Evaluating concurrent design approaches for a Delta parallel manipulator

Abstract

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

“…Both algorithms were executed with their default parameters; in this sense, it is possible that the PSO improves its performance if the best execution parameters are used; nevertheless, this requires additional research and computational time for each design problem. On the other hand, the BUMDA requires a single execution parameter, the population size, which is not required to be tuned, according to the recommended settings of 10 times the number of optimization variables [8,32]. Thus, we recommend the use of the BUMDA by default, and to use the PSO if the solution with the BUMDA is not satisfactory or if the trajectory is highly complex, although using the PSO could require one to look for optimal execution parameters.…”

“…Working methods vary under a system's complexity and the number of objectives to optimize. According to Botello et al [8,9], the optimization problems of robotic manipulators can be classified into three categories: The first is the static design problem, in which a homogeneous transformation or zero-order differential equation needs to be solved. Typical problems of this group are dexterity, stiffness, workspace volume, and manipulability maximization.…”

“…Nevertheless, there are a few proposals that consider an optimization framework that integrates several objectives into a single process [22][23][24][25][26]. For instance, a concurrent design has been tested through various design methods in delta parallel manipulators [8]. In this regard, a limitation for considering such a unified framework is that various objectives conflict.…”

Delta-type four-DOF force-feedback device composed of pneumatic artificial muscles and magnetorheological clutch and its application to lid opening

“…We calculate the position and orientation of end effector Q using geometric relations. The position of spherical joint P, (x p , y p , z p ), can be calculated from the joint angles [22].…”

New mechanism for press-fit processes: preliminary analysis

“…The originality of this work is mainly related to the analysis of the proposed solution, which is rather unusual if compared with classical devices that are commonly proposed in literature for similar applications [e.g. delta manipulators (Botello-Aceves et al , 2018) or Cartesian parallel manipulators such as the multipteron ones (Gosselin et al , 2007)].…”