Machine learning for motion control using geometric algebra

该奖学金将由ARM赞助，并在剑桥大学工程系（CUED）的信号处理小组进行。该项目将与仿生机器人、控制系统、推理和机器学习领域的研究人员建立合作关系。目的是使用机器学习来学习与人体运动相关的几何量。本课题将采用几何代数（GA）的数学框架。我们特别感兴趣的是研究三维欧几里得空间的5D表示的应用，称为共形几何代数（CGA）。在这个代数中，原始对象（叶片）可以表示点、线、面、圆、球和体积元。这些对象都继承了来自底层CGA的乘法规则。在这个代数中，这些对象之间的变换（旋转、平移和膨胀）也被表示为简单对象。我们要学习的正是遗传算法的这些基本要素。除了理解数学框架和编程机器学习环境外，该项目还将涉及在硬件中实例化机器学习算法的各个方面。有大量关于FPGA硬件上的GA实现的文献，主要用于刀片乘法，在这里，我们将研究将这项工作扩展到更复杂的机器学习工作负载的可行性。

Machine learning for motion control using geometric algebraThis studentship will be sponsored by ARM and carried out in the Signal Processing Group of the Cambridge University Engineering Department (CUED). The project will establish collaborations with researchers in the fields of bio-inspired robotics, control systems and inference and machine learning.The aim will be to use Machine Learning to learn the geometric quantities associated with human motion. The mathematical framework of Geometric Algebra (GA) will be employed for this project. In particular we are interested in studying the application of a 5D representation of 3D Euclidean space, called Conformal Geometric Algebra (CGA). In this algebra primitive objects (blades) can represent points, lines, planes, circles, spheres and volume elements. These objects all inherit a multiplication rule from the underlying CGA. Transformations between these objects (rotations, translations and dilations) are also represented as simple objects in this algebra. It is these primitives of GA that we aim to learn.As well as understanding the mathematical framework and programming the machine learning environment, the project will also involve instantiating aspects of the machine learning algorithms in hardware. There is a substantial literature of GA implementations on FPGA hardware, mainly for blade multiplication, and here we will investigate the feasibility of extending this work to more complex machine learning workloads.