Optimization of third-order trajectory to reduce the vibration in a point-to-point motion system

Rupesh Tatte; Hemant Jawale; Hemant Thorat

doi:10.15625/2525-2518/20303

Author affiliations

Authors

Rupesh Tatte Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, 43F2+7JR, S Ambazari Rd, Ambazari, Nagpur, 440010, India https://orcid.org/0000-0002-8296-0210
Hemant Jawale Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, 43F2+7JR, S Ambazari Rd, Ambazari, Nagpur, 440010, India
Hemant Thorat Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, 43F2+7JR, S Ambazari Rd, Ambazari, Nagpur, 440010, India https://orcid.org/0000-0001-7526-6311

DOI:

https://doi.org/10.15625/2525-2518/20303

Keywords:

Motion profile, Motion parameters, Motion time, Weights

Abstract

In point-to-point motion transfer applications, where motion is executed from one point to another along a pre-planned path with high speed and precision, the occurrence of vibration is a common problem. This problem is addressed through motion profile planning, where an S-curve motion profile is reported to produce lesser vibration than a trapezoidal velocity profile. This paper introduces an optimization method designed to optimize a polynomial-function-based 7-segment third-order symmetrical (7-STOS) S-curve motion profile to minimize vibration. The method aims to achieve lower vibration amplitude for a given distance travelled and motion time (MT) without considering the dynamics of the system. The optimization method is developed using a novel unitization and the weighted sum method. The effectiveness of the proposed method is demonstrated using an experimental setup of a flexible rotating link. The modelling of flexible rotating links is provided to facilitate the validation of experimental results with simulated results.

Downloads

Download data is not yet available.

References

1. Li H., Le M. D., Gong Z. M., Lin W. - Motion profile design to reduce residual vibration of high-speed positioning stages, IEEE/ASME Trans. Mechatronics 14 (2009) 264-269. https://doi.org/10.1109/TMECH.2008.2012160

2. Li H. Z., Gong Z. M., Lin W., Lippa T. - Motion profile planning for reduced jerk and vibration residuals, SIM Tech. 8 (2015) 32-37. https://doi.org/10.13140/2.1.4211.2647

3. Perumaal S., Jawahar N. - Synchronized trigonometric S-curve trajectory for jerk-bounded time-optimal pick and place operation, Int. J. Robot. Autom. 27 (2012) 385-395. https://doi.org/10.2316/Journal.206.2012.4.206-3780

4. Nguyen K. D., Ng T. C., Chen I. M. - On algorithms for planning s-curve motion profiles, Int. J. Adv. Robot. Syst. 5 (2008) 99-106. https://doi.org/10.5772/5652

5. Ouyang H., Hu J., Zhang G., Mei L., Deng X. - Decoupled linear model and S-shaped curve motion trajectory for load sway reduction control in overhead cranes with double-pendulum effect, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 233 (2019) 3678-3689. https://doi.org/10.1177/0954406218819029

6. Ding H., Member S., Wu J. - Point-to-point motion control for a high-acceleration positioning table via cascaded learning schemes, IEEE Trans. Ind. Electron. 54 (2007) 2735-2744. https://doi.org/10.1109/TIE.2007.894702

7. Erkorkmaz K., Altintas Y. - High speed CNC system design . Part I : jerk limited trajectory generation and quintic spline interpolation, Int. J. Mach. Tools. Manuf. 6955 (2001) 2-5. https://doi.org/10.1016/S0890-6955(01)00002-5

8. Garcia Martinez J. R., Rodriguez Resendiz J., Martinez Prado M. A., Cruz Miguel E. E. - Assessment of jerk performance s-curve and trapezoidal velocity profiles, 13th Int. Eng. Congr. (2017). https://doi.org/10.1109/CONIIN.2017.7968187

9. Lee S. Y., Kang C. S., Hyun C. H., Park M. - S-curve profile switching method using fuzzy system for position control of DC motor under uncertain load, Int. Conf. Control Autom. Syst. (2012) 91-95.

