Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T03:18:25.007Z Has data issue: false hasContentIssue false
  • English
  • Français

A new method of applying differential kinematics through dual quaternions

Published online by Cambridge University Press:  24 November 2015

Andre Schneider de Oliveira ,
Edson Roberto De Pieri  and
Ubirajara Franco Moreno
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
*
*Corresponding author. E-mail: andreoliveira@utfpr.edu.br, edson.pieri@ufsc.br, moreno@das.ufsc.br
Get access Rights & Permissions [Opens in a new window]

Summary

Differential kinematics is a traditional approach to linearize the mapping between the workspace and joint space. However, a Jacobian matrix cannot be inverted directly in redundant systems or in configurations where kinematic singularities occur. This work presents a novel approach to the solution of differential kinematics through the use of dual quaternions. The main advantage of this approach is to reduce “drift” error in differential kinematics and to ignore the kinematic singularities. An analytical dual-quaternionic Jacobian is defined, which allows for the application of this approach in any robotic system.

Keywords

Differential kinematicsJacobianDual quaternionsSingularities
Type
Articles
Information
Robotica , Volume 35 , Issue 4 , April 2017 , pp. 907 - 921
Copyright
Copyright © Cambridge University Press 2015 

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. Zhou, W., Chen, W., Liu, H. and Li, X., “A new forward kinematic algorithm for a general stewart platform,” Mech. Mach. Theory 87 (0), 177–190 (2015).CrossRefGoogle Scholar
2. Park, H. and Lee, C., “Cooperative-Dual-Task-Space-Based Whole-Body Motion Balancing for Humanoid robots,” IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe (2013), pp. 4797–4802.Google Scholar
3. Marinho, M., Bernardes, M. and Bo, A., “A Programmable Remote Center-of-Motion Controller for Minimally Invasive Surgery Using the Dual Quaternion Framework,” Proceedings of the 5th IEEE/RAS/EMBS International Conference on Biomedical Robotics and Biomechatronics, Sao Paulo (Aug. 2014) pp. 339–344.Google Scholar
4. Filipe, N., Kontitsis, M. and Tsiotras, P., “Extended kalman filter for spacecraft pose estimation using dual quaternions,” J. Guid. Control Dyn. 38 (Special Issue in Honor of Richard Battin), 1–17 (2015).Google Scholar
5. Filipe, N. and Tsiotras, P., “Adaptive position and attitude-tracking controller for satellite proximity operations using dual quaternions,” J. Guid. Control Dyn. 38 (4), 1–12 (2015).Google Scholar
6. Wang, J., Liang, H., Sun, Z., Wu, S. and Zhang, S., “Relative motion coupled control based on dual quaternion,” Aerosp. Sci. Technol. 25 (1), 102–113 (2013).Google Scholar
7. Seo, D., “Fast adaptive pose tracking control for satellites via dual quaternion upon non-certainty equivalence principle,” Acta Astronaut. 115 (0), 32–39 (2015).Google Scholar
8. Figueredo, L., Adorno, B., Ishihara, J. and Borges, G., “Robust Kinematic Control of Manipulator Robots Using Dual Quaternion Representation,” IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe (2013) pp. 1949–1955.Google Scholar
9. Heidari, O., Daniali, H. and Varedi, S., “Geometric Design of 3r Manipulators for Three Precision Poses using Dual Quaternions,” Proceedings of the 2nd RSI/ISM International Conference on Robotics and Mechatronics (ICRoM), Tehran (2014) pp. 601–606.Google Scholar
10. Lazarevic, M., Kvrgic, V., Dancuo, Z. and Ferenc, G., “Advanced quaternion forward kinematics algorithm including overview of different methods for robot kinematics,” FME Trans. 42 (3), 189–199 (2014).Google Scholar
11. Wang, X. and Zhu, H., “On the comparisons of unit dual quaternion and homogeneous transformation matrix,” Adv. Appl. Clifford Algebras 24 (1), 213–229 (2014).Google Scholar
12. Thomas, F., “Approaching dual quaternions from matrix algebra,” IEEE Trans. Robot. 30 (5), 1037–1048 (2014).Google Scholar
13. Condurache, D. and Burlacu, A., “Recovering Dual Euler Parameters from Feature-Based Representation of Motion,” Advances in Robot Kinematics (Springer International Publishing, Switzerland, 2014) pp. 295–305.CrossRefGoogle Scholar
14. Radavelli, L., De Pieri, E., Martins, D. and Simoni, R., “Points, Lines, Screws and Planes in Dual Quaternions Kinematics,” Advances in Robot Kinematics (Springer International Publishing, Switzerland, 2014) pp. 285–293.Google Scholar
15. Sharf, I., Wolf, A. and Rubin, M., “Arithmetic and geometric solutions for average rigid-body rotation,” Mech. Mach. Theory 45 (9), 1239–1251 (2010).CrossRefGoogle Scholar
16. Rooney, J., “Generalised Complex Numbers in Mechanics,” Advances on Theory and Practice of Robots and Manipulators, Mechanisms and Machine Science, vol. 22 (Springer International Publishing, Switzerland, 2014) pp. 55–62.Google Scholar
17. Oliveira, A. S., De Pieri, E. and Moreno, U., “Optimal trajectory tracking of underwater vehicle-manipulator systems through the clifford algebras and of the davies method,” Adv. Appl. Clifford Algebras 23 (2), 453–467 (2013).CrossRefGoogle Scholar
18. Oliveira, A. S., De Pieri, E., Moreno, U. and Martins, D., “A new approach to singularity-free inverse kinematics using dual-quaternionic error chains in the davies method,” Robotica 4 (1), 1–15 (2015).Google Scholar
19. Kenwright, B., “Inverse kinematics with dual-quaternions, exponential-maps, and joint limits,” Int. J. Adv. Intell. Syst. 1 (6), 53–65 (2013).Google Scholar
20. Leclercq, G., Lefèvre, P. and Blohm, G., “3d kinematics using dual quaternions: Theory and applications in neuroscience,” Frontiers Behav. Neurosci. 7 (1), 1–25 (2013).Google Scholar
21. Huang, T., Liu, H. and Chetwynd, D., “Generalized jacobian analysis of lower mobility manipulators,” Mech. Mach. Theory 46 (6), 831–844 (2011).Google Scholar
22. Selig, J., “Clifford algebra of points, lines and planes,” Robotica 18 (5), 545–556 (2000).Google Scholar
23. Altmann, S. L., Rotation, Quaternions and Doubles Groups (Oxford University Press, England, 2005).Google Scholar
24. Conway, J. H. and Smith, D. A., “On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry (AK Peters, Ltd., EUA, 2003).Google Scholar
25. Sciavicco, L. and Siciliano, B., Modelling and Control of Robot Manipulators, vol. 2 (Springer, Spain, 2000).Google Scholar