scholar 

  23. P. Zhang, X. Z. Lai, and Y. W. Wang, “Chaos-PSO-based motion planning and accurate tracking for position-posture control of a planar underactuated manipulator with disturbance,” International Journal of Control, Automation, and Systems, vol. 19, no. 10, pp. 3511–3521, 2021.

    Article  Google Scholar 

  24. M. Locatelli, “Convergence properties of simulated annealing for continuous global optimization,” Journal of Applied Probability, vol. 33, no. 4, pp. 1127–1140, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  25. Z. Wang, H. Chen, X. Y. Yao, and D. L. Li, “Adaptive tracking of double pendulum crane with payload hoisting/lowering,” Automation in Construction, vol. 141, pp. 1–15, 2022.

    Google Scholar 

  26. H. Chen and N. Sun, “An output feedback approach for regulation of 5-DOF offshore cranes with ship yaw and roll perturbations,” IEEE Transactions on Industrial Electronics, vol. 69, no. 2, pp. 1705–1716, 2021.

    Article  MathSciNet  Google Scholar 

  27. J. X. Zhao, H. W. Wang, and W. Z. Liu, “A learning-based multiscale modelling approach to real-time serial manipulator kinematics simulation,” Neurocomputing, vol. 390, pp. 280–293, 2020.

    Article  Google Scholar 

  28. C. H. Zheng, Y. X. Su, and P. C. Müller, “Simple online smooth trajectory generations for industrial systems,” Mechatronics, vol. 19, no. 4, pp. 571–576, 2009.

    Article  Google Scholar 

  29. Y. Guo and L. Guang, “Review of joint space trajectory planning and optimization for industrial robot,” Journal of Mechanical Transmission, vol. 44, no. 2, pp. 154–165, 2020.

    MathSciNet  Google Scholar 

  30. R. Y. Xu, J. Y. Tian, and X. P. Zhai, “Research on improved hybrid polynomial interpolation algorithm for rail inspection robot,” Proc. of 5th International Conference on Electronic Information Technology and Computer Engineering, pp. 1207–1213, 2021.

  31. J. Kennedy and R. Eberhart, “Particle swarm optimization,” Proc. of International Conference on Neural Networks, vol. 4, pp. 1942–1948, 1995.

    Article  Google Scholar 

  32. J. Min and D. Wu, “Collision-free and energy-saving trajectory planning for large-scale redundant manipulator using improved PSO,” Mathematical Problems in Engineering, pp. 1–8,2013.

  33. Y. Shi and R. Eberhart, “A modified particle swarm optimizer,” Proc. of IEEE International Conference on Evolutionary Computation Proceedings and IEEE World Congress on Computational Intelligence, pp. 69–73, 1998.

  34. K. M. Zheng, Y. M. Hu, and B. Wu, “Trajectory planning of multi-degree-of-freedom robot with coupling effect,” Journal of Mechanical Science and Technology, vol. 33, no. 1, pp. 413–421, 2019.

    Article  Google Scholar 

  35. C. Y. Si, T. Lan, and J. J. Hu, “Penalty parameter of the penalty function method,” Control and Decision, vol. 29, no. 9, pp. 1707–1710, 2014.

    Google Scholar 

  36. F. Javidrad and M. Nazari, “A new hybrid particle swarm and simulated annealing stochastic optimization method,” Applied Soft Computing, vol. 60, pp. 634–654, 2017.

    Article  Google Scholar 

  37. N. Metropolis, A. W. Rosenbluth, and M. N. Rosenbluth, “Equation of state calculations by fast computing machines,” The Journal of Chemical Physics, vol. 21, no. 6, pp. 1087–1092, 1953.

    Article  MATH  Google Scholar 

  38. D. Yang, T. Lu, and W. X. Guo, “MIT image reconstruction method based on simulated annealing particle swarm algorithm,” Journal of Northeastern University(Natural Science), vol. 42, no. 4, pp. 531–537, 2021.

    Google Scholar 

  39. P. J. M. V. Laarhoven and H. L. A. Aarts, Simulated Annealing: Theory and Applications, Springer, Dordrecht, 1987.

    Book  MATH  Google Scholar 

  40. L. Y. Zhang, Y. Z. Ma, and M. M. Ren, “Multi-response robust parameter design based on RMS error modeling,” Statistics and Decision, vol. 36, no. 6, pp. 20–25, 2020.

    Google Scholar 

  41. M. Y. Li, H. Chen, and R. Zhang, “An input dead zones considered adaptive fuzzy control approach for double pendulum cranes with variable rope lengths,” IEEE/ASME Transactions on Mechatronics, vol. 27, no. 5, pp. 3385–3396, 2022.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Electrical and Power Engineering, Taiyuan University of Technology, 79 Yingze-west-street, Taiyuan, Shanxi, China

    Ruoyu Xu, Jianyan Tian, Jifu Li & Xinpeng Zhai

Authors
  1. Ruoyu Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianyan Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jifu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xinpeng Zhai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianyan Tian.

Ethics declarations

The authors declare that there is no competing financial interest or personal relationship that could have appeared to influence the work reported in this paper.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was supported by the Nature Science Foundation of Shanxi Province of China under Grant 201901D111092.

Ruoyu Xu received his B.S. degree from the School of Electrical Engineering from Southwest Jiaotong University, ChengDu, China in 2019. He is an M.S. student in the College of Electrical and Power Engineering, Taiyuan University of Technology, China. His research interests include intelligent robots and robot control.

Jianyan Tian received her B.S. degree in automation and her M.S. degree in control science and engineering both from Taiyuan University of Technology (TYUT), TaiYuan, China, in 1988 and 1993, respectively. She received her Ph.D. degree in system engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2008. She is a Professor at College of Electrical and Power Engineering, TYUT. Her research interests include modeling of complex systems, intelligent control systems, and intelligent robot.

Jifu Li received his B.S. degree from the School of Automation from Beijing Institute of Technology, BeiJing, China, in 2017 and his M.S. degree from the Department of Electrical & Computer Engineering from Texas A&M University, Texas, USA, in 2019. He is a Ph.D. student in the College of Electrical and Power Engineering, Taiyuan University of Technology, China. His research interests include intelligent robots.

Xinpeng Zhai received his B.S. degree from the School of Electrical Engineering and Automation from Qilu University of Technology, Jinan, China, in 2017 and his M.S. degree in automatization from Institute of Automation Shandong Academy of Sciences, Jinan, China, in 2019. He is a Ph.D. student in the College of Electrical and Power Engineering, Taiyuan University of Technology, China. His research interests include intelligent robot and robot control.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, R., Tian, J., Li, J. et al. Trajectory Planning of Rail Inspection Robot Based on an Improved Penalty Function Simulated Annealing Particle Swarm Algorithm. Int. J. Control Autom. Syst. 21, 3368–3381 (2023). https://doi.org/10.1007/s12555-022-0163-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-022-0163-z

Keywords

Search

Navigation