Exp[licit]-A Robot modeling Software based on Exponential Maps

TL;DR

This paper introduces Exp[licit], open-source software for robot modeling using exponential maps, simplifying the derivation of equations of motion by reducing coordinate frame choices compared to traditional methods.

Contribution

It presents a novel approach using differential geometry with exponential maps for robot modeling, along with an open-source software implementation.

Findings

Reduces coordinate frame choices to two with exponential maps

Demonstrates benefits over traditional Denavit-Hartenberg method

Provides practical software tools and examples

Abstract

$ $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.