Reliability-Based Optimization of Flexible Manipulators

Purpose 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. Methods 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. Results 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. Conclusions 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.