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Open Access | Online First

Improved time-parameter B-spline algorithm with NSGA-II and feedrate constraints

Mingyang HUANGaShi-tao HEaLi-yong SHENa( )Chun-ming YUANb,a
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
KLMM, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China
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Abstract

In computer numerical control machining, achieving high precision and speed requires the effective smoothing of tool paths defined by G01 codes. This study proposes an integrated time-parameter B-spline method that combines global smoothing techniques with geometric and kinematic approaches, significantly enhancing processing efficiency while adhering to both geometric and kinematic constraints. To optimize the kinematic properties of the B-spline curve, a non-dominated sorting genetic algorithm is employed to refine the knot vector, resulting in improved machining efficiency. Additionally, the incorporation of tangential velocity constraints leads to a robust trajectory planning algorithm that aligns with practical machining demands. Experimental results confirm the superiority of the proposed algorithm.

References

1

Yan G, Zhang D, Xu J, et al. Corner smoothing for CNC machining of linear tool path: A review. J Adv Manuf Sci Technol 2023;3(2):2023001.

2

Beudaert X, Lavernhe S, Tournier C. 5-axis local corner rounding of linear tool path discontinuities. Int J Mach Tools Manuf 2013;73:9-16.

3

Du X, Huang J, Zhu LM, et al. An error-bounded B-spline curve approximation scheme using dominant points for CNC interpolation of micro-line toolpath. Robot Comput-Integr Manuf 2020;64:101930.

4

Lei WT, Sung MP, Lin LY, et al. Fast real-time NURBS path interpolation for CNC machine tools. Int J Mach Tools Manuf 2007;47(10):1530-1541.

5

Tulsyan S, Altintas Y. Local toolpath smoothing for five-axis machine tools. Int J Mach Tools Manuf 2015;96:15-26.

6

Wang JB, Yau HT. Real-time NURBS interpolator: application to short linear segments. Int J Adv Manuf Technol 2009;41:1169-1185.

7

Wang X, Liu B, Mei X, et al. Global smoothing for five-axis linear paths based on an adaptive NURBS interpolation algorithm. Int J Adv Manuf Technol 2021;114(7):2407-2420.

8

Xiao QB, Wan M, Qin XB, et al. Real-time smoothing of G01 commands for five-axis machining by constructing an entire spline with the bounded smoothing error. Mech Mach Theory 2021;161:104307.

9

Yan G, Zhang D, Xu J, et al. A C3 continuous double circumscribed corner rounding method for five-axis linear tool path with improved kinematics performance. J Comput Des Eng 2023;10(4):1490-1506.

10

Yan G, Liang J, Xu J. Overlap classification-based and kinematically coordinated corner rounding using double asymmetrical transitions for five-axis short-segmented tool path. J of Manuf Proc 2023;85:1077-1095.

11

Yang J, Yuen A. An analytical local corner smoothing algorithm for five-axis CNC machining. Int J Mach Tools Manuf 2017;123:22-35.

12

Yau HT, Wang JB. Fast Bezier interpolator with real-time lookahead function for high-accuracy machining. Int J Mach Tools Manuf 2007;47(10):1518-1529.

13

Zhang K, Yuan CM, Gao XS, et al. A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk. Robot Comput-Integr Manuf 2012;28(4):472-483.

14

Duan M, Okwudire C. Minimum-time cornering for CNC machines using an optimal control method with NURBS parameterization. Int J Adv Manuf Technol 2016;85:1405-1418.

15

Hu Y, Jiang X, Huo G, et al. A novel feed rate scheduling method with acc-jerk-continuity and round-off error elimination for non-uniform rational B-spline interpolation. J Comput Des Eng 2023;10(1):294-317.

16
Lin MT, Lee JC, Shen CC, et al. Local corner smoothing with kinematic and real-time constraints for five-axis linear tool path. In: 2018 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM); 2018. p. 816-821.
17
Nshama EW, Uchiyama N. Time and energy optimal trajectory generation in feed drive systems using kinematic corner smoothing with interrupted acceleration. In: 2018 26th Mediterranean Conference on Control and Automation (MED); 2018. p. 102-107.
18

Tajima S, Sencer B. Global tool-path smoothing for CNC machine tools with uninterrupted acceleration. Int J Mach Tools Manuf 2017;121:81-95.

