Hostname: page-component-74d7c59bfc-6nqbt Total loading time: 0 Render date: 2026-01-28T03:20:15.861Z Has data issue: false hasContentIssue false
  • English
  • Français

Evaluating concurrent design approaches for a Delta parallel manipulator

Published online by Cambridge University Press:  09 March 2018

Salvador Botello-Aceves ,
S. Ivvan Valdez ,
Héctor M. Becerra  and
Eusebio Hernandez
Salvador Botello-Aceves
Affiliation:
Centro de Investigación en Matemáticas (CIMAT), Guanajuato, México. E-mails: salvador.botello@cimat.mx, hector.becerra@cimat.mx
S. Ivvan Valdez
Affiliation:
Universidad de Guanajuato, División de Ingenierías Campus Irapuato-Salamanca (DICIS), Salamanca, Guanajuato, México. E-mail: si.valdez@ugto.mx
Héctor M. Becerra
Affiliation:
Centro de Investigación en Matemáticas (CIMAT), Guanajuato, México. E-mails: salvador.botello@cimat.mx, hector.becerra@cimat.mx
Eusebio Hernandez*
Affiliation:
Instituto Politécnico Nacional, SEPI ESIME Ticomán, Ciudad de México, México
*
*Corresponding author. E-mail: euhernandezm@ipn.mx
Get access Rights & Permissions [Opens in a new window]

Summary

This paper addresses the problem of optimal mechanisms design, for the geometric structure and control parameters of mechanisms with complex kinematics, which is one of the most intricate problems in contemporary robot modeling. The problem is stated by means of task requirements and performance constraints, which are specified in terms of the end-effector's position and orientation to accomplish the task. Usually, this problem does not fulfill the characteristics needed to use gradient-based optimization algorithms. In order to circumvent this issue, we introduce case studies of optimization models using evolutionary algorithms (EAs), which deal with the concurrent optimization of both: structure and control parameters. We define and review several optimization models based on the workspace, task and dexterity requirements, such that they guarantee an adequate performance under a set of operating and joint constraints, for a Delta parallel manipulator. Then, we apply several methodologies that can approximate optimal designs. Additionally, we compare the EAs with a quasi-Newton method (the BFGS), in order to show that the last kind of methods is not capable of solving the problem if the initial point is not very close to a local optimum. The results provide directions about the best state-of-the-art EA for addressing different design problems.

Keywords

DesignDimensional synthesisEvolutionary algorithmsMechanisms with complex kinematicsDelta robotConcurrent designCMA-ES, GA, BUMDA

Information

Type
Articles
Information
Robotica , Volume 36 , Issue 5 , May 2018 , pp. 697 - 714
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.)

