Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-24T04:00:22.189Z Has data issue: false hasContentIssue false

On redundancy resolution and energy consumption of kinematically redundant planar parallel manipulators

Published online by Cambridge University Press:  24 January 2018

Andrés Gómez Ruiz
Affiliation:
Department of Mechanical Engineering, São Carlos School of Engineering, University of São Paulo, Av. Trabalhador São-Carlense, 400, 13566-590 São Carlos-SP, Brazil. E-mails: andresgomezruiz@usp.br, joao.cv.santos@gmail.com
João Cavalcanti Santos
Affiliation:
Department of Mechanical Engineering, São Carlos School of Engineering, University of São Paulo, Av. Trabalhador São-Carlense, 400, 13566-590 São Carlos-SP, Brazil. E-mails: andresgomezruiz@usp.br, joao.cv.santos@gmail.com
Jan Croes
Affiliation:
Production Engineering, Machine Design and Automation (PMA) Section, Katholieke Universiteit Leuven, Celestijnenlaan 300, 3001 Leuven, Belgium. E-mails: jan.croes@kuleuven.br, wim.desmet@kuleuven.be Flanders Make, Oude Diestersebaan 133, 3920 Lommel, Belgium
Wim Desmet
Affiliation:
Production Engineering, Machine Design and Automation (PMA) Section, Katholieke Universiteit Leuven, Celestijnenlaan 300, 3001 Leuven, Belgium. E-mails: jan.croes@kuleuven.br, wim.desmet@kuleuven.be Flanders Make, Oude Diestersebaan 133, 3920 Lommel, Belgium
Maíra Martins da Silva*
Affiliation:
Department of Mechanical Engineering, São Carlos School of Engineering, University of São Paulo, Av. Trabalhador São-Carlense, 400, 13566-590 São Carlos-SP, Brazil. E-mails: andresgomezruiz@usp.br, joao.cv.santos@gmail.com
*
*Corresponding author. E-mail: mairams@sc.usp.br

Summary

Novel kinematic architectures can be alternatives for designing energy efficient robotic systems. In this work, the impact of kinematic redundancies in the energy consumption of a planar PKM, the 3PRRR manipulator, is experimentally verified. Because of the presence of the kinematic redundancies, the inverse kinematic problem presents infinity solutions. In this way, a redundancy resolution scheme based on the Model Predictive Control technique is proposed and exploited. It can be concluded that the energy consumption of the non-redundant parallel manipulator 3RRR for executing predefined tasks can be considerably reduced by the inclusion of kinematic redundancies.