19

Tajima S, Sencer B. Kinematic corner smoothing for high-speed machine tools. Int J Mach Tools Manuf 2016;108:27-43.

20

Tsai MS, Huang YC. A novel integrated dynamic acceleration/deceleration interpolation algorithm for a CNC controller. Int J Adv Manuf Technol 2016;87(1):279-292.

21

Zhang Q, Gao XS, Li HB, et al. Minimum time corner transition algorithm with confined feedrate and axial acceleration for NC machining along linear tool path. Int J Adv Manuf Technol 2017;89:941-956.

22

Lin F, Shen LY, Yuan CM, et al. Certified space curve fitting and trajectory planning for CNC machining with cubic B-splines. Comput Aided Des 2019;106:13-29.

23

Du Y, Xie L, Liu J, et al. Multi-objective optimization of reverse osmosis networks by lexicographic optimization and augmented epsilon constraint method. Desalination 2014;333(1):66-81.

24
Fan Z, Li H, Wei C, et al. An improved epsilon constraint handling method embedded in MOEA/D for constrained multi-objective optimization problems. In: 2016 IEEE Symposium Series on Computational Intelligence (SSCI); 2016. p. 1-8.
25

Hu CF, Teng CJ, Li SY. A fuzzy goal programming approach to multiobjective optimization problem with priorities. Eur J Oper Res 2007;176(3):1319-1333.

26

Kaddani S, Vanderpooten D, Vanpeperstraete JM, et al. Weighted sum model with partial preference information: Application to multiobjective optimization. Eur J Oper Res 2017;260(2):665-679.

27

Marler RT, Arora JS. The weighted sum method for multi-objective optimization: new insights. Struct Multidiscip Optim 2010;41:853-862.

28

Wang R, Zhou Z, Ishibuchi H, et al. Localized weighted sum method for many-objective optimization. IEEE Trans Evol Comput 2016;22 (1):3-18.

29

Akyürek HA, Ülker E, Koçer B. Automatic knot adjustment using dolphin echo-location algorithm for B-spline curve approximation. J of Macro-Trends in Technol and Innova 2016;4(1):100-109.

30

Bureick J, Alkhatib H, Neumann I. Fast converging elitist genetic algorithm for knot adjustment in B-spline curve approximation. J Appl Geod 2019;13(4):317-328.

31
Tongur V, Ülker E. B-spline curve knot estimation by using niched Pareto genetic algorithm (NPGA). In Proceeding: Intelligent and Evolutionary Systems: The 19th Asia Pacific Symposium, IES 2015, Bangkok, Thailand, November. 2015.p. 305-316.
32

Ülker E, Arslan A. Automatic knot adjustment using an artificial immune system for B-spline curve approximation. Inf Sci 2009;179(10):1483-1494.

33
Valenzuela O, Pasadas M, Rojas I, et al. Automatic knot adjustment for B-spline smoothing approximation using improved clustering algorithm. In: 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE); 2013. p. 1-6.
34

Hu L, Zhang W. NSGA-Ⅱ approach for proper choice of nodes and knots in B-spline curve interpolation. Comput Aided Des 2020;127:102885.

35

Deb K, Pratap A, Agarwal S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ. IEEE Trans Evol Comput 2002;6(2):182-197.

36

Thévenaz P, Blu T, Unser M. Interpolation revisited[medical images application. IEEE Trans Med Imaging 2000;19(7):739-758.

37

Wu Q, Yuan CM, Shen LY, et al. Cubic time-spline fitting and interpolation for five-axis CNC machining. J Comput Des Eng 2023;10(6):2345-2360.

Journal of Advanced Manufacturing Science and Technology
Article number: 2025019
Cite this article:
HUANG M, HE S-t, SHEN L-y, et al. Improved time-parameter B-spline algorithm with NSGA-II and feedrate constraints. Journal of Advanced Manufacturing Science and Technology, 2024, https://doi.org/10.51393/j.jamst.2025019

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Received: 10 November 2024
Revised: 22 November 2024
Accepted: 09 December 2024
Published: 23 December 2024
© 2025 JAMST

This is an Open Access article distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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