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A swarm optimization approach for solving workspace determination of parallel manipulators

Published online by Cambridge University Press:  10 March 2014

V. B. Saputra ,
S. K. Ong  and
A. Y. C. Nee
V. B. Saputra
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore117576
S. K. Ong*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore117576
A. Y. C. Nee
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore117576
*
*Corresponding author. E-mail: mpeongsk@nus.edu.sg
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Summary

This paper presents a novel method to determine the workspace of parallel manipulators using a variant of the Firefly Algorithm, which is one of the emerging techniques in swarm artificial intelligence. The workspace is defined as a set of all the coordinates in the search space that are accessible by the parallel manipulator end effector. The workspace formulation of the parallel manipulator considered in this paper has actuated and passive joint displacements which values are limited by their physical constraints. A special fitness function that discriminates between accessible and inaccessible coordinates is formulated based on the joint limitations. By finding these coordinates using the proposed Firefly Algorithm, the workspace of the manipulator can be constructed. The proposed method is an easy-to-implement alternative solution to the current numerical methods for workspace determination. The method consists of two stages of operation. The first stage maps the workspace to find the initial results with a space filling approach, in which a number of coordinates in the workspace are identified. The second stage refines the results with a boundary detection approach which focuses on the mapping of the boundaries of the workspace. The method is illustrated by its application to determine the 2D, 3D, and 6D workspaces of a Gough--Stewart Platform manipulator. Furthermore, the method is compared with a more rigorous interval analysis method in terms of computational cost and accuracy.

Keywords

Parallel manipulatorWorkspaceFirefly algorithmMultimodal optimizationStewart platform
Type
Articles
Information
Robotica , Volume 33 , Issue 3 , March 2015 , pp. 649 - 668
Copyright
Copyright © Cambridge University Press 2014 

