Robotic optimization with high-dimensional Pareto front visualization

Document Type : Research Article

Author

Federal Research Center ``Computer Science and Control'' of the Russian Academy of Sciences (FRC CSC RAS), Moscow, Russia

Abstract

In this paper, we consider an approach for multi-criteria optimization of key design characteristics for robots. We use 5 criteria: Workspace Area, Space Utilization Index, Global Dexterity Index, Global Manipulability Index and Global Resistivity Index. The first two characterize workspace, while the latter three evaluate kinematic performance throughout the workspace. The Pareto-set visualization for such problem can be a challenging task, since the objective space is five-dimensional. We consider clustering approach for efficient reduction of the number of Pareto points. The calculation of the indexes is performed automatically using interval analysis techniques. The experimental validation was performed for three parallel manipulators: 2-RPR, DexTar, PRRRP. We compare the proposed approach with random sampling method and exact Pareto front, calculated with ``brute force'' algorithm.

Keywords

Main Subjects

References

[1] S. Caro, D. Chablat, A. Goldsztejn, D. Ishii, C. Jermann, A branch and prune algorithm for the computation of generalized aspects of parallel robots, Artif. Intell. 211 (2014) 34--50.
[2] Y. Chen, X. Han, F. Gao, Z. Wei, Y. Zhang, Workspace analysis of a 2-dof planar parallel mechanism, International Conference of Electrical, Automation and Mechanical Engineering, (2015) 192--195.
[3] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput. 6(2) (2002) 182--197.
[4] M. Ehrgott, Multicriteria Optimization, Springer Science & Business Media, 2005.
[5] M. Gallant, R. Boudreau, The synthesis of planar parallel manipulators with prismatic joints for an optimal, singularity-free workspace, J. Robot. Syst. 19(1) (2002) 13--24.
[6] C. Gosselin, J. Angeles, A global performance index for the kinematic optimization of robotic manipulators, J. Mech. Des. 113 (1991) 220--226.
[7] C. Gosselin, J. Angeles, Singularity analysis of closed-loop kinematic chains, IEEE Trans. Robot. Autom. 6(3) (1990) 281--290.
[8] C. Gosselin, Dexterity indices for planar and spatial robotic manipulators, Proc. IEEE Int. Conf. Robot. Autom. (1990) 650--655.
[9] E. Hansen, S. Sengupta, Bounding solutions of systems of equations using interval analysis, BIT 21(2) (1981) 203--211.
[10] T. Huang, M. Li, Z. Li, D. Chetwynd, D. Whitehouse, Optimal kinematic design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index, IEEE Trans. Robot. Autom. 20(3) (2004) 538--543.
[11] D. Lera, M. Posypkin, Y. Sergeyev, Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics, Appl. Math. Comput. 390 (2021) 125660.
[12] A. Maminov, Automated Multi-criteria Optimization of Parallel Robots, Lecture Notes in Comput. Sci. 15218 (2024) 125--138.
[13] A. Maminov, M. Posypkin, Constrained multi-objective robot's design optimization, IEEE Conf. Russ. Young Res. Electr. Electron. Eng. (2020) 1992--1995.
[14] A. Maminov, M. Posypkin, S. Shary, Reliable bounding of the implicitly defined sets with applications to robotics, Procedia Comput. Sci. 186 (2021) 227--234.
[15] J.-P. Merlet, Parallel robots, Springer Science & Business Media, 2012.
[16] Y.-J. Nam, M.-K. Park, Workspace optimization and kinematic performance evaluation of 2-DOF parallel mechanisms, J. Mech. Sci. Technol. 20(10) (2006) 1614--1625.
[17] S. Opricovic, G.-H. Tzeng, Extended VIKOR method in comparison with outranking methods, Eur. J. Oper. Res. 178(2) (2007) 514--529.
[18] Z. Qu, P. Zhang, Y. Hu, H. Yang, T. Guo, K. Zhang, J. Zhang, Optimal design of agricultural mobile robot suspension system based on NSGA-III and TOPSIS, Agriculture 13(1) (2023) 207.
[19] K. Sinaga, M.-S. Yang, Unsupervised K-means clustering algorithm, IEEE Access 8 (2020) 80716--80727.
[20] V. Pandey, H. Dincer, A review on TOPSIS method and its extensions for different applications with recent development, Soft Comput. 27(23) (2023) 18011--18039.
Journal of Mathematical Modeling
Volume 14, Issue 3
August 2026
Pages 1093-1105

Files

Share

How to cite

Statistics