A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators
This paper introduces a two-stage method based on bio-inspired algorithms for the design optimization of a class of general Stewart platforms. The first stage performs a mono-objective optimization in order to reach, with sufficient dexterity, a regular target workspace while minimizing the elements...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/5/543 |
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| author | Alejandra Ríos Eusebio E. Hernández S. Ivvan Valdez |
| author_facet | Alejandra Ríos Eusebio E. Hernández S. Ivvan Valdez |
| author_sort | Alejandra Ríos |
| collection | DOAJ |
| description | This paper introduces a two-stage method based on bio-inspired algorithms for the design optimization of a class of general Stewart platforms. The first stage performs a mono-objective optimization in order to reach, with sufficient dexterity, a regular target workspace while minimizing the elements’ lengths. For this optimization problem, we compare three bio-inspired algorithms: the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), and the Boltzman Univariate Marginal Distribution Algorithm (BUMDA). The second stage looks for the most suitable gains of a Proportional Integral Derivative (PID) control via the minimization of two conflicting objectives: one based on energy consumption and the tracking error of a target trajectory. To this effect, we compare two multi-objective algorithms: the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) and Non-dominated Sorting Genetic Algorithm-III (NSGA-III). The main contributions lie in the optimization model, the proposal of a two-stage optimization method, and the findings of the performance of different bio-inspired algorithms for each stage. Furthermore, we show optimized designs delivered by the proposed method and provide directions for the best-performing algorithms through performance metrics and statistical hypothesis tests. |
| first_indexed | 2024-03-09T05:32:17Z |
| format | Article |
| id | doaj.art-6374f0aecbbd43498e0d26854192bad8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:32:17Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6374f0aecbbd43498e0d26854192bad82023-12-03T12:31:57ZengMDPI AGMathematics2227-73902021-03-019554310.3390/math9050543A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel ManipulatorsAlejandra Ríos0Eusebio E. Hernández1S. Ivvan Valdez2Instituto Politécnico Nacional, ESIME Ticomán, Mexico City 07738, MexicoInstituto Politécnico Nacional, ESIME Ticomán, Mexico City 07738, MexicoCONACYT, Centro de Investigación en Ciencias de Información Geoespacial, CENTROGEO A.C., Querétaro 76703, MexicoThis paper introduces a two-stage method based on bio-inspired algorithms for the design optimization of a class of general Stewart platforms. The first stage performs a mono-objective optimization in order to reach, with sufficient dexterity, a regular target workspace while minimizing the elements’ lengths. For this optimization problem, we compare three bio-inspired algorithms: the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), and the Boltzman Univariate Marginal Distribution Algorithm (BUMDA). The second stage looks for the most suitable gains of a Proportional Integral Derivative (PID) control via the minimization of two conflicting objectives: one based on energy consumption and the tracking error of a target trajectory. To this effect, we compare two multi-objective algorithms: the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) and Non-dominated Sorting Genetic Algorithm-III (NSGA-III). The main contributions lie in the optimization model, the proposal of a two-stage optimization method, and the findings of the performance of different bio-inspired algorithms for each stage. Furthermore, we show optimized designs delivered by the proposed method and provide directions for the best-performing algorithms through performance metrics and statistical hypothesis tests.https://www.mdpi.com/2227-7390/9/5/543two-stage methodmono and multi-objective optimizationmulti-objective optimizationoptimal designGough–Stewartparallel manipulator |
| spellingShingle | Alejandra Ríos Eusebio E. Hernández S. Ivvan Valdez A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators Mathematics two-stage method mono and multi-objective optimization multi-objective optimization optimal design Gough–Stewart parallel manipulator |
| title | A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators |
| title_full | A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators |
| title_fullStr | A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators |
| title_full_unstemmed | A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators |
| title_short | A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators |
| title_sort | two stage mono and multi objective method for the optimization of general ups parallel manipulators |
| topic | two-stage method mono and multi-objective optimization multi-objective optimization optimal design Gough–Stewart parallel manipulator |
| url | https://www.mdpi.com/2227-7390/9/5/543 |
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