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APPLICATION OF GRASSMANN GEOMETRY TO CLOSENESS MEASURE OF SINGULAR CONFIGURATION ON THE HEXA-PARALLEL ROBOT

机译：基层几何在六角升降机机器人上奇异配置的近距离应用

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摘要

In order to allow effective and safety application of parallel robots, the development of special control functionalities particularly the proximity of the structure to direct kinematic singularities are of particular importance. Based on Grassmann geometry, such singularities of the HEXA-parallel robot are detected and an index for measure the closeness to these configurations is established. All the direct kinematic singularities of parallel robots are associated to one or more Grassmann variety. Therefore, it is possible to obtain a closeness index based on a distance measure between geometric elements (planes and lines) which indicate the proximity of the parallel robot to a singularity. The index is experimentally compared on the HEXA-parallel robot with other indexes based on the optimization of physical quantities as power and frequency based methods. The comparison results are analyzed and special characteristics of the closeness indexes are presented.
机译：为了允许平行机器人的有效和安全应用，特殊控制功能的发展特别是对直接运动奇异性的结构接近是特别重要的。基于基于Grassmann几何形状，检测到六角形机器人的这种奇点，并建立了测量对这些配置的近距离的索引。并联机器人的所有直接运动奇异性与一个或多个Grassmann品种相关联。因此，可以基于几何元件（平面和线）之间的距离测量来获得密闭指数，其指示并联机器人对奇异性的接近度。基于物理量的优化作为电力和频率的方法，将指数与其他索引进行实验。分析了比较结果，并提出了近距离的特殊特征。

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