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A new approach to singularity-free inverse kinematics using dual-quaternionic error chains in the Davies method

Published online by Cambridge University Press:  24 July 2014

Andre Schneider de Oliveira ,
Edson Roberto De Pieri ,
Ubirajara Franco Moreno  and
Daniel Martins
Andre Schneider de Oliveira*
Affiliation:
Department of Informatics, Federal University of Technology - Parana, Curitiba, PR, Brazil
Edson Roberto De Pieri
Affiliation:
Department of Automation and Systems, Federal University of Santa Catarina, Florianopolis, SC, Brazil E-mails: edson@das.ufsc.br, moreno@das.ufsc.br
Ubirajara Franco Moreno
Affiliation:
Department of Automation and Systems, Federal University of Santa Catarina, Florianopolis, SC, Brazil E-mails: edson@das.ufsc.br, moreno@das.ufsc.br
Daniel Martins
Affiliation:
Department of Mechanical Engineering, Federal University of Santa Catarina, Florianopolis, SC, Brazil E-mail: daniel@emc.ufsc.br
*
*Corresponding author. E-mail: andreoliveira@utfpr.edu.br
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Summary

The manipulation in singular regions promotes an instantaneous reduction in mechanism mobility, which can result in some disturbances in the trajectory tracking. The application of the quaternionic elements for motion representation not only guarantees an orthonormal transformation but also results in the smallest variance and minimizes the acceleration peaks. The use of a unit quaternion avoids these phenomena, but there are dimensional limitations that make it impossible to translate the representation. This work presents a methodology for using dual quaternions in the analysis of robot kinematics using the Davies method, which avoids kinematic singularities and ensures the optimal torque profiles.

Keywords

Mechanism mobilityKinematic singularitiesDavies methodDual quaternionsOptimal torque profiles
Type
Articles
Information
Robotica , Volume 34 , Issue 4 , April 2016 , pp. 942 - 956
Copyright
Copyright © Cambridge University Press 2014 

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References

1.Siciliano, B., Sciavicco, L., Villani, L. and Oriolo, G., Robotics: Modelling, Planning and Control (Springer Verlag, 2008).Google Scholar
2.Nagi, F., Ahmed, S. K., Abidin, A. A. Z. and Nordin, F. H., “Fuzzy bang-bang relay controller for satellite attitude control system,” Fuzzy Sets Syst. 161 (15), 2104–2125 (2010).CrossRefGoogle Scholar
3.Xu, W., Li, C., Wang, X., Liu, Y., Liang, B. and Xu, Y., “Study on non-holonomic cartesian path planning of a free-floating space robotic system,” Adv. Robot., 23, 1 (2), 113–143 (2009).CrossRefGoogle Scholar
4.Bai, S., Hansen, M. R. and Andersen, T. O., “Modelling of a special class of spherical parallel manipulators with euler parameters,” Robotica, 27 (2), 161–170 (2009).CrossRefGoogle Scholar
5.Erdong, J. and Zhaowei, S., “Passivity-based control for a flexible spacecraft in the presence of disturbances,” Int. J. Non-Linear Mech. (2010).CrossRefGoogle Scholar
6.Castillo-Cruces, R. A. and Wahrburg, J., “Virtual fixtures with autonomous error compensation for human–robot cooperative tasks,” Robotica, 28 (2), 267–277 (2010).CrossRefGoogle Scholar
7.Tabandeh, S., Melek, W. W. and Clark, C. M., “An adaptive niching genetic algorithm approach for generating multiple solutions of serial manipulator inverse kinematics with applications to modular robots,” Robotica, 28 (4), 493–507 (2010).CrossRefGoogle Scholar
8.Johnson, S. M., Williams, J. R. and Cook, B. K., “On the application of quaternion-based approaches in discrete element methods,” Eng. Comput.: Internation J. Comput.-Aided Eng. 26 (6), 610–620 (2009).CrossRefGoogle Scholar
9.Sahu, S., Biswal, B. B. and Subudhi, B., “A Novel Method for Representing Robot Kinematics Using Quaternion Theory,” Proceedings of the IEEE Sponsored Conference on Computational Intelligence, Control and Computer Vision in Robotics & Automation, 76–82 (2008).Google Scholar
10.Qiao, S., Liao, Q., Wei, S. and Su, H., “Inverse kinematic analysis of the general 6r serial manipulators based on double quaternions,” Mech. Mach. Theory 45 (2), 193–199 (2010).CrossRefGoogle Scholar
11.Sariyildiz, E. and Temeltas, H., “Solution of Inverse Kinematic Problem for Serial Robot Using Dual Quaternions and Plucker Coordinates,” Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 338–343, (2009).CrossRefGoogle Scholar
12.Campos, A., Guenther, R. and Martins, D., “Differential kinematics of serial manipulators using virtual chains,” J. Brazi. Soc. Mech. Sci. Eng. 27, 345–356 (2005).Google Scholar
13.Simas, H., Guenther, R., da Cruz, D. F. M. and Martins, D., “A new method to solve robot inverse kinematics using assur virtual chains,” Robotica, 27 (7), 1017–1026 (2009).CrossRefGoogle Scholar
14.Tsai, L. W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (Wiley-Interscience, 1999).Google Scholar
15.Caccavale, F., Siciliano, B. and Villani, L., “The role of euler parameters in robot control,” Asian J. Control 1 (1), 25–34 (1999).CrossRefGoogle Scholar
16.Beiner, L., “Singularity avoidance for scara robots,” Robot. Auton. Syst. 10 (1), 63–69 (1992).CrossRefGoogle Scholar
17.Surdilovic, D. and Simon, H., “Singularity Avoidance and Control of New Cobotic Systems with Differential Cvt,” Proceedings of the IEEE International Conference on Robotics and Automation, 715–720 (2004).CrossRefGoogle Scholar
18.Alshamasin, M. S., Ionescu, F. and Al-Kasasbeh, R. T., “Kinematic modeling and simulation of a scara robot by using solid dynamics and verification by matlab/simulink,” Eur. J. Sci. Res. 37 (3), 388–405 (2009).Google Scholar
19.Rooney, J., “On the three types of complex number and planar transformations,” Environ. Plan. B 5, 89–99 (1978).CrossRefGoogle Scholar
20.Selig, J. M., “Clifford algebra of points, lines and planes,” Robotica, 18 (5), 545–556 (2001).CrossRefGoogle Scholar
21.Huang, Y. C., Qu, D. K., Xu, F. and Zhang, W. X., “An approach dealing with wrist singularity of six-dof industrial robots,” Adv. Mater. Res. 490, 1936–1940 (2012).CrossRefGoogle Scholar
22.Zanchettin, A. M. and Rocco, P., “Dual-arm Redundancy Resolution Based on Null-space Dynamically-scaled Posture Optimization,” Proceedings of the IEEE International Conference on Robotics and Automation, 311–316, (2012).CrossRefGoogle Scholar
23.Akyar, B., “Dual quaternions in spatial kinematics in an algebraic sense,” Turk. J. Math. 32 (4), 373–391 (2008).Google Scholar
24.Zhang, Y. and Ting, K.-L., “On point-line geometry and displacement,” Mech. Mach. Theory 39 (10), 1033–1050 (2004).CrossRefGoogle Scholar
25.Funda, J. and Paul, R. P., “A computational analysis of screw transformations in robotics,” IEEE Trans. Robot. Autom. 6 (3), 348–356 (1990).CrossRefGoogle Scholar