论文标题
多项式不变式和多螺钉的sagbi基础
Polynomial Invariants and SAGBI Bases for Multi-screws
论文作者
论文摘要
用于机器人操纵器的多项式不变性及其关节是欧几里得组在其Lie代数，无穷小曲折或螺钉的空间上的伴随作用。本文的目的是确定多个螺钉生成多项式的基本集。引入了来自Sagbi基础理论的技术。结果，为螺钉对的多项式不变性提供了完整的描述，并获得了一些螺丝三元的结果。事实证明，不变性与Denavit-Hartenberg参数有关。
Polynomial invariants for robot manipulators and their joints arise from the adjoint action of the Euclidean group on its Lie algebra, the space of infinitesimal twists or screws. The aim of this paper is to determine basic sets of generating polynomials for multiple screws. Techniques from the theory of SAGBI bases are introduced. As a result, a complete description is provided of the polynomial invariants for screw pairs and some results for screw triples are obtained. The invariants are shown to be related to Denavit-Hartenberg parameters.
