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 relati...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.展开更多
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)
文摘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.
