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.

翻译：特殊伽利略群（通常记作SGal(3)）是一个十维李群，其重要子群包括特殊正交群、特殊欧几里得群以及扩展位姿群。本文简要描述SGal(3)及其李代数结构，并阐明该群结构如何支持时空不确定性的统一表征。我们的目标在于揭示该群在若干机器人学问题中的潜在应用价值。