In this paper we study a path-following problem on R3 with a non-holonomic constraint. The geometric structure associated to the velocity constraint is explored, and general principles for constructing guiding vector fields are obtained, fulfilling the path-following requirements on a neighborhood of the desired path while allowing the design of vector fields to be conducted in global coordinates.
@article{arxiv.2604.08873,
title = {Structure of Motion under Constraints and non-Holonomic Path-Following on $R^3$},
author = {Bohuan Lin and Weijia Yao},
journal= {arXiv preprint arXiv:2604.08873},
year = {2026}
}