Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space

TL;DR

This paper derives explicit formulas for extremal controls in a specific sub-Riemannian problem on the Euclidean motion group, providing insights into optimal control strategies under fixed initial momenta.

Contribution

It introduces explicit formulas for extremal controls in a particular sub-Riemannian setting with fixed initial momenta, advancing understanding of control solutions in this context.

Findings

Explicit formulas for extremal controls derived

Special case with fixed initial momenta analyzed

Enhances methods for solving sub-Riemannian control problems

Abstract

For the sub-Riemannian problem on the group of motions of Euclidean space we present explicit formulas for extremal controls in a special case, when one of the initial momenta is fixed.