$ $Deriving a robot's equation of motion typically requires placing multiple coordinate frames, commonly using the Denavit-Hartenberg convention to express the kinematic and dynamic relationships between segments. This paper presents an alternative using the differential geometric method of Exponential Maps, which reduces the number of coordinate frame choices to two. The traditional and differential geometric methods are compared, and the conceptual and practical differences are detailed. The open-source software, Exp[licit], based on the differential geometric method, is introduced. It is intended for use by researchers and engineers with basic knowledge of geometry and robotics. Code snippets and an example application are provided to demonstrate the benefits of the differential geometric method and assist users to get started with the software.

翻译：推导机器人的运动方程通常需要设置多个坐标系，常用方法是采用Denavit-Hartenberg约定来表达各构件之间的运动学和动力学关系。本文提出了一种替代方法，即使用指数映射的微分几何方法，该方法将坐标系选择的数量减少至两个。本文对传统方法与微分几何方法进行了比较，并详细阐述了二者在概念与实践层面的差异。此外，本文介绍了基于微分几何方法的开源软件Exp[licit]，该软件面向具备基础几何与机器人学知识的研究人员与工程师。文中提供了代码片段与示例应用，以展示微分几何方法的优势，并帮助用户快速上手该软件。