Making Space for Time: The Special Galilean Group and Its Application to Some Robotics Problems

TL;DR

This paper explores the special Galilean group SGal(3), a 10-dimensional Lie group, and demonstrates its potential to unify space and time representations of uncertainty for robotics applications.

Contribution

It introduces the structure of SGal(3) and shows how it can be used to model uncertainty in space and time within robotics contexts.

Findings

SGal(3) provides a unified framework for space-time uncertainty.

The group structure supports applications in robotics.

Potential for improved modeling of dynamic systems.

Abstract

The special Galilean group, usually denoted SGal(3), is a 10-dimensional Lie group whose important subgroups include the special orthogonal group, the special Euclidean group, and the group of extended poses. We briefly describe SGal(3) and its Lie algebra and show how the group structure supports a unified representation of uncertainty in space and time. Our aim is to highlight the potential usefulness of this group for several robotics problems.