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Dual arm-angle parameterisation and its applications for analytical inverse kinematics of redundant manipulators

Published online by Cambridge University Press:  29 April 2015

Wenfu Xu ,
Lei Yan ,
Zonggao Mu  and
Zhiying Wang
Wenfu Xu*
Affiliation:
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, P. R. China Shenzhen Engineering Laboratory of Digital Stage Performance Robot, Shenzhen, P. R. China
Lei Yan
Affiliation:
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, P. R. China Shenzhen Engineering Laboratory of Digital Stage Performance Robot, Shenzhen, P. R. China
Zonggao Mu
Affiliation:
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, P. R. China Aerospace Dongfanghong Development Ltd, Shenzhen, P. R. China
Zhiying Wang
Affiliation:
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, P. R. China
*
*Corresponding author. E-mail: [email protected]
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Summary

An S-R-S (Spherical-Revolute-Spherical) redundant manipulator is similar to a human arm and is often used to perform dexterous tasks. To solve the inverse kinematics analytically, the arm-angle was usually used to parameterise the self-motion. However, the previous studies have had shortcomings; some methods cannot avoid algorithm singularity and some are unsuitable for configuration control because they use a temporary reference plane. In this paper, we propose a method of analytical inverse kinematics resolution based on dual arm-angle parameterisation. By making use of two orthogonal vectors to define two absolute reference planes, we obtain two arm angles that satisfy a specific condition. The algorithm singularity problem is avoided because there is always at least one arm angle to represent the redundancy. The dual arm angle method overcomes the shortcomings of traditional methods and retains the advantages of the arm angle. Another contribution of this paper is the derivation of the absolute reference attitude matrix, which is the key to the resolution of analytical inverse kinematics but has not been previously addressed. The simulation results for typical cases that include the algorithm singularity condition verified our method.

Keywords

Redundant manipulatorsAnalytical inverse kinematicsArm-angle parameterisationAlgorithm singularityRedundancy resolution
Type
Articles
Information
Robotica , Volume 34 , Issue 12 , December 2016 , pp. 2669 - 2688
Copyright
Copyright © Cambridge University Press 2015 

