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arXiv · 2601.10734

Cohomological Equation for Robotic Screw Motion on the Lie Group SE(3)

Amanze C. Egere
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Abstract

We study the cohomological equation associated with screw motions on the Euclidean motion group SE(3). Working on the smooth manifold M = T^3 x SO(3), we combine Fourier analysis in the translational variables with Peter-Weyl theory on SO(3) to reduce the equation to a family of finite-dimensional linear transport systems along frequency orbits induced by the rotational component. In the case of finite-order rotations, solvability is governed by explicit finite-dimensional linear obstructions encoded by monodromy operators. An explicit screw motion along the z-axis illustrates the resulting resonance conditions. Since rigid motions on SE(3) arise naturally as configuration spaces in robotic kinematics, the results provide a precise description of obstruction phenomena relevant to robotic rigid-body motion.

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Amanze C. Egere. 2026-01-07. Cohomological Equation for Robotic Screw Motion on the Lie Group SE(3). https://arxiv.org/abs/2601.10734

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