Intrinsic Path Following on SO(3)
Abstract
This paper studies intrinsic path following for fully actuated rigid-body attitude dynamics over a broad class of attitude paths, namely arbitrary smooth embedded closed curves on SO(3). We construct a tangential--transverse state decomposition on a tubular neighborhood using normal and pullback bundle geometry. The resulting second-order dynamics admit a smooth feedback transformation that independently assigns tangential and transverse covariant accelerations. A transverse proportional--derivative law renders the path-following manifold invariant and locally uniformly exponentially stable on an explicit forward-invariant neighborhood, while leaving the tangential dynamics freely assignable. This allows independent regulation of progression along the path, stabilization of a selected attitude on the path, or tracking of a time-varying motion. For a representative fiber path, the tubular coordinates are obtained in closed form up to the natural cut-locus obstruction, and simulations illustrate point stabilization and trajectory tracking.
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BibTeX
@misc{akhtar2026intrinsic,
title = {{Intrinsic Path Following on $\mathsfSO(3)$}},
author = {Adeel Akhtar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04332},
eprint = {2610.04332},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04332},
}
RIS
TY - UNPB
TI - Intrinsic Path Following on SO(3)
AU - Adeel Akhtar
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04332
UR - https://arxiv.org/abs/2610.04332
AB - This paper studies intrinsic path following for fully actuated rigid-body attitude dynamics over a broad class of attitude paths, namely arbitrary smooth embedded closed curves on SO(3). We construct a tangential--transverse state decomposition on a tubular neighborhood using normal and pullback bundle geometry. The resulting second-order dynamics admit a smooth feedback transformation that independently assigns tangential and transverse covariant accelerations. A transverse proportional--derivative law renders the path-following manifold invariant and locally uniformly exponentially stable on an explicit forward-invariant neighborhood, while leaving the tangential dynamics freely assignable. This allows independent regulation of progression along the path, stabilization of a selected attitude on the path, or tracking of a time-varying motion. For a representative fiber path, the tubular coordinates are obtained in closed form up to the natural cut-locus obstruction, and simulations illustrate point stabilization and trajectory tracking.
ER -