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References

1. Yoshida, E., Esteves, C., Belousov, I., Laumond, J. P., Sakaguchi, T. and Yokoi, K., “Planning 3D collision-free dynamic robotic motion through iterative reshaping,” IEEE Trans. Robot. 24 (5), 1186–1198 (2008).CrossRefGoogle Scholar
2. Yoshida, K., Kurazume, R. and Umetani, Y., “Torque optimisation control in space robots with a redundant arm,” Proceedings of the IEEE/RSJ International Workshop on Intelligent Robots and Systems, Osaka, Japan, (1991) pp. 1647–1652.Google Scholar
3. Ben-Gharbia, K. M., “Kinematic design of redundant robotic manipulators for spatial positioning that are optimally fault tolerant,” IEEE Trans. Robot. 29 (5), 1300–1307 (2013).CrossRefGoogle Scholar
4. Abdi, H., Nahavandi, S., Frayman, Y. and Maciejewski, A. A., “Optimal mapping of joint faults into healthy joint velocity space for fault-tolerant redundant manipulators,” Robotica 30 (4), 635–648 (2012).CrossRefGoogle Scholar
5. Neil, K. A. O, Cheng, Y. C. and Seng, J., “Removing singularities of resolved motion rate control of mechanisms, including self-motion,” IEEE Trans. Robot. Autom. 13 (5), 741–751 (1997).CrossRefGoogle Scholar
6. Li, K. and Zhang, Y., “State adjustment of redundant robot manipulator based on quadratic programming,” Robotica 30 (3), 477–489 (2012).CrossRefGoogle Scholar
7. Cocuzza, S., Pretto, I. and Debei, S., “Novel reaction control techniques for redundant space manipulators: Theory and simulated microgravity tests,” Acta Astronaut. 68 (11–12), 1712–1721 (2011).CrossRefGoogle Scholar
8. Angeles, J. and Park, F. C., “Performance Evaluation and Design Criteria,” In: Springer Handbook of Robotics (Chapter 10), (Siciliano, B. and Khatib, O., eds.) (Springer-Verlag, 2008) pp. 229–244.CrossRefGoogle Scholar
9. Chiaverini, S., Oriolo, G. and Walker, I. D., “Kinematically Redundant Manipulators,” In: Springer Handbook of Robotics (Chapter 11), (Siciliano, B. and Khatib, O., eds.) (Springer-Verlag, 2008) pp. 245–268.CrossRefGoogle Scholar
10. Coleshill, E., Oshinowo, L., Rembala, R., Bina, B., Rey, D. and Sindelar, S., “Dextre: Improving maintenance operations on the international space station,” Acta Astronaut. 64 (9–10), 869–874 (2009).CrossRefGoogle Scholar
11. Boumans, R. and Heemskerk, C., “European robotic arm for the international space station,” Robot. Auton. Syst. 23 (1–2), 17–27 (1998).CrossRefGoogle Scholar
12. Nokleby, S. B., “Singularity analysis of the canadarm2,” Mech. Mach. Theory 42 (4), 442–454 (2007).CrossRefGoogle Scholar
13. Haddadin, S., Albu-Schäffer, A. and Hirzinger, G., “Requirements for safe robots: Measurements, analysis and new insights,” Int. J. Robot. Res. 28 (11–12), 1507–1527 (2009).CrossRefGoogle Scholar
14. Boudreau, R. and Podhorodeski, R. P., “Singularity analysis of a kinematically simple class of 7-jointed revolute manipulators,” Trans. Canadian Soc. Mech. Eng. 34 (1), 105–117 (2010).CrossRefGoogle Scholar
15. Soechting, J. F. and Flanders, M., “Evaluating an integrated musculoskeletal model of the human arm,” J. Neurophysiol. 119 (1), 93–102 (1997).Google ScholarPubMed
16. Liu, D. and Todorov, E., “Hierarchical Optimal Control of a 7-DOF Arm Model,” Proceedings of the IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning, Nashville, TN, (2009) pp. 50–57.Google Scholar
17. Lee, S. and Bejczy, A. K., “Redundant arm kinematic control based on parameterisation,” Proceedings of the IEEE Intemational Conference on Robotics and Autmaticm, Sacramento, California, (1991) pp. 458–465.Google Scholar
18. Moradi, H. and Lee, S., “Joint limit analysis and elbow movement minimisation for redundant manipulators using closed form method,” In: Advances in Intelligent Computing, vol. 3645, (Berlin: Springer, 2005) pp. 423–432.CrossRefGoogle Scholar
19. Asfour, T. and Dillmann, R., “Human-Like Motion of a Humanoid Robot Arm Based on a Closed-Form Solution of the Inverse Kinematics Problem,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, Nevada, (2003) pp. 1407–1412.Google Scholar
20. Tondu, B., “A Closed-form Inverse Kinematic Modelling of a 7R Anthropomorphic Upper Limb based on a Joint Parametrisation,” Proceedings of the IEEE-RAS International Conference on Humanoid Robots, Genova, (2006) pp. 390–397.Google Scholar
21. Shimizu, M., Kakuya, H., Yoon, W., Kitagaki, K. and Kosuge, K., “Analytical inverse kinematic computation for 7-DOF redundant manipulators with joint limits and its application to redundancy resolution,” IEEE Trans. Robot. 24 (5), 1131–1142 (2008).CrossRefGoogle Scholar
22. Kreutz-Delgado, K., Long, M. and Seraji, H., “Kinematic analysis of 7-DOF manipulators,” Int. J. Robot. Res. 11 (5), 469–481 (1992).CrossRefGoogle Scholar
23. Seraji, H., Long, M. K. and Lee, T. S., “Motion control of 7-DOF arms: The configuration control approach,” IEEE Trans. Robot. Autom. 9 (2), 125–139 (1993).CrossRefGoogle Scholar
24. Xu, W., She, Y. and Xu, Y., “Analytical and semi-analytical inverse kinematics of SSRMS-type manipulators with single joint locked failure,” Acta Astronaut. 105 (1), 201–217 (2014).Google Scholar
25. Ding, X. and Fang, C., “A novel method of motion planning for an anthropomorphic arm based on movement primitives,” IEEE/ASME Trans. Mechatronics 18 (2), 624–636 (2013).Google Scholar