Type
Articles
Copyright
Copyright © Cambridge University Press 2018 

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. da Silva, M. M., de Oliveira, L. P. R., Bruls, O., Michelin, M., Baradat, C., Tempier, O., De Caigny, J., Swevers, J., Desmet, W., and Van Brussel, H., “Integrating structural and input design of a 2-DOF high-speed parallel manipulator: A flexible model-based approach,” Mech. Mach. Theory 45 (11), 15091519 (2010). https://doi.org/10.1016/j.mechmachtheory.2016.05.004Google Scholar
2. Li, Y. and Bone, G. M., “Are Parallel Manipulators More Energy Efficient?,” Proceedings of the IEEE International Symposium on Computational Intelligence in Robotics and Automation (2001) pp. 41–46. https://doi.org/10.1109/CIRA.2001.1013170Google Scholar
3. Clement, G. and Jorge, A., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281290 (1990). https://doi.org/10.1109/70.56660Google Scholar
4. Kotlarski, J., Heimann, B. and Ortmaier, T., “Influence of kinematic redundancy on the singularity-free workspace of parallel kinematic machines,” Fron. Mech. Eng. 7 (2), 120134 (2012). https://doi.org/10.1007/s11465-012-0321-8.Google Scholar
5. Mohamed, M. G. and Gosselin, C. M., “Design and analysis of kinematically redundant parallel manipulators with configurable platforms,” IEEE Trans. Robot. 21 (3), 277287 (2005). https://doi.org/10.1109/TRO.2004.837234Google Scholar
6. Cha, S. H., Lasky, T. A. and Velinsky, S. A., “Singularity Avoidance for the 3-RRR Mechanism Using Kinematic Redundancy,” Proceedings of IEEE International Conference on Robotics and Automation (ICRA) (2007) pp. 1195–1200. https://doi.org/10.1109/ROBOT.2007.363147.Google Scholar
7. Thanh, T. D., Kotlarski, J., Heimann, B. and Ortmaier, T., “Dynamics identification of kinematically redundant parallel robots using the direct Search method,” Mech. Mach. Theory 52, 277295 (2012). https://doi.org/10.1016/j.mechmachtheory.2012.02.002Google Scholar
8. Gosselin, C., Laliberte, T. and Veillette, A., “Singularity-free kinematically redundant planar parallel mechanisms with unlimited rotational capability,” IEEE Trans. Robot. 31 (2), 457467 (2015). https://doi.org/10.1109/TRO.2015.2409433Google Scholar
9. Kotlarski, J., Heimann, B. and Ortmaier, T., “Experimental Validation of the Influence of Kinematic Redundancy on the Pose Accuracy of Parallel Kinematic Machines,” Proceedings of IEEE International Conference on Robotics and Automation (ICRA) (2011) pp. 1923–1929. https://doi.org/10.1109/ICRA.2011.5980056Google Scholar
10. Xie, F., Liu, X. J. and Wang, J., “Performance evaluation of redundant parallel manipulators assimilating motion/force transmissibility,” Int. J. Adv. Robot. Syst. 8 (5), 113124 (2011). https://doi.org/10.5772/50904.CrossRefGoogle Scholar
11. Zhao, Y. and Gao, F., “Dynamic formulation and performance evaluation of the redundant parallel manipulator,” Robot. Comput.-Integr. Manuf. 25 (4–5), 770781 (2009). https://doi.org/10.1016/j.rcim.2008.10.001Google Scholar
12. Fontes, J. V. and da Silva, M. M., “On the dynamic performance of parallel kinematic manipulators with actuation and kinematic redundancies,” Mech. Mach. Theory 103 148166 (2016). https://doi.org/10.1016/j.mechmachtheory.2016.05.004Google Scholar
13. Luces, M., Mills, J. K. and Benhabib, B., “A review of redundant parallel kinematic mechanisms,” Intell. Robot Syst. 86 (2), 175198 (2017). http://dx.doi:10.1007/s10846-016-0430-4Google Scholar
14. Muller, A., “On the terminology and geometric aspects of redundant parallel manipulators, ” Robotica, 31 (1), 137147 (2013). http://doi:10.1017/S0263574712000173Google Scholar
15. Ahuactzin, J. M. and Gupta, K. K., “The kinematic Roadmap: A motion planning based global approach for inverse kinematics of redundant robots,” IEEE Trans. Robot. Autom. 15 (4), 653669 (1999). https://doi.org/10.1109/70.781970Google Scholar
16. Siciliano, B., “Kinematic control of redundant robot manipulators: A tutorial,” J. Intell. Robot. Syst. 3, 201212 (1990). https://doi.org/10.1007/BF00126069CrossRefGoogle Scholar
17. Santos, J. C. and da Silva, M. M., “Redundancy resolution of kinematically redundant parallel manipulators via differential dynamic programming,” J. Mech. Robot. 9 (4), 041016 (2017) https://doi.org/10.1115/1.4036739Google Scholar
18. Joseph, F. O. M., Behera, L., Tamei, T., Shibata, T., Dutta, A., A. and Saxena, A., “On redundancy resolution of the human thumb, index and middle fingers in cooperative object translation,” Robotica 35 (10), 19922017 (2017). http://dc.doi.org/10.1017/S0263574716000680Google Scholar
19. Faulwasser, T. and Findeisen, R., “Nonlinear model predictive control for Constrained output path following,” IEEE Trans. Autom. Control 61 (4), 10261039 (2016). https://doi.org/10.1109/TAC.2015.2466911Google Scholar
20. Bock, M. and Kugi, A., “Real-time nonlinear model predictive path-following control of a laboratory tower crane,” IEEE Trans. Control Syst. Technol. 22 (4), 14611473 (2014). https://doi.org/10.1109/TCST.2013.2280464Google Scholar
21. Avanzini, G. B., Zanchettin, A. M. and Rocco, P., “Constrained model predictive control for mobile robotic manipulators,” Robotica 36 (1), 19922017 (2018). http://dx.doi:10.1017/S0263574717000133Google Scholar
22. Belda, K., Bohm, J. and Valasek, M., “State-space generalized predictive control for redundant parallel robots,” Mech. Based Des. Struct. Mach. 31 (3), 413432 (2003). https://doi.org/10.1081/SME-120022857Google Scholar
23. Wen, S., Qin, G., Zhang, B., Lam, H. K., Zhao, Y. and Wang, H., “The study of model predictive control algorithm based on the force/position control scheme of the 5-DOF redundant actuation parallel robot,” Robot. Autom. Syst. 79, 1225 (2016). https://doi.org/10.1016/j.robot.2016.02.002Google Scholar
24. Hufnagel, T., Reichert, C. and Schramm, D., “Centralized non-linear model predictive control of a redundantly actuated parallel manipulator,” New Trends Mech. Mach. Sci. 7, 621629 (2013). https://doi.org/10.1007/978-94-007-4902-3-6Google Scholar
25. Lee, G., Park, S., Kim, H., Jeong, J. and Kim, J., “Energy saving effect mapping of redundant actuation in workspace,” Procedia CIRP 26, 145149 (2015). https://doi.org/10.1016/j.procir.2014.07.071CrossRefGoogle Scholar
26. Ruiz, A. G., Fontes, J. V. C. and da Silva, M. M., “The Influence of Kinematic Redundancies in the Energy Efficiency of Planar Parallel Manipulators,” Proceedings of the ASME International Mechanical Engineering Congress and Exposition, No. IMECE2015-50278, https://doi.org/10.1115/IMECE2015-50278Google Scholar
27. Boyd, S. and Vandenberghe, L., Convex Optimization (Cambridge University Press, Cambridge, 2014).Google Scholar