Abstract
Robot design in contexts such as computer-assisted medical interventions remains challenging. Compact, dexterous mechanisms with particular mobilities are needed, the synthesis of which requires a systematic evaluation of workspace and singular positions. The evaluation of singular positions and their classification are still difficult to perform in a systematic manner. In this paper, an automated method is presented and evaluated on a complex planar mechanism. A higher-order continuation method is used to provide continuous and accurate representation of singular locii. Classification is then performed by testing all the existing singularity types through a direct evaluation. Only the mechanism loop-closure equations are required thanks to automatic differentiation and the Diamanlab software developed for use of continuation. The evaluation of the method shows promising results.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Stands for Différentiation Automatique de la Méthode Asymptotique Numérique Typée.
References
Bohigas, O., Zlatanov, D., Manubens, M., Ros, L.: On the numerical classification of the singularities of robot manipulators. In: ASME 2012 International Design Engineering Technical Conferences, pp. 1287–1296 (2012)
Charpentier, I.: On higher-order differentiation in nonlinear mechanics. Optim. Methods Softw. 27, 221–232 (2012)
Gosselin, C., Angeles, J.: Singularity analysis of closed-loop kinematic chains. IEEE Trans. Robot. Autom. 6(3), 281–290 (1990)
Hascoet, L., Pascual, V.: The Tapenade automatic differentiation tool: principles, model, and specification. ACM Trans. Math. Softw. 39, 20:1–20:43 (2013)
Haug, E.J., Luh, C.M., Adkins, F.A., Wang, J.Y.: Numerical algorithms for mapping boundaries of manipulator workspaces. ASME J. Mech. Design 118, 228–234 (1996)
Hentz, G., Charpentier, I., Renaud, P.: Higher-order continuation for the determination of robot workspace boundaries. Comptes Rendus Mécanique 344(2), 95–101 (2016)
Merlet, J.P.: A formal-numerical approach for robust in-workspace singularity detection. IEEE Trans. Robot. 23(3), 393–402 (2007)
Park, F., Kim, J.W.: Singularity analysis of closed kinematic chains. J. Mech. Design 121(1), 32–38 (1999)
Seydel, R.: Practical Bifurcation and Stability Analysis, 3rd edn. Springer, Berlin (2009)
Zlatanov, D., Fenton, R.G., Benhabib, B.: A unifying framework for classification and interpretation of mechanism singularities. ASME J. Mech. Design 117(4), 566–572 (1995)
Acknowledgements
This work was supported by the French government research program Investissements d’avenir through the Robotex Equipment of Excellence (ANR-10-EQPX-44).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Hentz, G., Charpentier, I., Rubbert, L., Renaud, P. (2018). A Taylor-Based Continuation Method for the Determination and Classification of Robot Singularities. In: Lenarčič, J., Merlet, JP. (eds) Advances in Robot Kinematics 2016. Springer Proceedings in Advanced Robotics, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-56802-7_43
Download citation
DOI: https://doi.org/10.1007/978-3-319-56802-7_43
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-56801-0
Online ISBN: 978-3-319-56802-7
eBook Packages: EngineeringEngineering (R0)