Exp[licit] An Educational Robot Modeling Software based on Exponential Maps

Deriving a robot’s equations 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, $\operatorname{Exp}[\text { licit }]^{\mathrm{TM}}$, based on the differential geometric method, is introduced. It is intended for use by researchers and engineers with basic knowledge of geometry and robotics and aims to serve as a supportive resource during the study of differential geometric approaches. 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.