Endpoint geodesic formulas on SE3, SO3 × R3 and subspaces of SE3

Abstract

The special Euclidean group SE3 and the closely related group SO3×R3 are important spaces in many fields of application. Explicit embeddings into matrix subgroups are being studied and it is shown that these spaces are extrinsic symmetric with respect to their embeddings. Furthermore, endpoint geodesic formulas are derived explicitly in both cases, as well as for certain subspaces of SE3. Ultimately, the formulas could be used to solve for geodesics that connect two given points on these spaces.