Skip to main content
×
×
Home

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

  • Taha Chettibi (a1)
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.

Copyright
Corresponding author
*Corresponding author. E-mail: tahachettibi@gmail.com
References
Hide All
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:10.1002/9780470612286
2. Siciliano, B. and Khatib, O., Springer Handbook of Robotics ISBN: 978-3-540-23957-4 (Springer-Verlag, Berlin, 2008).
3. Biagiotti, L. and Melchiorri, C., Trajectory Planning for Automatic Machines and Robots, ISBN: 978-3-540-85628-3 (Springer-Verlag, Berlin, 2008).
4. John, J. Craig, Introduction to Robotics. Mechanics and Control, 3rd ed., ISBN 0-13-123629-6 (Pearson Prentice Hall, London, 2005).
5. de Boor, C., A Practical Guide to Splines (Springer-Verlag, New York, 1978).
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:19940293
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), 10661073 (1983).
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).
9. Simon, D. and Isik, C., “Optimal trigonometric robot joint trajectories,” Robotica 9, Part 4, 379386 (1991).
10. Simon, D. and Isik, C., “A trigonometric trajectory generator for robotic arms,” Int. J. Control, 57 (3), 505517 (1993).
11. Visioli, A., “Trajectory planning of robot manipulators by using algebraic and trigonometric splines,” Robotica 18, 611631 (2000).
12. Gasparetto, A. and Zanotto, V., “A new method for smooth trajectory planning of robot manipulators,” Mech. Mach. Theory 42 (4), 455471 (2007).
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.
14. Dyllong, E. and Visioli, A., “Planning and real-time modifications of a trajectory using spline techniques,” Robotica 21, 475482. doi:10.1017/S0263574703005009 (2003).
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).
16. Buhmann, M. D., Radial Basis Functions: Theory and Implementations, (Cambridge University Press, Cambridge, UK, 2003). doi:10.1017/CBO9780511543241
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).
18. Skala, V., “RBF Interpolation with CSRBF of Large Data Sets,” Procedia Comp. Sci. vol. 108, pp. 2373–2377 (2017).
19. John, T., Betts Practical Methods for Optimal Control Using Nonlinear Programming, ISBN 0-89871-488-5, (SIAM edition, Philadelphia, PA, USA, 2001).
20. Mirinejad, H. and Inanc, T., “An RBF collocation method for solving optimal control problems,” Robot. Autonomous Syst. 87, 219225 (2017). doi /10.1016/j.robot.2016.10.015 09218890.
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), 13941416 (2014).
22. Hardy, R. L., “Multiquadric equations of topography and other irregular surfaces,” J. Geophys. Res. 76 (8), 19051915 (1971).
23. Hardy, R. L., “Theory and applications of the multiquadric-biharmonic method,” Comput. Math. Appl. 19 (8/9), 163208 (1990).
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), 131143 (2007). ISSN 19708734.
25. Huang, J., Hu, P., Wu, K. and Zeng, M., “Optimal time-jerk trajectory planning for industrial robots,” Mech. Mach. Theory 121, 530544 (2018).
26. Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T., “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6, 182197 (2002). doi:10.1109/4235.996017.
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. 327. (Springer, Cham, 2015) doi:10.1007/978-3-319-14705-5_1.
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, 197219 (2011). doi:10.1007/s10846-010-9533-5.
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.
30. Gasparetto, A. and Zanotto, V., “A technique for time-jerk optimal planning of robot trajectories,” Robot. Comput. Integr. Manuf. 24, 415426 (2008). doi:10.1016/j.rcim.2007.04.001.
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.
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.
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), 275293 (2005).
34. Piazzi, A. and Visioli, A., “Global minimum-jerk trajectory planning of robot manipulators,” IEEE Trans. Ind. Electron. 47 (1), 140149 (Feb. 2000).
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.
36. Yazdani, M., Gamble, G., Henderson, G. and Hecht-Nielsen, R., “A simple control policy for achieving minimum jerk trajectories,” Neural Networks 27, 7480 (2012).
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), 379392 (2014).
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.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Robotica
  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed