A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators

Alejandra Ríos, Eusebio E. Hernández and S. Ivvan Valdez
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Alejandra Ríos: Instituto Politécnico Nacional, ESIME Ticomán, Mexico City 07738, Mexico
Eusebio E. Hernández: Instituto Politécnico Nacional, ESIME Ticomán, Mexico City 07738, Mexico
S. Ivvan Valdez: CONACYT, Centro de Investigación en Ciencias de Información Geoespacial, CENTROGEO A.C., Querétaro 76703, Mexico

Mathematics, 2021, vol. 9, issue 5, 1-20

Abstract: 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.

Keywords: two-stage method; mono and multi-objective optimization; multi-objective optimization; optimal design; Gough–Stewart; parallel manipulator; performance metrics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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