摘要
This paper presents an approach to algebraic detection of relative form closure for a multi-fingered grasp G and gives an attention to the classification of relative form closures.Whether or not a grasp G is of relative form closure has been verified by the geometric criterion 0?rintC[G](Xiong Y L,Xiong X R.Algebraic structure and geometric interpretation of rigid complex fixture system.IEEE Trans Autom Sci Eng,2007,4:252–264;Xiong Y L.Theory of point contact restraint and qualitative analysis of robot grasping.Sci China Ser A-Math,1994,37:629–640).Our aim is at transferring the geometric criterion into an algebraic formulation by a theorem that a grasp G is relative form closure,if,and only if the origin 0 can be represented as a positive convex combination of G.So we develop a constructive procedure called ri-simplex algorithm to find a positive convex combination of G when it has relative form closure.Form closure is considered as a special case of relative form closure,when the grasp G can affinely span the whole space,while partly relative form closure is referred to as form closed relative to a subset G1 of G.
This paper presents an approach to algebraic detection of relative form closure for a multi-fingered grasp G and gives an attention to the classification of relative form closures. Whether or not a grasp G is of relative form closure has been verified by the geometric criterion 0?rintC[G](Xiong Y L, Xiong X R. Algebraic structure and geometric interpretation of rigid complex fixture system. IEEE Trans Autom Sci Eng, 2007, 4: 252–264; Xiong Y L. Theory of point contact restraint and qualitative analysis of robot grasping. Sci China Ser A-Math, 1994, 37: 629–640). Our aim is at transferring the geometric criterion into an algebraic formulation by a theorem that a grasp G is relative form closure, if, and only if the origin 0 can be represented as a positive convex combination of G. So we develop a constructive procedure called ri-simplex algorithm to find a positive convex combination of G when it has relative form closure. Form closure is considered as a special case of relative form closure, when the grasp G can affinely span the whole space, while partly relative form closure is referred to as form closed relative to a subset G1 of G.
基金
supported by the National Natural Science Foundation of China(Grant No.51327801)
the National Key Basic Research Program of China(Grant No.2013CB035803)
关键词
代数形式
形封闭
测试
几何解释
单纯形算法
夹具系统
代数结构
IEEE
relative form closure
algebraic test
PCC(positive convex combination)
ri-simplex algorithm
simplex grasp
complex grasp