Hostname: page-component-cb9f654ff-w5vf4 Total loading time: 0 Render date: 2025-08-08T04:26:57.941Z Has data issue: false hasContentIssue false
  • English
  • Français

Smooth point-to-point trajectory planning for robot manipulators by using radial basis functions

Published online by Cambridge University Press:  31 October 2018

Taha Chettibi
Taha Chettibi*
Affiliation:
Laboratoire Mécanique des Structures, U.E.R.M.A., E.M.P., Bordj El Bahri, Algiers 16111, Algeria
*
*Corresponding author. E-mail: tahachettibi@gmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

The paper introduces the use of radial basis functions (RBFs) to generate smooth point-to-point joint trajectories for robot manipulators. First, Gaussian RBF interpolation is introduced taking into account boundary conditions. Then, the proposed approach is compared with classical planning techniques based on polynomial and trigonometric models. Also, the trajectory planning problem involving via-points is solved using the proposed RBF interpolation technique. The obtained trajectories are then compared with those synthesized using algebraic and trigonometric splines. Finally, the proposed method is tested for the six-joint PUMA 560 robot in two cases (minimum time and minimum time-jerk) and results are compared with those of other planning techniques. Numerical results demonstrate the advantage of the proposed technique, offering an effective solution to generate trajectories with short execution time and smooth profile.

