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在旋量空间中引入正线性组合、仿射组合和凸组合等概念,采用几何表示方法,定义点接触约束的“相对形封闭性”,推导相应的对偶等价定理、拓朴等价定理和代数等价定理。构造判别函数J_0,实现了形封闭的计算机智能判断,在两对偶的旋量空间中分别定义约束锥和自由锥,提出在点接触作用下刚体的单向自由度和单向约束度,用以描述刚体在点接触约束下的瞬时运动和受力状态,规定机器人抓取的定性指标,讨论实现相对形封闭抓取的具体步骤。
Introducing the concept of positive linear combination, affine combination and convex combination in the spin space, the geometrical representation method is used to define the “relative closedness” of the point contact constraint, and the corresponding dual equivalence theorem, topological equivalence theorem and Algebra Equivalence Theorem. The discriminant function J_0 is constructed to realize the shape-closed computer intelligent judgment. The constraint cone and the free cone are respectively defined in two dual spin space, and the one-way freedom degree and one-way constraint degree of the rigid body under point contact are proposed Describe the rigid body under the point of contact constraints of the instantaneous movement and stress state, the provisions of the robot grasp the qualitative indicators to discuss the relative closed-shaped grasp the specific steps.