Algebro-geometric techniques in kinematics of robots

该项目涉及对具有6条手臂的机器人闭合连杆的详细研究。这些物体由6个臂组成，通过旋转或螺旋运动的关节连接成一个封闭的链。众所周知，这种随机连杆是刚性的。一个关键的问题是对所有这些非刚性连杆进行分类，因为它们在工程中很有用，而且成本效益很高，因为6是此类模型的最佳数字。代数几何技术指导了具有转动关节的连杆机构的研究。该项目将开发新的（代数）技术来处理关节的螺旋运动。这个项目基本上是跨学科的，因为它使用现代代数和几何的机器来解决机器人的理论问题，并在工程上有潜在的应用。

The project involves a detailed study of robot closed linkages with 6 arms. These objects consist of 6 arms forming a closed chain connected via joints that rotate or have screw motion. It is known that a random such linkages is rigid. A crucial question is to classify all such linkages that are non-rigid, as they are useful in engineering and cost effective as 6 is the optimal number for such models.Algebro-Geometric techniques have guided the study of linkages with rotational joints. The project will develop new (algebraic) techniques that deal with screw motion of the joints. The project is fundamentally interdisciplinary, as it uses modern machinery of algebra and geometry to tackle theoretical questions in robotics with potential applications in engineering.