추가 잉여 입력 상태에 따른 직렬형 로봇의 속도 타원 사이의 기하적 관계 분석

Abstract

This paper presents an in-depth analysis of the geometric relationship among the velocity ellipsoids of a serial robot according to the combination of additional extra inputs. In this paper, one or more extra inputs are added to a non-redundant or redundant serial robot, and no assumption is made on the linear independency of the additional extra inputs. First, in the case of one additional input, the relationship of two velocity ellipsoids before and after the addition of extra input is expressed by means of the freezing of the extra input, which defines a constraint hyperplane in the output space. Using the constraint hyperplane, the geometric relationship between two velocity ellipsoids with zero and one extra input is obtained. Second, the case of two additional inputs is treated as the addition of extra input twice in a row, and two constraint hyperplanes corresponding to the freezing of the two extra inputs are defined. Using the two constraint hyperplanes, the geometric relationship among three velocity ellipsoids with zero, one, two extra inputs is obtained. It is shown that the resulting geometric relationship should change depending on the linear independency of the two extra inputs. Third, the analysis for the case of two extra input is extended to the case of r(≥ 3) additional inputs, which is treated as the addition of extra input r times in a row. Using r constraint hyperplanes corresponding to the freezing of the (r+1) extra inputs, the geometric relationship among r velocity ellipsoids with zero up to r extra inputs is identified. It is shown that the inclusion relationship between two velocity ellipsoids before and after the addition of r extra inputs should change depending on the linear independency of the r extra inputs. Fourth, simulation results of planar and spatial serial robots are provided to illustrate the varying geometric relationship among the velocity ellipsoids of a serial robot according to the combination of additional extra inputs.