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Annual Review of Control, Robotics, and Autonomous Systems

Volume 5, 2022

Observer Design for Nonlinear Systems with Equivariance

Abstract

Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models of mechatronic and navigation systems. Such systems admit a symmetry, associated with the equivariance, that provides structure enabling the design of robust and high-performance observers. A key insight is to pose the observer state to lie in the symmetry group rather than on the system state space. This allows one to define a global intrinsic equivariant error but poses a challenge in defining internal dynamics for the observer. By choosing an equivariant lift of the system dynamics for the observer internal model, we show that the error dynamics have a particularly nice form. Applying the methodology of extended Kalman filtering to the equivariant error state yields a filter we term the equivariant filter. The geometry of the state-space manifold appears naturally as a curvature modification to the classical Riccati equation for extended Kalman filtering. The equivariant filter exploits the symmetry and respects the geometry of an equivariant system model, and thus yields high-performance, robust filters for a wide range of mechatronic and navigation systems.

Keyword(s): equivariant filter, equivariant systems theory, extended Kalman filter, filter, Lie group, observer
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2022-05-03
2024-05-14
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/content/journals/10.1146/annurev-control-061520-010324
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Observer Design for Nonlinear Systems with Equivariance
Annual Review of Control, Robotics, and Autonomous Systems 5, 221 (2022); https://doi.org/10.1146/annurev-control-061520-010324
/content/journals/10.1146/annurev-control-061520-010324
/content/journals/10.1146/annurev-control-061520-010324
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