Article purchase

Temporarily unavailable

References

1. Park, J. H. and Asada, H., “Concurrent Design Optimization of Mechanical Structure and Control for High Speed Robots,” Proceedings of the American Control Conference (1993) pp. 2673–2679.Google Scholar
2. Navajas, G. H. T., Raad, J. A. P. and Prada, S. R., “Concurrent Design Optimization and Control of a Custom Designed Quadcopter,” Proceedings of the 16th International Conference on Research and Education in Mechatronics (2015) pp. 63–72.Google Scholar
3. Moulianitis, V. C., Synodinos, A. I., Valsamos, C. D. and Aspragathos, N. A., “Task-based optimal design of metamorphic service manipulators,” J. Mech. Robot. 8 (6), 061011 (2016).CrossRefGoogle Scholar
4. Borboni, A., Bussola, R., Faglia, R., Magnani, P. L. and Menegolo, A., “Movement optimization of a redundant serial robot for high-quality pipe cutting,” J. Mech. Des. 130 (8), 082301 (2008).CrossRefGoogle Scholar
5. Vijaykumar, R., Waldron, K. J. and Tsai, M. J., “Geometric optimization of serial chain manipulator structures for working volume and dexterity,” Int. J. Robot. Res. 5 (2), 91–103 (1986).CrossRefGoogle Scholar
6. Lum, M. J. H., Rosen, J., Sinanan, M. N. and Hannaford, B., “Optimization of a spherical mechanism for a minimally invasive surgical robot: Theoretical and experimental approaches,” IEEE Trans. Biomed. Eng. 53 (7), 1440–1445 (Jul. 2006).CrossRefGoogle ScholarPubMed
7. Merlet, J. P. and Daney, D., “Appropriate Design of Parallel Manipulators,” In: Smart Devices and Machines for Advanced Manufacturing (Wang, L. and Xi, J., eds.) (Springer, 2008) pp. 1–25.Google Scholar
8. Ganesh, M., Bihari, B., Rathore, V., Kumar, D., Kumar, C., Sree, A., Sowmya, K. and Dash, A., “Determination of the closed-form workspace area expression and dimensional optimization of planar parallel manipulators,” Robotica 35 (10), 2056–2075 (2016).CrossRefGoogle Scholar
9. Angeles, J. and Gosselin, C., “The optimum kinematic design of a planar three-degree-of-freedom parallel manipulator,” ASME J. Mech., Trans. Autom. Des. 110, 35–41 (1988).Google Scholar
10. Ottaviano, E. and Ceccarelli, M., “Optimal design of CaPaMan (Cassino Parallel Manipulator) with a specified orientation workspace,” Robotica 20 (02), 159–166 (2002).CrossRefGoogle Scholar
11. Zhang, D., Xu, Z., Mechefske, C. and Xi, F., “Optimum design of parallel kinematic toolheads with genetic algorithms,” Robotica 22 (1), 77–84 (2004).CrossRefGoogle Scholar
12. Carretero, J. A., Podhorodeski, R. P., Nahon, M. A. and Gosselin, C. M., “Kinematic analysis and optimization of a new three degree-of-freedom spatial parallel manipulator,” ASME. J. Mech. Des. 122 (1), 17–24 (1999).CrossRefGoogle Scholar
13. Pittens, K. H. and Podhorodeski, R. P., “A family of stewart platforms with optimal dexterity,” J. Field Robot. 10 (4), 463–479 (1993).Google Scholar
14. Lou, Y., Liu, G. and Li, Z., “Randomized optimal design of parallel manipulators,” IEEE Trans. Autom. Sci. Eng. 5 (2), 223–233 (Apr. 2008).Google Scholar
15. Armada, M., Sanfeliu, A. and Ferre, M., “Dexterity optimization of a three degrees of freedom delta parallel manipulator,” Adv. Intell. Syst. Comput. 253, 719–726 (2014).Google Scholar
16. Courteille, E., Deblaise, D. and Maurine, P., “Design Optimization of a Delta-Like Parallel Robot Through Global Stiffness Performance Evaluation,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS (2009) pp. 5159–5166.Google Scholar
17. Miller, K., “Optimal design and modeling of spatial parallel manipulators,” Int. J. Robot. Res. 23 (2), 127–140 (2004).CrossRefGoogle Scholar
18. Lou, Y., Zhang, Y., Huang, R., Chen, X., and Li, Z., “Optimization algorithms for kinematically optimal design of parallel manipulators,” IEEE Trans. Autom. Sci. Eng. 11 (2), 574–584 (2014).CrossRefGoogle Scholar
19. Riaño, C., Peña, C. and Pardo, A., “Approach in the Optimal Development of Parallel Robot for Educational Applications,” Proceedings of the WSEAS International Conference on Recent Advances in Intelligent Control, Modelling and Simulation (ICMS) (WSEAS Press, Cambridge, MA, USA, 2014) p. 145.Google Scholar
20. Liu, X. J. and Wang, J., “A new methodology for optimal kinematic design of parallel mechanisms,” Mech. Mach. Theory 42 (9), 1210–1224 (2007).CrossRefGoogle Scholar
