Guaranteed solution of direct kinematic problems for general configurations of parallel manipulators

IEEE Transactions on Robotics and Automation

Volumn 14, Issue 2, 1998, Pages 259-266

  Didrit, Olivier ^a   Petitot, Michel ^a   Walter, Eric ^a  

^a CNRS   (France)

Author keywords

Direct kinematic problem; Guaranteed computations; Interval arithmetic; Nonlinear equations; Parallel manipulator

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; KINEMATICS; NONLINEAR EQUATIONS; PERSONAL COMPUTERS; PROBLEM SOLVING;

DIRECT KINEMATIC PROBLEMS; HANSEN'S ALGORITHM; INTERNAL ARITHMETIC; PARALLEL MANIPULATORS;

MANIPULATORS;

EID: 0032050255     PISSN: 1042296X     EISSN: None     Source Type: Journal    
DOI: 10.1109/70.681244     Document Type: Article

References (24)

1. J. P. Merlet, Les Robots Parallèles. Paris, France: Hermes, 1990.
2. D. Stewart, "A platform with 6 degrees of freedom," in Proc. Inst. Mech. Eng., vol. 180, no. 1, pp. 371-386, 1965.
3. D. Lazard, "Stewart platform and Gröbner basis," in 3rd Int. Workshop Adv. Robot Kinemat., Ferrare, Italy, 1992, pp. 136-142.
4. B. Mourrain, "The 40 generic positions of a parallel robot," in Int. Symp. Symbol. Algebraic Computat., M. Bronstein, Ed. Kiev, Ukraine: ACM, July 1993, pp. 173-182.
5. P. Nanua, K. J. Waldron, and V. Murthy, "Direct kinematic solution of a Stewart platform," IEEE Trans. Robot. Automat., vol. 6, pp. 438-443, 1990.
6. L-C. T. Wang and C. C. Chen, "On the numerical kinematic analysis of general parallel robotic manipulators," IEEE Trans. Robot. Automat., vol. 9, pp. 272-285, 1993.
7. C. W. Wampler, "Forward displacement analysis of general six-in-parallel SPS (Stewart) platform manipulators using soma coordinates," Mech. Mach. Theory, vol. 31, no. 3, pp. 331-337, 1996.
8. M. L. Husty, "An algorithm for solving the direct kinematics of general Stewart-Gough platforms," Mech. Mach. Theory, vol. 31, no. 4, pp. 365-379, 1996.
9. H. Lee and B. Roth, "A closed form solution of the forward displacement analysis of a class of in-parallel mechanism," in Proc. IEEE Int. Conf. Robot. Automat., 1993, vol. 1, pp. 720-724.
10. D. Lazard, "Generalized Stewart platform: How to compute with rigid motions?" in Proc. IMACSSC-93, Lille, France, 1993, pp. 85-88.
11. M. Raghavan, "The Stewart platform of general geometry has 40 configurations," ASME J. Mech. Design, vol. 115, pp. 277-282, 1993.
12. J.-C. Faugère and D. Lazard, "The combinatorial classes of parallel manipulators," Mech. Mach. Theory, vol. 30, no. 6, pp. 765-776, 1995.
13. F. Wen and C. G. Liang, "Displacement analysis of the Stewart platform mechanisms," Mech. Mach. Theory, vol. 29, no. 4, pp. 547-557, 1994.
14. J. P. Merlet, "An algorithm for the forward kinematics of general parallel manipulators," in Proc. Int. Conf. Adv. Robot., Pisa, Italy, 1991, pp. 1131-1135.
15. T. Becker and V. Weispfenning, Groebner Bases. Berlin, Germany: Springer Verlag, 1993.
16. L. T. Watson, "Globally convergent homotopy methods: A tutorial," Appl. Math. Computat., vol. 31, pp. 369-396, 1989.
17. A. M. Bellido, "Construction de fonctions d'itération pour le calcul simultané des solutions d'équations et de systèmes d'équations algébriques," Ph.D. dissertation, Univ. Paul Sabatier, Toulouse, France, Sept. 1992.
18. R. E. Moore, Methods and Applications of Interval Analysis. Philadelphia, Pennsylvania: SIAM, 1979.
19. E. R. Hansen, Global Optimization Using Interval Analysis. New York: Marcel Dekker, 1992.
20. R. Klate, U. W. Kulish, A. Wiethoff, C. Lawo, and M. Rauch, C-XSC : AC++ Class Library For Extended Scientific Computing. Heidelberg, Germany: Springer-Verlag, 1993.
21. R. B. Kearfott, M. Dawande, K. S. Du, and C. Hu, "INTLIB: A portable FORTRAN 77 elementary function library," Interval Computat., vol. 3, no. 5, pp. 96-105, 1992.
22. R. B. Kearfott, "Interval arithmetic methods for nonlinear systems and nonlinear optimization: Introduction and status," in Impact of Recent Computer Advances on Operations Research. Amsterdam, The Netherlands: North-Holland, 1989, pp. 533-542.
23. A. Neumaier, Interval Methods for Systems of Equations. Cambridge, U.K.: Cambridge Univ. Press, 1990.
24. O. Didrit, "Analyse par intervalles pour l'automatique, Résolution globale et garantie de problèmes non linéaires en robotique et en commande robuste," Ph.D. dissertation, Univ. Paris Sud, Orsay, June 1997.