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arXiv · 2411.07998

A Symmetry-Preserving Reduced-Order Observer

Jeremy W. Hopwood·Craig A. Woolsey
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Abstract

A symmetry-preserving, reduced-order state observer is presented for the unmeasured part of a system's state, where the nonlinear system dynamics exhibit symmetry under the action of a Lie group. Leveraging this symmetry with a moving frame, the observer dynamics are constructed such that they are invariant under the Lie group's action. Sufficient conditions for the observer to be asymptotically stable are developed by studying the stability of an invariant error system. As an illustrative example, the observer is applied to the problem of rigid-body velocity estimation, which demonstrates how exploiting the symmetry of the system can simplify the stabilization of the estimation error dynamics.

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BibTeXRIS

Jeremy W. Hopwood, Craig A. Woolsey. 2025-08-28. A Symmetry-Preserving Reduced-Order Observer. https://doi.org/10.23919/acc63710.2025.11107972

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