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COBEM 2021
26th International Congress of Mechanical Engineering
COMPARISON BETWEEN TWO SINGULARITY AVOIDANCE INDICES FOR PLANAR PARALLEL KINEMATICALLY REDUNDANT MANIPULATORS
Submission Author:
Felipe Marques Farias Filho , AL , Brazil
Co-Authors:
Felipe Marques Farias Filho, Maíra Martins da Silva, João Vitor de Carvalho Fontes
Presenter: Felipe Marques Farias Filho
doi://10.26678/ABCM.COBEM2021.COB2021-0059
Abstract
Parallel manipulators (PMs) have potential advantages compared to their serial counterparts, such as higher accuracy, higher stiffness, higher dynamic performance, and high load capacity to mass ratio. The main drawback is their limited workspace and the presence of singularities within it. Kinematic redundancy might reduce the presence of singular regions, but the inverse kinematic problem of kinematically redundant PMs present infinite solutions. Therefore, an optimization problem, denoted as redundancy resolution, can be stated, aiming to select the best solution among the others. Adequate performance indices, among them singularity avoidance indices, should compose the objective function. One of the most commonly used is the inverse of the condition number of the end-effector's Jacobian matrix, also known as the Local Conditioning Index (LCI). Another candidate is the Normalised Scaled Incircle Radius (NSIR), based on the manipulator's geometrical characteristics and the inverse kinematics Jacobian matrix. This work aims to compare the use of indices in redundancy resolution schemes of a planar parallel kinematically redundant manipulator, the 3PRRR. The prepositioning and the ongoing redundancy resolution schemes and four pre-defined end-effector trajectories, straight line, circle, spiral, and square, are numerically investigated. The optimization algorithm used for redundancy resolution is solved offline by exploring Genetic Algorithms (GA) and Sequential Quadratic Programming (SQP). The design variables are the positions of the redundant active joints. Whilst NSIR obtains better performance indices, it takes longer to be derived since it requires more calculations. Therefore, the LCI should be preferred for real-time applications, while the NSIR would be more advantageous for offline applications.
Keywords
redundancy resolution, Normalised Scaled Incircle Radius, Local Conditioning Index, Optimization, Robotics
