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Equivariant Filter Design for Kinematic Systems on Lie Groups
arXiv - CS - Systems and Control Pub Date : 2020-04-02 , DOI: arxiv-2004.00828
Robert Mahony; Jochen Trumpf

It is known that invariance and equivariance properties for systems on Lie groups can be exploited in the design of high performance and robust observers and filters for real-world robotic systems. This paper proposes an analysis framework that allows any kinematic system on a Lie group to be embedded in a natural manner into an equivariant kinematic system. This framework allows us to characterise the properties of, and relationships between, invariant systems, group affine systems, and equivariant systems. We propose a new filter design, the Equivariant Filter (EqF), that exploits the equivariance properties of the system embedding and can be applied to any kinematic system on a Lie group.
更新日期:2020-04-03

 

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