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References

1.Ceccarelli, M. and Sorli, M., “The effects of design parameters on the workspace of a turin parallel robot,” Int. J. Robot. Res. 17 (8), 886–902 (1998).CrossRefGoogle Scholar
2.Stewart, D., “A platform with six degrees of freedom,” Proc. Inst. Mech. Eng. 180, 25–28 (1965).CrossRefGoogle Scholar
3.Fichter, E. F. and McDowell, E. D., “A Novel Design for a Robot Arm,” Proceedings, ASME International Computer Technology Conference, San Francisco (1980) pp. 250–256.Google Scholar
4.Bajpaj, A. and Roth, B., “Workspace and mobility of a closed-loop manipulator,” Int. J. Robot. Res. 5 (2), 131–142 (1986).CrossRefGoogle Scholar
5.Gosselin, C. and Angeles, J., “The optimum kinematic design of a planar three-degree-of-freedom parallel manipulator,” ASME J. Mech. Trans. Autom. Des. 110, 35–41 (1988).CrossRefGoogle Scholar
6.Liu, K., Fitzgerald, J. M. and Lewis, F. L., “Kinematic analysis of a stewart platform manipulator,” IEEE Trans. Ind. Electr. Control Instrum. 40 (2), 282–293 (1993).CrossRefGoogle Scholar
7.Wang, L. C. T. and Hsieh, J. H., “Extreme reaches and reachable workspace analysis of general parallel robot manipulators,” J. Robot. Syst. 15, 145–159 (1997).3.0.CO;2-Q>CrossRefGoogle Scholar
8.Gosselin, C., “Determination of the workspace of 6-dof parallel manipulators,” ASME J. Mech. Des. 112 (3), 331–336 (1990).CrossRefGoogle Scholar
9.Merlét, J. P., “Parallel Robots: Open Problems,” Proceedings of Ninth International Symposium of Robotic Research (1999) pp. 27–32.Google Scholar
10.Merlét, J. P., Gosselin, C. M. and Mouly, N., “Workspaces of planar parallel manipulators,” Mech. Mach. Theory 33 (1–2), 7–20 (1998).CrossRefGoogle Scholar
11.Merlét, J. P., “Parallel manipulators: state of the art and perspectives,” J. Adv. Robot. 8, 589–596 (1994).CrossRefGoogle Scholar
12.Merlét, J. P., Gosselin, C. M. and Mouly, N., “Workspaces of planar parallel manipulators,” Mech. Mach. Theory 33, 7–20 (1998).CrossRefGoogle Scholar
13.Fichter, E. F., “A Stewart platform-based manipulator: general theory and practical construction,” Int. J. Robot. Res., 5 (2), 157–181 (1986).CrossRefGoogle Scholar
14.Wang, Z., Wang, Z. X., Liu, W. T. and Lei, Y. C., “A study on workspace, boundary workspace analysis and workpiece positioning for parallel machine tools,” Mech. Mach. Theory 36 (5), 605–622 (2001).CrossRefGoogle Scholar
15.Pernkopf, F. and Husty, M., “Workspace analysis of Stewart–Gough type parallel manipulators,” Proc. Inst. Mech. Eng. 220, 1019–1032 (2006).Google Scholar
16.Merlét, J. P., Parallel Robots, Solid Mechanics and Its Applications (Springer-Verlag, 2006).Google Scholar
17.Merlét, J. P., “Determination of the orientation workspace of parallel manipulators,” J. Intell. Robot. Syst. 13, 143–160 (1995).CrossRefGoogle Scholar
18.Gosselin, C. M. and Angeles, J., “The optimum kinematic design of a spherical three degree-of-freedom parallel manipulator,” ASME J. Mech. Transm. Autom. Des. 111 (2), 202–207 (1989).CrossRefGoogle Scholar
19.Jo, D. Y. and Haug, E. J., “Workspace analysis of multibody mechanical systems using continuation methods,” ASME J. Mech. Transm. Autom. Des. 111, 581–589 (1989).CrossRefGoogle Scholar
20.Haug, E. J., Luh, C. M., Adkins, F. A. and Wang, J. Y., “Numerical algorithms for mapping boundaries of manipulator workspaces,” ASME J. Mech. Des. 118 (2), 228–234 (1996).CrossRefGoogle Scholar
21.Snyman, J. A., Du Plessis, L. J. and Duffy, J., “An optimization approach to the determination of the boundaries of manipulator workspaces,” ASME J. Mech. Des. 122 (4), 447–456 (2000).CrossRefGoogle Scholar
22.Du Plessis, L. J. and Snyman, J. A., “A numerical method for the determination of dexterous workspaces of Gough–Stewart platforms,” Int. J. Numer. Methods Eng. 52, 345–369 (2001).CrossRefGoogle Scholar
23.Hay, A. M. and Snyman, J. A., “The chord method for the determination of non-convex workspaces of planar manipulators,” Comput. Math Appl. 43, 1135–1151 (2002).CrossRefGoogle Scholar
24.Hay, A. M. and Snyman, J. A., “Methodologies for the optimal design of parallel manipulators,” Int. J. Numer. Methods Eng. 59, 131–152 (2004).CrossRefGoogle Scholar
25.Hay, A. M. and Snyman, J. A., “Optimization of a planar tendon-driven manipulator for a maximal dexterous workspace,” Eng. Optim. 37, 217–236 (2005).CrossRefGoogle Scholar
26.Hay, A. M. and Snyman, J. A., “A multi-level optimization methodology for determining the dexterous workspaces of planar parallel manipulators,” Struct. Multidiscip. Optim. 30, 422–427 (2005).CrossRefGoogle Scholar
27.Merlét, J. P., “Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries,” Int. J. Robot. Res. 18 (9), 902–916 (1999).CrossRefGoogle Scholar
28.Kennedy, J. and Eberhart, R. C., “Particle Swarm Optimization,” Proceedings of the IEEE International Joint Conference on Neural Networks (1995) pp. 1942–1948.Google Scholar
29.Yang, X. S., Nature-Inspired Metaheuristic Algorithms (Luniver Press, 2008).Google Scholar
30.Yang, X. S., “Firefly Algorithms for Multimodal Optimization,” Stochastic Algorithms: Foundations and Applications, SAGA 2009, Lecture Notes in Computer Sciences, Vol. 5792 (2009) pp. 169–178.Google Scholar
31.Lukasik, S. and Zak, S., “Firefly algorithm for continuous constrained optimization task,” Lecture Notes in Computer Sciences 5796, 97–106 (2009).CrossRefGoogle Scholar
32.Yang, X. S., Hosseini, S. S. and Gandomi, H., “Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect”, Appl. Soft Comput. 13 (2), 1180–1186 (2012).CrossRefGoogle Scholar
33.Saputra, V. B., Ong, S. K. and Nee, A. Y. C., “A PSO Algorithm for Mapping the Workspace Boundary of Parallel Manipulators,” IEEE International Conference on Robotics and Automation, Anchorage (2010) pp. 4691–4696.Google Scholar
34.Rump, S. M., “INTerval LABoratory Version 3.” INTLAB http://www.ti3.tu-harburg.de/~rump/intlab/index.htmlGoogle Scholar
35.Kubota, N. and Sato, W., “Robot Design Support System Based on Interactive Evolutionary Computation using Boltzmann Selection,” IEEE Congress on Evolutionary Computation Barcelona (Jul. 18–23, 2010) pp. 1–8.Google Scholar
36.Kwok, N. M., Liu, D. K. and Dissanayake, G., “Evolutionary computing based mobile robot localization,” Eng. Appl. Artif. Intell. 18 (8), 857–868 (2006).CrossRefGoogle Scholar
37.Saska, M., Macas, M., Preucil, L. and Lhotska, L., “Robot Path Planning using Particle Swarm Optimization of Ferguson Splines,” IEEE Conference on Emerging Technologies and Factory Automation, Prague (Sep. 20–22, 2006) pp. 833–839.CrossRefGoogle Scholar