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.

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.

In this paper, a structure-control design methodology for simultaneously optimizing both mechanical structure and control of a parallelogram linkage robot is proposed. It takes into count the dynamical model and the mechanical parameters for the optimization process along with the controller. Thus, proportional-integral-derivative (PID) control and geometric variables are optimized in a simultaneously way. Through the concurrent procedure an optimal combination of the robot structure and controller gains is obtained. The global optimization problem is tackled by using an estimation of distribution algorithm (EDA) based on the Boltzmann distribution. The EDA seeks for the global optimum by estimating and sampling a probability distribution. The proposed methodology is verified through simulation experiments and applied to the design process of a parallelogram linkage system. The results obtained in experiments show the effectiveness of the proposal. This approach is generic and could be applied to other mechanisms in similar way when for concurrent process both kinematic and dynamic models are available along with the controller. In particular, the results are promising when the optimization parameters are uncorrelated, namely control and mechanical parameters.