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On the inverse kinematics of an a priori unknown general 6R-Robot

Published online by Cambridge University Press:  14 August 2012

Friedemann Groh ,
Konrad Groh  and
Alexander Verl
Friedemann Groh
Affiliation:
Industrielle Steuerungstechnik GmbH (ISG), Stuttgart, Germany
Konrad Groh*
Affiliation:
Institut ür Steuerungstechnik der Werkzeugmaschinen und Fertigungseinrichtungen (ISW), Universität Stuttgart, Stuttgart, Germany
Alexander Verl
Affiliation:
Institut ür Steuerungstechnik der Werkzeugmaschinen und Fertigungseinrichtungen (ISW), Universität Stuttgart, Stuttgart, Germany
*
*Corresponding author. E-mail: [email protected].
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Summary

This paper looks at the inverse kinematics problem of an a priori unknown 6R-Robot from the representation point of view. It describes a new representation of the Euclidean motion group. With this representation, the inverse kinematics problem can be treated entirely numerical. No symbolical methods are required.

Keywords

RoboticsInverse kinematicsRepresentationEuclidean motion group
Type
Articles
Information
Robotica , Volume 31 , Issue 3 , May 2013 , pp. 455 - 463
Copyright
Copyright © Cambridge University Press 2012

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References

1.Brockett, R. W., “Robotic manipulators and the product of exponentials formula,” LNCS 58, 120–129 (1984).Google Scholar
2.H.-Y., Lee and Liang, C.-G., “A new vector theory for the analysis of spatial mechanisms,” Mech. Mach. Theory 23 (3), 209–217 (1988).Google Scholar
3.Lee, H.-Y. and Liang, C.-G., “Displacement analysis of the general spatial 7-link 7r mechanism,” Mech. Mach. Theory 23 (3), 219–226 (1988).CrossRefGoogle Scholar
4.Raghavan, M. and Roth, B., “Kinematic Analysis of the 6r Manipulator of General Geometry,” In: Proceedings of the 5th International Symposium on Robotics Research (Miura, H. and Arimoto, S., eds.) (MIT Press, Cambridge, MA, 1990) pp. 263–269.Google Scholar
5.Raghavan, M. and Roth, B., “Inverse kinematics of the general 6r manipulator and related linkages,” J. Mech. Des. 115, 502–508 (1993).CrossRefGoogle Scholar
6.Murray, R., Li, Z. and Sastry, S., A Mathematical Introduction to Robotic Manipulation (CRC Press, London, 1994).Google Scholar
7.Ghazini, M., “Reducing the Inverse Kinematics of Manipulators to the Solution of a Generalized Eigen Problem,” In: Computational Kinematics (Angeles, J., Hommel, G. and Kovács, P., eds.) (Kluwer, Dordrecht, 1993) pp. 15–26.CrossRefGoogle Scholar
8.Manocha, D. and Canny, J. F., “Efficient inverse kinematics for general 6r manipulators,” IEEE Trans. Robot. Autom. 10 (5), 648–657 (1994).CrossRefGoogle Scholar
9.Wampler, C. W., Morgan, A. P. and Sommerse, A. J., “Numerical continuation methods for solving polynomial systems arising in kinematics,” ASME J. Mech. Des. 112, 59–68 (1990).CrossRefGoogle Scholar
10.Tsai, L.-W. and Morgan, A. P., “Solving the kinematics of the most general six- and five degree of freedom manipulators by continuation methods,” ASME J. Mech. Transm. Autom. Des. 107 (2), 189–200 (1985).CrossRefGoogle Scholar
11.Wampler, C. W. and Morgan, A. P., “Solving the inverse position problem using a generic-case solution methodology,” Mech. Mach. Theory 26 (1), 91–106 (1991).CrossRefGoogle Scholar
12.Allgower, E. L. and Georg, K., Introduction to Numerical Continuation Methods (Colorado State University, Fort Collins, CO, 1990).CrossRefGoogle Scholar
13.Sommese, A. J., Verschelde, J. and Wampler, C. W., “Advances in polynomial continuation for solving problems in kinematics,” ASME J. Mech. Des. 126 (2), 262–268 (2004).CrossRefGoogle Scholar
14.Sommese, A. J. and Wampler, C. W., Numerical Solutions of Systems of Polynomials Arising in Engineering and Science (World Scientific, Singapore, 2005).CrossRefGoogle Scholar
15.Wampler, C. W. and Sommese, A. J., “Numerical algebraic geometry and algebraic kinematics,” Acta Numerica 20, 469–567 (2011).CrossRefGoogle Scholar
16.Cox, D., Little, J. and O'Shea, D., Ideals, Varieties, and Algorithms, 3rd ed. (Springer, New York, 2007).CrossRefGoogle Scholar
17.Stetter, H. J., Numerical Polynomial Algebra (SIAM, Philadelphia, PA, 2004).CrossRefGoogle Scholar
18.Faugère, J.-C., “A new efficient algorithm for computing Gröbner basis,” J. Pure Appl. Algebra 139, 61–88 (1999).CrossRefGoogle Scholar
19.Buchberger, B., “Applications of Gröbner bases in nonlinear computational geometry,” Trends Comput. Algebra, LNCS 296, 52–80 (1988).CrossRefGoogle Scholar
20.Ablamowicz, R., Some Applications of Gröbner Bases in Robotics and Engineering (Technical Report, Tennessee Technological University, Cookeville, TN, 2008).Google Scholar
21.Selig, J. M., Geometric Fundamentals of Robotics (Springer, New York, 2005).Google Scholar
22.Husty, M. L., Pfurner, M. and Schröcker, H.-P., “A new and efficient algorithm for the inverse kinematics of a general serial 6R manipulator,” Mech. Mach. Theory 42, 66–81 (2007).CrossRefGoogle Scholar
23.Rocco, S. di, Eklund, E., Sommese, A. J. and Wampler, C. W., “Algebraic C*-Actions and the inverse kinematics of a general 6r manipulator,” Appl. Math. Comput. 216 (9), 2512–2524 (2010).Google Scholar
24.Castellet, A. and Thomas, F., “An Algorithm for the Solution of Kinematics Problems Based on an Interval Method,” In: Advances in Robot Kinematics (Husty, M. and Lenarcic, J., eds.) (Kluwer Academic, Norwell, MA, 1998) pp. 393–403.Google Scholar
25.Chirikjian, G. S. and Kyatkin, A. B., Engineering Applications of Noncommutative Harmonic Analysis with Emphasis on Rotation and Motion Groups (CRC Press, Boca Raton, FL, 2001).Google Scholar
26.Selig, J. M., Introductory Robotics (Prentice Hall, Englewood Cliffs, NJ, 1992).Google Scholar
27.Nielson, J. and Roth, B., “On the kinematic analysis of robotic mechanisms,” Int. J. Robot. Res. 18 (2), 1147–1160 (1999).CrossRefGoogle Scholar
28.Gantmacher, F. R., Matrizenrechnung (VEB Deutscher Verlag der Wissenschaften, 1958).Google Scholar
29.Manseur, R. and Doty, K. L., “A robot manipulator with 16 real inverse kinematic solution sets,” Int. J. Robot. Res. 8 (5), 75–79 (1989).CrossRefGoogle Scholar
30.Cortes, J., Carrion, S., Curco, D., Renaud, M. and Aleman, C., “Relaxation of amorphous multichain polymer systems using inverse kinematics,” Polymer 21, 4008–4014 (2010).CrossRefGoogle Scholar