SUMMARY: This paper addresses the problem of optimal mechanisms design, for the geometric structure and control parameters of mechanisms with complex kinematics, which is one of the most intricate problems in contemporary robot modeling. The problem is stated by means of task requirements and performance constraints, which are specified in terms of the end-effector's position and orientation to accomplish the task. Usually, this problem does not fulfill the characteristics needed to use gradient-based optimization algorithms. In order to circumvent this issue, we introduce case studies of optimization models using evolutionary algorithms (EAs), which deal with the concurrent optimization of both: structure and control parameters. We define and review several optimization models based on the workspace, task and dexterity requirements, such that they guarantee an adequate performance under a set of operating and joint constraints, for a Delta parallel manipulator. Then, we apply several methodologies that can approximate optimal designs. Additionally, we compare the EAs with a quasi-Newton method (the BFGS), in order to show that the last kind of methods is not capable of solving the problem if the initial point is not very close to a local optimum. The results provide directions about the best state-of-the-art EA for addressing different design problems.

A concurrent optimum design of a manipulator is to find the best geometrical and control parameters in the same optimization process. One of the main contributions of this article is a concurrent method for optimum design and its comparison versus a sequential one, where the last requires several optimization stages. Besides, we statistically compare three metaheuristics: the Omnioptimizer, the CMA-ES, and the BUMDA for the two methodologies, in order to elucidate directions about which metaheuristic performs the best for this kind of problem, and whether it must be used in a sequential or concurrent fashion. These metaheuristics are compared with reported results in the specialized literature. In addition, we perform an analysis of results to statistically determine relations between the parameters and the objective function, as a consequence, we found the most impacting parameters to the manipulator performance.

Mathematical models are used for simulating the electrochemical phenomena of proton-exchange-membrane (PEM) fuel cells. They differ in the scale, modeling variables, precision in specific features, and the required parameters. Often, the input parameters are not measurable and need to be estimated by minimizing the error between the model output and experimental data; however, the estimated parameters could differ from one model to another, hence provoking uncertainty about the correct values and the model’s suitability for simulating the real phenomenon. To address these issues, we introduced a self-validating methodology using three different mathematical models: The first set of parameters was estimated with a semi-empirical (SE) model; then, it was used for computing several points of the polarization curve (PC). The SE parameters and points were used to estimate a second set of parameters and to compute a single point of the PC with a macro-homogeneous (MH) model. The parameters and concentration profiles from the MH solution were used to estimate the last set of parameters with the reaction–convection–diffusion (SP-RCD) model, increasing the detail of the simulation. The SP-RCD parameters were returned to the MH model to recover the complete PC. The proposed methodology requires a few data points to consistently recover the same PC from the three models through estimating parameters in one model and validating them in the others. As output, the method provides complete information about several variables and the physical properties of the catalysts. In addition to the consistent simulation, the numerical results are consistent with those reported in the literature, thus validating the proposed method.