Set Inversion and Box Contraction on Lie Groups Using Interval Analysis
Автор: Interval methods in control engineering
Загружено: 2024-04-15
Просмотров: 59
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Speaker:
Nicolas Merlinge (ONERA, Département traitement de l’information et systèmes - Identification, Guidage, Navigation et Contrôle (IGNC), Palaiseau, France)
Abstract:
Set inversion and box contraction consist in finding bounded solutions to an equation where variables belong to bounded sets. These problems are classic in Euclidean spaces and can be solved using interval analysis (e.g. with the SIVIA method and with interval contractors). However, they quickly become complex when dealing with non-Euclidean manifolds.
This presentation introduces a way to solve these problems when variables belong to generic Lie groups (e.g. the set of rotation matrices SO(3)). The core idea is to treat Lie group subsets via interval analysis in the vector space of the Lie algebra using the exponential mapping as a local bijection. Under this "Lie group interval" framework, SIVIA and generic contractors can be used, e.g. to solve bounded attitude estimation problems.
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