Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T08:48:01.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Closeness to singularities of robotic manipulators measured by characteristic angles

Published online by Cambridge University Press:  12 December 2014

Wanghui Bu
Wanghui Bu*
Affiliation:
School of Mechanical Engineering, Tongji University, Shanghai 200092, P. R. China
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Singularities have a great influence on kinematics and dynamics of both serial and parallel robots. In order to prevent a robot from entering singular configurations, it needs to measure the “distance” between the robot current configuration and the singular configuration. This paper presents a novel approach based on characteristic angles to measure closeness to singularities. For the problem of inconsistent dimensions in the scalar product of screws, the physical meanings of twists and wrenches are reinterpreted. For the problem of the metric invariant to origin selection, the origin of the screw frame is required to coincide with the origin of the robotic tool frame. The major merit of the proposed metric lies in the identical result of measuring similar mechanisms with different sizes. Moreover, the measurement is insensitive to screw magnitude, since the metric expression is dimensionless. Furthermore, the geometrical meaning of the determinant of a screw matrix is clarified.

Keywords

Parallel manipulatorsSingularityMetricsScrew theory
Type
Articles
Information
Robotica , Volume 34 , Issue 9 , September 2016 , pp. 2105 - 2115
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Müller, A., “On the manifold property of the set of singularities of kinematic mappings: Genericity conditions,” ASME J. Mech. Robot. 4 (1), 011006, 1–9 (2012).Google Scholar
2. Jiang, Q. and Gosselin, C. M., “Determination of the maximal singularity-free orientation workspace for the Gough–Stewart platform,” Mech. Mach. Theory 44 (6), 1281–1293 (2009).Google Scholar
3. Kong, X., “Forward displacement analysis and singularity analysis of a special 2-DOF 5R spherical parallel manipulator,” ASME J. Mech. Robot. 3 (2), 024501, 1–6 (2011).Google Scholar
4. Liu, G. F., Lou, Y. J. and Li, Z. X., “Singularities of parallel manipulators: A geometric treatment,” IEEE Trans. Robot. Autom. 19 (4), 579–594 (2003).Google Scholar
5. Park, F. C. and Kim, J. W., “Singularity analysis of closed kinematic chains,” ASME J. Mech. Des. 121 (1), 32–38 (1999).Google Scholar
6. Collins, C. L. and McCarthy, J. M., “The quartic singularity surface of planar platforms in the Clifford algebra of the projective plane,” Mech. Mach. Theory 33 (7), 931–944 (1998).Google Scholar
7. Murray, R. M., Li, Z. and Sastry, S. S., A Mathematical Introduction to Robotic Manipulation, (CRC Press, Boca Raton, USA, 1994).Google Scholar
8. Zlatanov, D., Bonev, I. A. and Gosselin, C. M., “Constraint Singularities of Parallel Manipulators,” IEEE International Conference on Robotics and Automation, Washington, DC, (2002) pp. 496–502.Google Scholar
9. Zlatanov, D., Fenton, R. G. and Benhabib, B., “Identification and classification of the singular configurations of mechanisms,” Mech. Mach. Theory 33 (6), 743–760 (1998).Google Scholar
10. Conconi, M. and Carricato, M., “A new assessment of singularities of parallel kinematic chains,” IEEE Trans. Robot. 25 (4), 757–770 (2009).Google Scholar
11. Yoshikawa, T., “Manipulability of robotic mechanisms,” Int. J. Robot. Res. 4 (2), 3–9 (1985).Google Scholar
12. Merlet, J. P., “Jacobian, manipulability, condition number, and accuracy of parallel robots,” ASME J. Mech. Des. 128 (1), 199–206 (2006).Google Scholar
13. Doty, K. L., Melchiorri, C., Schwartz, E. M. and Bonivento, C., “Robot manipulability,” IEEE Trans. Robot. Autom. 11 (3), 462–468 (1995).Google Scholar
14. Lipkin, H. and Duffy, J., “The elliptic polarity of screws,” ASME J. Mech. Des. 107 (9), 377–386 (1985).Google Scholar
15. Voglewede, P. A. and Ebert-Uphoff, I., “Overarching framework for measuring closeness to singularities of parallel manipulators,” IEEE Trans. Robot. 21 (6), 1037–1045 (2005).Google Scholar
16. Hubert, J. and Merlet, J. P., “Static of parallel manipulators and closeness to singularity,” ASME J. Mech. Robot. 1 (1), 11011, 1–6 (2009).Google Scholar
17. Hartley, D. M. and Kerr, D. R., “Invariant measures of the closeness to linear dependence of six lines or screws,” IMechE Part C: J. Mech. Eng. Sci. 215 (10), 1145–1151 (2001).Google Scholar
18. Kerr, D. R. and Hartley, D. M., “Invariant measures of closeness to linear dependency of screw systems,” IMechE Part C: J. Mech. Eng. Sci. 220 (7), 1033–1043 (2006).Google Scholar
19. Liu, X. J., Wu, C. and Wang, J., “A new approach for singularity analysis and closeness measurement to singularities of parallel manipulators,” ASME J. Mech. Robot. 4 (4), 041001, 1–10 (2012).Google Scholar
20. McCarthy, J. M., “Discussion: ‘The elliptic polarity of screws’,” ASME J. Mech. Des. 107 (9), 386–387 (1985).Google Scholar
21. Lee, J., Duffy, J. and Keler, M., “The optimum quality index for the stability of In-parallel planar platform devices,” ASME J. Mech. Des. 121 (3), 15–20 (1999).Google Scholar
22. Angeles, J., “The design of isotropic manipulator architectures in the presence of redundancies,” Int. J. Robot. Res. 11 (3), 196–201 (1992).Google Scholar
23. Angeles, J., “Is there a characteristic length of a rigid-body displacement?,” Mech. Mach. Theory, 41 (8), 884–896 (2006).Google Scholar
24. Selig, J. M., Geometric Fundamentals of Robotics, (Springer, New York, USA, 2004).Google Scholar
25. Joshi, S. A. and Tsai, L. W., “Jacobian analysis of limited-DOF parallel manipulators,” ASME J. Mech. Des. 124 (6), 254–258 (2002).Google Scholar
26. Hong, M. B. and Choi, Y. J., “Formulation of unique form of screw based jacobian for lower mobility parallel manipulators,” ASME J. Mech. Robot. 3 (1), 011002, 1–6 (2011).Google Scholar
27. Zhao, J. S., Feng, Z. J. and Dong, J. X., “Computation of the configuration degree of freedom of a spatial parallel mechanism by using reciprocal screw theory,” Mech. Mach. Theory, 41 (12), 1486–1504 (2006).Google Scholar