Abstract
Different methods are known for giving all the solutions to the inverse kinematics problem for general serial-link manipulators. One of these is Raghavan and Roth’s algebraic algorithm. An eigenvalue problem based on this, which is numerically robust, was formulated by various authors. Practical implementation requires algebraic precomputation, because the underlying equations are computationally involved. This can be done by “computer algebra systems” (CAS). We show here a notational concept that avoids the use of CAS. Therefore the algorithm can be implemented on every personal computer by every programming language; even for those who have no access to CAS. But even more importantly, the solution process is much faster.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ghazvini, M. (1993). Reducing the inverse kinematics of manipulators to the solutionof a generalized eigenproblem. In Angeles, J., Hommel, G., and Kovacs, P., editors, Computational Kinematics, pages 15–26. Kluwer Academic Publishers.
Kohli, D. and Osvatic, M. (1992a). Inverse kinematics of general 4r2p, 3r3p, 4rlc, 2r2c and 3c serial manipulators. In Robotics, Spatial Mechanisms and Mechanical Systems, DE-Vol. 45, volume 47 of Flexible Mechanisms, Dynamics and Analysis, pages 619–627. ASME.
Kohli, D. and Osvatic, M. (1992b). Inverse kinematics of general 6r and 5r,p serial manipulators. In Flexible Mechanisms, Dynamics and Analysis, DE- Vol. 47, volume 47 of Flexible Mechanisms, Dynamics and Analysis, pages 619–627. ASME.
Korb, W., Barthold, S., Bendl, R., Echner, G., Grosser, K., Pastyr, O., Treuer, H., Sturm, V., and Schlegel, W. (2001). Entwicklung eines Hochpräzisionsmanipulators für die stereotaktische Neurochirurgie. In Wörn, H., Mühling, J., Vahl, C., and Meinzer, H.-P., editors, Proc. of “Rechner-und Sensorgestützte Chirurgie”, pages 336–343, Heidelberg/Germany. DFG.
Kovacs, P. (1993). Rechnergestützte Symbolische Kinematik. Fortschritte der Robotik. Vieweg, Braunschweig, Wiesbaden.
Lee, H.-Y. and Liang, C.-G. (1988). Displacement analysis of the general spatial 7-link 7r mechanism Mechanism and Machine Theory, 23 (3): 219–226.
Manocha, D. (1992). Algebraic and Numeric Techniques for Modelling and Robotics. PhD thesis, Dept. of Electrical Engineering and Computer Science, Univ. of California at Berkeley. chap. 6.
Manocha, D. and Zhu, Y. (1994). A fast algorithm and system for the inverse kinematics of general serial manipulators. In Proc. Of IEEE Conf. On Robotics and Automation, pages 3348–3354, San Diego, CA.
Mavroidis, C., Ouezdou, F., and Bidaud, P. (1994). Inverse kinematics of six-degree of freedom “general” and “special” manipulators using symbolic computation. Robotica, 12: 421–430.
Paul, R. and Zhang, H. (1986). Computationally efficient kinematics for manipulators with spherical wrists based on the homogeneous transformation representation. The International Journal of Robotics Research, 5 (2): 32–44.
Primrose, E. (1986). On the input-output equation of the general 7r-mechanism. Mechanism and Machine Theory, 21 (6): 509–510.
Raghavan, M. and Roth, B. (1990). Kinematic analysis of the 6r manipualtor of general geometry. In Miura, H. and Arimoto, S., editors, Proc. of the 5th Internat. Symp. on Robotics Research, pages 263–269, Cambridge. MIT Press.
Raghavan, M. and Roth, B. (1991). A general solution for the inverse kinematics of all series chains. In Proc. of the 8th CISM-IFToMM Symp. on Robots and Manipulators, Cracow, Poland, 1990, pages 24–31, Warsaw. Univ. of Technology.
Sciavicco, L. and Siciliano, B. (2000). Modelling and Control of Robot Manipulators. Advanced Textbooks in Control and Signal Processing. Springer, London, 2 edition.
Tsai, L.-W. and Morgan, A. (1985). Solving the kinematics of the most general six-and five-degree-of-freedom manipulators by continuation methods. Journal of Mechanisms, Transmissions and Automation in Design, 107: 189–200.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Korb, W., Schlegel, W., Schlöder, J.P., Bock, H.G. (2002). Algebraic Solution of Inverse Kinematics Revisited. In: Lenarčič, J., Thomas, F. (eds) Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0657-5_30
Download citation
DOI: https://doi.org/10.1007/978-94-017-0657-5_30
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6054-9
Online ISBN: 978-94-017-0657-5
eBook Packages: Springer Book Archive