Characterization of The Fourth-Order S-curve Trajectory Using Unitization Method
Keywords:
Critical motion parameter, Multiplication factor, Velocity, Unitized valueAbstract
In point-to-point motion transfer applications such as CNC machines, where the tool is required to move along a pre-planned path with high speed and precision, vibration is a common issue that can lead to degradation of positional accuracy. This issue is addressed with the help of trajectory planning, where the implementation of an S-curve trajectory is reported to result in high positional accuracy compared to a trapezoidal velocity trajectory. This paper introduces the different properties of fourth-order symmetrical S-curve trajectory for the point-to-point motion transfer system. Complex mathematics is required to acquire the desired values of motion parameters of the trajectory. Therefore, the paper proposes a novel unitization approach that treats time and displacement as one unit each and simplifies the complex mathematics. This method provides a single generalized solution for any displacement and motion time value. The paper illustrates graphical relationships among motion parameters such as peak values of velocity, acceleration, jerk, and snap, which can serve as nomograms for choosing appropriate values to design displacement trajectories. Using these graphs, the paper outlines simple guidelines for selecting suitable values of motion parameters adapted to common situations. Finally, a case study is presented to validate feasibility of the proposed method.
Downloads
References
H. Z. Li, Z. M. Gong, W. Lin, and T. Lippa, “Motion profile planning for reduced jerk and vibration residuals,” SIM Tech, vol. 8, pp. 32-37, 2015.
S. Perumaal and N. Jawahar, “Synchronized trigonometric S-curve trajectory for jerk-bounded time-optimal pick and place operation,” Int J Robot Autom, vol. 27, no. 4, pp. 385–395, 2012.
K. D. Nguyen, T. C. Ng, and I. M. Chen, “On Algorithms for Planning S-Curve Motion Profiles,” Int J Adv Robot Syst, vol. 5, no. 1, pp. 99–106, 2008.
H. Ouyang, J. Hu, G. Zhang, L. Mei, and X. Deng, “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, vol. 233, no. 10, pp. 3678–3689, 2019.
H. Ding, S. Member, and J. Wu, “Point-to-Point Motion Control for a High-Acceleration Positioning Table via Cascaded Learning Schemes,” IEEE Trans Ind Electron, vol. 54, no. 5, pp. 2735–2744, 2007.
K. Erkorkmaz and Y. Altintas, “High speed CNC system design . Part I : jerk limited trajectory generation and quintic spline interpolation,” Int. J Mach Tools Manuf, vol. 6955, pp. 2–5, 2001.
J. R. Garcia Martinez, J. Rodriguez Resendiz, M. A. Martinez Prado, and E. E. Cruz Miguel, “Assessment of jerk performance s-curve and trapezoidal velocity profiles,” 13th Int Eng Congr, 2017.
P. H. Meckl, P. B. Arestides, and M. C. Woods, “Optimized S-curve motion profiles for minimum residual vibration,” Proc Am Control Conf, vol. 5, pp. 2627–2631, 1998.
K. H. Rew and K. S. Kim, “A closed-form solution to asymmetric motion profile allowing acceleration manipulation,” IEEE Trans Ind Electron, vol. 57, no. 7, pp. 2499–2506, 2010.
[10] C. W. Ha, K. H. Rew, and K. S. Kim, “A complete solution to asymmetric S-curve motion profile: Theory & experiments,” Int Conf Control Autom Syst, pp. 2845–2849, 2008.
[11] K. H. Rew and K. S. Kim, “Using asymmetric S-curve profile for fast and vibrationless motion,” Int Conf Control Autom Syst, pp. 500–504, 2007.
[12] K. H. Rew, C. W. Ha, and K. S. Kim, “A practically efficient method for motion control based on asymmetric velocity profile,” Int J Mach Tools Manuf, vol. 49, no. 7–8, pp. 678–682, 2009.
C. W. Ha, K. H. Rew, and K. S. Kim, “Robust zero placement for motion control of lightly damped systems,” IEEE Trans Ind Electron, vol. 60, no. 9, pp. 3857–3864, 2013.
D. M. Tsay and C. F. Lin, “Asymmetrical inputs for minimizing residual response,” IEEE Int Conf Mechatronics, pp. 235–240, 2005.
F. Zou, D. Qu, and F. Xu, “Asymmetric s-curve trajectory planning for robot point-to-point motion,” IEEE Int Conf Robot Biomimetics, pp. 2172–2176, 2009.
R. Bearee and A. Olabi, “Dissociated jerk-limited trajectory applied to time-varying vibration reduction,” Robot Comput Integr Manuf, vol. 29, no. 2, pp. 444–453, 2013.
Y. Bai, X. Chen, H. Sun, and Z. Yang, “Time-Optimal Freeform S-Curve Profile under Positioning Error and Robustness Constraints,” IEEE/ASME Trans Mechatronics, vol. 23, no. 4, pp. 1993–2003, 2018.
Y. Chen, X. Ji, Y. Tao, and H. Wei, “Look-ahead algorithm with whole s-curve acceleration and deceleration,” Adv Mech Eng, vol. 5, pp. 1-9, 2013.
T. C. Lu and S. L. Chen, “Genetic algorithm-based S-curve acceleration and deceleration for five-axis machine tools,” Int J Adv Manuf Technol, vol. 87, no. 1–4, pp. 219–232, 2016.
Y. Fang, J. Hu, W. Liu, Q. Shao, J. Qi, and Y. Peng, “Smooth and time-optimal S-curve trajectory planning for automated robots and machines,” Mech Mach Theory, vol. 137, pp. 127–153, 2019.
P. Lambrechts, M. Boerlage, and M. Steinbuch, “Trajectory planning and feedforward design for electromechanical motion systems,” Control Eng Pract, vol. 13, pp. 145–157, 2005.
F. Song, S. Yu, and T. Chen, “Research on CNC simulation system with instruction interpretations possessed of wireless communication,” J Supercomput, vol. 72, pp. 2703–2719, 2016.
W. Fan, X. S. Gao, W. Yan, and C. M. Yuan, “Interpolation of parametric CNC machining path under confined jounce,” Int J Adv Manuf Technol, vol. 62, no. 5–8, pp. 719–739, 2012.
R. Tatte, H. Thorat, and H. Jawale, “Optimization of higher ‑ order S ‑ curve motion profile using unitization method aiming to reduce the vibration of a lightly damped system,” J Brazilian Soc Mech Sci Eng, vol. 46, no. 183, pp. 1-28, 2024.
D. Lee and C. W. Ha, “Optimization process for polynomial motion profiles to achieve fast movement with low vibration,” IEEE Trans Control Syst Technol, vol. 28, no. 5, pp. 1892–1901, 2020.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
All papers should be submitted electronically. All submitted manuscripts must be original work that is not under submission at another journal or under consideration for publication in another form, such as a monograph or chapter of a book. Authors of submitted papers are obligated not to submit their paper for publication elsewhere until an editorial decision is rendered on their submission. Further, authors of accepted papers are prohibited from publishing the results in other publications that appear before the paper is published in the Journal unless they receive approval for doing so from the Editor-In-Chief.
IJISAE open access articles are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. This license lets the audience to give appropriate credit, provide a link to the license, and indicate if changes were made and if they remix, transform, or build upon the material, they must distribute contributions under the same license as the original.
