Projeto ótimo de robôs manipuladores 3r considerando a topologia do espaço de trabalho

Abstract

Several studies have investigated the properties of the workspace of opened robotic chains (or serial) with the purpose of emphasizing its geometric and kinematic characteristics, to devise analytical algorithms and procedures for its design. The workspace of a robot manipulator is considered of great interest from theoretical and practical viewpoint. In classical applications in industry, manipulators need to pass through singularities in the joint space to change their posture. A 3-DOF manipulator can execute a non-singular change of posture if and only if there is at least one point in its workspace which has exactly three coincident solutions of the Inverse Kinematic Model (IKM). It is very difficult to express this condition directly from the kinematic model. Thus, in this work, the algebraic tool Gröbner basis is used to obtain an equation for splitting the regions with different types of 3R orthogonal manipulators. The determinant of Jacobian matrix of the direct kinematic model is considered equal to zero to obtain the other surfaces of separation. In addition, is presented a classification of 3R orthogonal manipulators related to the number of solutions in IKM, the number of cusp points and nodes. Some problems of multi-objective optimization are proposed to obtain the optimal design of robots. First considering a general case where the aim is to maximize the volume of the workspace, maximize the stiffness of the joint system and optimize the dexterity of the manipulator without the imposition of restrictions. Next, the optimization problem is subject to penalties that control the topology, making it possible to obtain solutions which satisfy the predetermined topologies. Solutions are presented for the case r3 null and r3 not null. The optimization problem is investigated by using a deterministic technique and two evolutionary algorithms. Some numerical applications are presented to show the efficiency of the proposed methodology.