10. Meckl P. H., Arestides P. B., Woods M. C. - Optimized S-curve motion profiles for minimum residual vibration, Proc. Am. Control Conf. 5 (1998) 2627-2631. https://doi.org/10.1109/ACC.1998.688324

11. Rew K. H., Kim K. S. - A closed-form solution to asymmetric motion profile allowing acceleration manipulation, IEEE Trans. Ind. Electron. 57 (2010) 2499-2506. https://doi.org/10.1109/TIE.2009.2036032

12. Ha C. W., Rew K. H., Kim K. S. - A complete solution to asymmetric S-curve motion profile: Theory & experiments, Int. Conf. Control Autom. Syst. (2008) 2845-2849. https://doi.org/10.1109/ICCAS.2008.4694244

13. Rew K. H., Kim K. S. - Using asymmetric S-curve profile for fast and vibrationless motion, Int. Conf. Control Autom. Syst. (2007) 500-504. https://doi.org/10.1109/ ICCAS.2007.4406961

14. Rew K. H., Ha C. W., Kim K. S. - A practically efficient method for motion control based on asymmetric velocity profile, Int. J. Mach. Tools Manuf. 49 (2009) 678-682. https://doi.org/10.1016/j.ijmachtools.2009.01.008

15. Ha C. W., Rew K. H., Kim K. S. - Robust zero placement for motion control of lightly damped systems, IEEE Trans. Ind. Electron. 60 (2013) 3857-3864. https://doi.org/ 10.1109/TIE.2012.2206334

16. Tsay D. M., Lin C. F. - Asymmetrical inputs for minimizing residual response, IEEE Int. Conf. Mechatronics (2005) 235-240. https://doi.org/10.1109/ICMECH.2005.1529259

17. Zou F., Qu D., Xu F. - Asymmetric s-curve trajectory planning for robot point-to-point motion, IEEE Int. Conf. Robot Biomimetics (2009) 2172-2176. https://doi.org/ 10.1109/ROBIO.2009.5420482

18. Bearee R., Olabi A. - Dissociated jerk-limited trajectory applied to time-varying vibration reduction, Robot Comput. Integr. Manuf. 29 (2013) 444-453. https://doi.org/10.1016/ j.rcim.2012.09.014

19. Chen Y., Ji X., Tao Y., Wei H. - Look-ahead algorithm with whole s-curve acceleration and deceleration, Adv. Mech. Eng. 5 (2013) 1-9. https://doi.org/10.1155/2013/974152

20. Lu T. C., Chen S. L. - Genetic algorithm-based S-curve acceleration and deceleration for five-axis machine tools, Int. J. Adv. Manuf. Technol. 87 (2016) 219-232. https://doi.org/ 10.1007/s00170-016-8464-0

21. Bai Y., Chen X., Sun H., Yang Z. - Time-optimal freeform s-curve profile under positioning error and robustness constraints. IEEE/ASME Trans, Mechatronics 23 (2018) 1993-2003. https://doi.org/10.1109/TMECH.2018.2835830

22. Lu T. C., Chen S. L., Yang E. C. Y. - Near time-optimal s-curve velocity planning for multiple line segments under axis constraints, IEEE Trans. Ind. Electron. 65 (2018) 9582-9592. https://doi.org/10.1109/TIE.2018.2818669

23. Lambrechts P., Boerlage M., Steinbuch M. - Trajectory planning and feedforward design for electromechanical motion systems, Control Eng. Pract. 13 (2005) 145-157. https://doi.org/10.1016/j.conengprac.2004.02.010

24. Fan W., Gao X. S., Yan W., Yuan C. M. - Interpolation of parametric CNC machining path under confined jounce, Int. J. Adv. Manuf. Technol. 62 (2012) 719-739. https://doi.org/10.1007/s00170-011-3842-0

25. Lee D., Ha C. W. - Optimization process for polynomial motion profiles to achieve fast movement with low vibration. IEEE Trans, Control Syst. Technol. 28 (2020) 1892-1901. https://doi.org/10.1109/TCST.2020.2998094

26. Marler R. T., Arora J. S. - The weighted sum method for multi-objective optimization: New insights, Struct. Multidiscip. Optim. 41 (2010) 853-862. https://doi.org/10.1007/s00158-009-0460-7

27. Model S., Sun C., He W., Member S., Hong J., Member S. - Neural network control of a flexible robotic manipulator using the lumped spring-mass model, IEEE Trans. Syst. Man. Cybern. 47 (2016) 1-12. https://doi.org/10.1109/TSMC.2016.2562506.