21. Laribi, M. A., Romdhane, L. and Zeghloul, S., Advanced Synthesis of the DELTA Parallel Robot for a Specified Workspace (InTech, Rijeka, 2008) pp. 207–224.Google Scholar
22. Lou, Y., Liu, G., Xu, J. and Li, Z., “A General Approach for Optimal Kinematic Design of Parallel Manipulators,” In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA '04), vol. 4 (2004) pp. 3659–3664.Google Scholar
23. Chiaverini, S., “Singularity-robust task-priority redundancy resolution for real-time kinematic control of robot manipulators,” IEEE Trans. Robot. Autom. 13 (3), 398–410 (1997).CrossRefGoogle Scholar
24. Ravichandran, T., Heppler, G. R. and Wang, D. W. L., Task-based Optimal Manipulator/Controller Design Using Evolutionary Algorithms, Technical Report (University of Waterloo, Ontario, Canada, 2004).Google Scholar
25. Reynoso-Meza, G., Sanchis, J., Blasco, X. and Martínez, M., “Algoritmos evolutivos y su empleo en el ajuste de controladores del tipo pid: Estado actual y perspectivas,” Rev. Iberoamer. Autom. Inf. Ind. 10 (3), 251–268 (2013).CrossRefGoogle Scholar
26. Xia, Y. and Wang, J., “A dual neural network for kinematic control of redundant robot manipulators,” IEEE Trans. Syst. Man, Cybern. Part B (Cybern.) 31 (1), 147–154 (2001).Google ScholarPubMed
27. dos Santos, R. R., Steffen, V. and Saramago, S. F., “Optimal task placement of a serial robot manipulator for manipulability and mechanical power optimization,” Intell. Inform. Manag. 2 (9), 512–525 (2010).Google Scholar
28. Clavel, R., “Delta, A Fast Robot with Parallel Geometry,” Proceedings of the 18th International Symposium on Industrial Robots, Lausanne (1988) pp. 91–100.Google Scholar
29. Mohamed, S., “Delta robot,” https://grabcad.com/library/delta-robot–2 (2012). [Online; upload 2012-12-04].Google Scholar
30. López, M., Castillo, E., García, G. and Bashir, A., “Delta robot: Inverse, direct, and intermediate jacobians,” Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 220 (1), 103–109 (2006).CrossRefGoogle Scholar
31. Larranaga, P. and Lozano, J. A., Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation, vol. 2 (Springer Science & Business Media, New York, NY, 2002).CrossRefGoogle Scholar
32. Schwefel, H. P. P., Evolution and Optimum Seeking: The Sixth Generation (John Wiley & Sons, Inc., New York, NY, USA, 1993).Google Scholar
33. Davis, L., Handbook of Genetic Algorithms (Van Nostrand, R., New York, NY, 1991).Google Scholar
34. Klanac, A. and Jelovica, J., “A Concept of Omni-Optimization for Ship Structural Design,” Advancements in Marine Structures, Proceedings of MARSTRUCT(2007)pp. 473–481.Google Scholar
35. Deb, K., “Multi-Objective Optimization Using Evolutionary Algorithms, vol. 16 (John Wiley & Sons, Inc., New York, NY, USA, 2001).Google Scholar
36. Srinivas, N. and Deb, K., “Muiltiobjective optimization using nondominated sorting in genetic algorithms,” Evolut. Comput. 2 (3), 221–248 (1994).CrossRefGoogle Scholar
37. Valdez, S. I., Hernández, A. and Botello, S., “A Boltzmann based estimation of distribution algorithm,” Inf. Sci. 236, 126–137 (2013).CrossRefGoogle Scholar
38. Hansen, N., Niederberger, A., Guzzella, L. and Koumoutsakos, P., “A method for handling uncertainty in evolutionary optimization with an application to feedback control of combustion,” IEEE Trans. Evolut. Comput. 13 (1), 180–197 (2009).CrossRefGoogle Scholar
39. Klein, C. A. and Blaho, B. E., “Dexterity measures for the design and control of kinematically redundant manipulators,” Int. J. Robot. Res. 6 (2), 72–83 (1987).CrossRefGoogle Scholar
40. Pond, G. and Carretero, J. A., “Formulating jacobian matrices for the dexterity analysis of parallel manipulators,” Mech. Mach. Theory 41 (12), 1505–1519 (2006).CrossRefGoogle Scholar
41. Gosselin, C. M., “Dexterity indices for planar and spatial robotic manipulators,” Proceedings of the IEEE International Conference on Robotics and Automation, Cincinnati, Oh (May, 1990) pp. 650–655.Google Scholar
42. Efron, B. and Tibshirani, R. J., An Introduction to the Bootstrap (Chapman & Hall, New York, NY, 1994).CrossRefGoogle Scholar
43. Nocedal, J. and Wright, S., Numerical Optimization (Springer Verlag, New York, NY, 2006).Google Scholar
44. Nelder, J. and Mead, R., “A simplex method for function minimization,” Comput. J. 7 (4), 308–313 (1965).CrossRefGoogle Scholar