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Reliability-Based Optimization of Flexible Manipulators

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This paper addresses the optimal design of flexible link manipulators to optimize the dynamic performance subject to the effect of the uncertainties quantified by a reliability index.


The links’ uncertain stiffness and inertial parameters are modeled using the stochastic finite-element method. A methodology is proposed to determine the design variables that maximize the performance and simultaneously maximize reliability that aims to optimize the flexible manipulators based on reliability-based optimization. This reliability-based optimization derives a multi-objective optimization problem that is solved using evolutionary algorithms.


Numerical results illustrate the dynamic modeling of the one-link flexible manipulator using the stochastic finite element method in terms of displacement of the manipulator’s tip and the frequency response function subjected to uncertainties. Moreover, the optimal design was carried out to maximize the reliability and optimize the elastodynamic performance; thus, the reliability of the manipulator is maximized, and several performance criteria such as the actuator power, manipulator mass, and the first mode natural frequency are optimized simultaneously.


The proposed methodology permitted optimizing critical operational characteristics of flexible manipulators, such as minimizing the elastic deflections, minimizing the power of actuators, and minimizing the mass of the manipulator subject to reliability constraints. Thus, the main contributions are (i) the stochastic modeling of flexible-link manipulators, (ii) the reliability optimization approach applied to the flexible-link manipulator, and (iii) a case study considering a one-link flexible manipulator with uncertain structural parameters to determine the optimal inertial parameters and geometric parameters.

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The authors are thankful for the financial support provided by CNPq (Process 427204/2018-6), and CAPES.

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Correspondence to Fabian Andres Lara-Molina.

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This study was funded by CNPq (427204/2018-6) and, CAPES. The authors declare that they have no conflict of interest.

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Appendix A Parameters of Flexible-Link Manipulator

Appendix A Parameters of Flexible-Link Manipulator

See Tables 5, 6.

Table 5 Physical and geometric parameters of flexible-link manipulator
Table 6 Definition bounds of optimization constraits

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Lara-Molina, F.A., Gonçalves, R.S. Reliability-Based Optimization of Flexible Manipulators. J. Vib. Eng. Technol. 11, 3147–3162 (2023).

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