**Page description appears here**

“Introduction of b-splines to trajectory planning for robot manipulators”

Authors: Per E. Koch and Kesheng Wang,
Affiliation: NTNU and SINTEF
Reference: 1988, Vol 9, No 2, pp. 69-80.

     Valid XHTML 1.0 Strict


Keywords: Robotics, trajectory planning, B-splines

Abstract: This paper describes how B-splines can be used to construct joint trajectories for robot manipulators. The motion is specified by a sequence of Cartesian knots, i.e., positions and orientations of the end effector of a robot manipulator. For a six joint robot manipulator, these Cartesian knots are transformed into six sets of joint variables, with each set corresponding to a joint. Splines, represented as linear combinations of B-splines, are used to fit the sequence of joint variables for each of the six joints. A computationally very simple, recurrence formula is used to generate the 8-splines. This approach is used for the first time to establish the mathematical model of trajectory generation for robot manipulators, and offers flexibility, computational efficiency, and a compact representation.

PDF PDF (1059 Kb)        DOI: 10.4173/mic.1988.2.2



DOI forward links to this article:
  [1] Per Erik Koch (1992), doi:10.1016/B978-0-12-460510-7.50030-6
  [2] Ammar Alzaydi (2018), doi:10.1117/1.OE.57.12.120901


References:
[1] BOLLINGER, J. DIFFIE, N. (1979). Computer algorithms for high speed continuous path robot manipulator, Ann. CIRP 28, 391-395.
[2] COOK, C.C., HO, C.Y. (1982). The application of spline functions to trajectory generation for computer-controlled manipulators, Digital Systems for Industrial Automation, 1, 325-333.
[3] COX, M.G. (1972). The numerical evaluation of B-splines, J. Inst. Math. Applic., 10, 134-149 doi:10.1093/imamat/10.2.134
[4] CRAIG, J.J. (1986). Introduction to robotics mechanics and control, Addison-Wesley Publishing Company pp. 191-219.
[5] CURRY, H.B., SCHOENBERG, I.J. (1966). On polya frequency functions IV: The fundamental spline functions and their limits, J. dŽAnalyse Math. 17, 71-107 doi:10.1007/BF02788653
[6] DE BOOR, C. (1972). On calculating with B-splines, J. Approximation Theory, 6, 50-62 doi:10.1016/0021-9045(72)90080-9
[7] DE BOOR, C. (1977). Package for calculating with B-splines, SIAM Journal of Numerical Analysis 14, 441-472 doi:10.1137/0714026
[8] DE BOOR, C. (1978). A practical guide to splines, New York : Springer Verlag pp. 219 and 138.
[9] GORDON, W.J., RIESENFELD, R.F. (1974). B-spline curves and surfaces in Computer aided geometric design, edited by Barnhill, R. E. and Riesenfeld, R. F.,.Academic Press, 95-126.
[10] LUH, J.Y.S., LIN, C.S., CHANG, P.R. (1983). Formulation and optimization of cubic polynomial joint trajectory for industrial robots, IEEE Trans. Automatic Control, 28, 1066-1074 doi:10.1109/TAC.1983.1103181
[11] NEWMAN, W.M., SPROULL, R.F. (1983). Principles of interactive computer graphics, McGraw-Hill Inc, pp. 320-325.
[12] PAUL, R.C. (1981). Robot manipulators: mathematics, programming and control, Cambridge: MIT Press, 119-155.
[13] POWELL, M.J.D. (1981). Approximation theory and methods, Cambridge University Press, pp. 227-236.
[14] RAO, S.S. (1978). Optimization Theory and Applications, Wiley Eastern Limited pp. 307.
[15] SCHOENBERG, I.J. (1946). Contribution to the problem of approximation of equidistant data by analytic functions, Quart. Appl. Math., 4, 45-49, 112-141.
[16] SCHOENBERG, I.J., WHITNEY, A. (1953). On polya frequency functions III: The positivity of translation determinant with applications to the interpolation problem by spline curves, Trans. Amer. Math. Soc., 74, 246-259 doi:10.2307/1990881
[17] WANG, K., LIEN, T.K. (1987). The planning of straight line trajectory in robotics using interactive computer graphics, Modeling, Identification and Control, 8, 125-135 doi:10.4173/mic.1987.3.1
[18] WANG, K., LIEN, T.K. (1987). The solution with closed form for the inverse kinematics of PUMA robot manipulator, Proceedings of the International Conference on The Robotic, Paper No. 10, Yugoslavia.


BibTeX:
@article{MIC-1988-2-2,
  title={{Introduction of b-splines to trajectory planning for robot manipulators}},
  author={Koch, Per E. and Wang, Kesheng},
  journal={Modeling, Identification and Control},
  volume={9},
  number={2},
  pages={69--80},
  year={1988},
  doi={10.4173/mic.1988.2.2},
  publisher={Norwegian Society of Automatic Control}
};

News

Oct 2018: MIC reaches 3000 DOI Forward Links. The last 1000 took 2 years and 5 months.


May 2016: MIC reaches 2000 DOI Forward Links. The first 1000 took 34 years, the next 1000 took 2.5 years.


July 2015: MIC's new impact factor is now 0.778. The number of papers published in 2014 was 21 compared to 15 in 2013, which partially explains the small decrease in impact factor.


Aug 2014: For the 3rd year in a row MIC's impact factor increases. It is now 0.826.


Dec 2013: New database-driven web-design enabling extended statistics. Article number 500 is published and MIC reaches 1000 DOI Forward Links.


Jan 2012: Follow MIC on your smartphone by using the RSS feed.

Smartphone


July 2011: MIC passes 1000 ISI Web of Science citations.


Mar 2010: MIC is now indexed by DOAJ and has received the Sparc Seal seal for open access journals.


Dec 2009: A MIC group is created at LinkedIn and Twitter.


Oct 2009: MIC is now fully updated in ISI Web of Knowledge.