Keywords

Gaussian RBFInterpolationTrajectory planningRobot manipulatorJerk

Information

Type
Articles
Information
Robotica , Volume 37 , Issue 3 , March 2019 , pp. 539 - 559
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Dombre, E. and Khalil, W., Robot Manipulators: Modelling, Performance Analysis and Control, ISBN-13: 978-1-905209-10-1 (Wiley-ISTE Ltd, London, 2010). doi:10.1002/9780470612286Google Scholar
2. Siciliano, B. and Khatib, O., Springer Handbook of Robotics ISBN: 978-3-540-23957-4 (Springer-Verlag, Berlin, 2008).Google Scholar
3. Biagiotti, L. and Melchiorri, C., Trajectory Planning for Automatic Machines and Robots, ISBN: 978-3-540-85628-3 (Springer-Verlag, Berlin, 2008).Google Scholar
4. John, J. Craig, Introduction to Robotics. Mechanics and Control, 3rd ed., ISBN 0-13-123629-6 (Pearson Prentice Hall, London, 2005).Google Scholar
5. de Boor, C., A Practical Guide to Splines (Springer-Verlag, New York, 1978).Google Scholar
6. Cao, B. and Dodds, G. I., “Time-optimal and smooth joint path generation for robot manipulators,” Proc. IEEE Int. Conf. Robot. Autom. 1853–1858 (1994). doi:10.1049/cp:19940293Google Scholar
7. Lin, C. S., Chang, P. R. and Luh, J. Y. S., “Formulation and optimization of cubic polynomial joint trajectories for industrial robots,” IEEE Trans. Autom. Control 28 (12), 1066–1073 (1983).Google Scholar
8. Chettibi, T., Lehtihet, H. E., Haddad, M. and Hanchi, S., “Minimum cost trajectory planning for industrial robots,” Eur. J. Mech A Solids 23, 703–715 (2004).Google Scholar
9. Simon, D. and Isik, C., “Optimal trigonometric robot joint trajectories,” Robotica 9, Part 4, 379–386 (1991).Google Scholar
10. Simon, D. and Isik, C., “A trigonometric trajectory generator for robotic arms,” Int. J. Control, 57 (3), 505–517 (1993).Google Scholar
11. Visioli, A., “Trajectory planning of robot manipulators by using algebraic and trigonometric splines,” Robotica 18, 611–631 (2000).Google Scholar
12. Gasparetto, A. and Zanotto, V., “A new method for smooth trajectory planning of robot manipulators,” Mech. Mach. Theory 42 (4), 455–471 (2007).Google Scholar
13. Dyllong, E. and Komainda, A. “Local Path Modifications of Heavy Load Manipulators,” Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Como, Italy, (2001) pp. 464–469.Google Scholar
14. Dyllong, E. and Visioli, A., “Planning and real-time modifications of a trajectory using spline techniques,” Robotica 21, 475–482. doi:10.1017/S0263574703005009 (2003).Google Scholar
15. Liu, H., Lai, X. and WU, W., “Time optimal and jerk-continuous trajectory planning for robot manipulators with kinematic constraints,” H. Robotics Comput.-Integrated Manuf. 29, 309–31 (2013).Google Scholar
16. Buhmann, M. D., Radial Basis Functions: Theory and Implementations, (Cambridge University Press, Cambridge, UK, 2003). doi:10.1017/CBO9780511543241Google Scholar
17. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P., Numerical Recipes The Art of Scientific Computing, 3rd ed., ISBN 978-0-511-33555-6, (Cambridge University Press, Cambridge, UK, 2007).Google Scholar
18. Skala, V., “RBF Interpolation with CSRBF of Large Data Sets,” Procedia Comp. Sci. vol. 108, pp. 2373–2377 (2017).Google Scholar
19. John, T., Betts Practical Methods for Optimal Control Using Nonlinear Programming, ISBN 0-89871-488-5, (SIAM edition, Philadelphia, PA, USA, 2001).Google Scholar
20. Mirinejad, H. and Inanc, T., “An RBF collocation method for solving optimal control problems,” Robot. Autonomous Syst. 87, 219–225 (2017). doi /10.1016/j.robot.2016.10.015 0921–8890.Google Scholar
21. Rad, J. A., Kazem, S. and Parand, K., “Radial basis functions approach on optimal control problems: A numerical investigation,” J. Vib. Control 20 (9), 1394–1416 (2014).Google Scholar
22. Hardy, R. L., “Multiquadric equations of topography and other irregular surfaces,” J. Geophys. Res. 76 (8), 1905–1915 (1971).Google Scholar
23. Hardy, R. L., “Theory and applications of the multiquadric-biharmonic method,” Comput. Math. Appl. 19 (8/9), 163–208 (1990).Google Scholar
24. Chettibi, T. and Lemoine, P., “Generation of point to point trajectories for robotic manipulators under electro-mechanical constraints,” International Review of Mechanical Engineering, 1 (2), 131–143 (2007). ISSN 1970–8734.Google Scholar
25. Huang, J., Hu, P., Wu, K. and Zeng, M., “Optimal time-jerk trajectory planning for industrial robots,” Mech. Mach. Theory 121, 530–544 (2018).Google Scholar
26. Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T., “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6, 182–197 (2002). doi:10.1109/4235.996017.Google Scholar
27. Gasparetto, A., Boscariol, P., Lanzutti, A. and Vidoni, R., “Path planning and trajectory planning algorithms: a general overview,” In: Carbone, G., Gomez-Bravo, F. (eds) Motion and Operation Planning of Robotic Systems. Mechanisms and Machine Science, 29, pp. 3–27. (Springer, Cham, 2015) doi:10.1007/978-3-319-14705-5_1.Google Scholar
28. Zanotto, V., Gasparetto, A., Lanzutti, A., Boscariol, P. and Vidoni, R., “Experimental validation of minimum time-jerk algorithms for industrial robots,” J. Intell. Robot. Syst. Theory Appl. 64, 197–219 (2011). doi:10.1007/s10846-010-9533-5.Google Scholar
29. Kyriakopoulos, K. J. and Saridis, G. N., “Minimum Jerk Path Generation,” Proceedings of the of 1988 IEEE International Conference on Robotics & Automation, (Philadelphia, PA, USA 1988) pp. 364–369. doi:10.1109/ROBOT.1988.12075.Google Scholar
30. Gasparetto, A. and Zanotto, V., “A technique for time-jerk optimal planning of robot trajectories,” Robot. Comput. Integr. Manuf. 24, 415–426 (2008). doi:10.1016/j.rcim.2007.04.001.Google Scholar
31. Olabi, A., Bearee, R., Nyiri, E. and Gibaru, O., “Enhanced Trajectory Planning for Machining with Industrial Six-axis Robots,” Proceedings of the IEEE International Conference on Industrial Technology, Vina del Mar, Chile (2010) pp. 500–506. doi:10.1109/ICIT.2010.5472749.Google Scholar
32. Shi, X., Fang, H. and Guo, L., “Multi-objective Optimal Trajectory Planning of Manipulators based on Quintic NURBS,” Proceedings of the IEEE International Conference on Mechatronics and Automation (ICMA), Harbin, China (2016) pp. 759–765. doi:10.1109/ICMA.2016.7558658.Google Scholar
33. Barre, P. J., Bearee, R., Borne, P. and Dumetz, E., “Influence of a jerk controlled movement law on the vibratory behaviour of high-dynamics systems,” J. Intell. Robot Syst. 42 (3), 275–293 (2005).Google Scholar
34. Piazzi, A. and Visioli, A., “Global minimum-jerk trajectory planning of robot manipulators,” IEEE Trans. Ind. Electron. 47 (1), 140–149 (Feb. 2000).Google Scholar
35. Huang, P., Chen, K., Yuan, J. and Xu, Y., “Motion Trajectory Planning of Space Manipulator for Joint Jerk Minimization,” Proceedings of the International Conference on Mechatronics and Automation, ICMA2007 IEEE, Harbin (Aug. 2007) pp. 3543–3548.Google Scholar
36. Yazdani, M., Gamble, G., Henderson, G. and Hecht-Nielsen, R., “A simple control policy for achieving minimum jerk trajectories,” Neural Networks 27, 74–80 (2012).Google Scholar
37. Lin, H. I., “A fast and unified method to find a minimum jerk robot joint trajectory using particle swarm optimization,” J. Intell. Robotic Syst. 75 (3–4), 379–392 (2014).Google Scholar
38. Abu-Dakka, F. J., Assad, I. F., Alkhdour, R. M. and Abderahim, Mohamed, “Statistical evaluation of an evolutionary algorithm for minimum time trajectory planning problem for industrial robots,” Int. J. Adv. Manuf. Technol. 89, 389 (2017). https://doi.org/10.1007/s00170-016-9050-1.Google Scholar