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We consider estimation of motion on spheres as a variational problem. The concept of variational estimation for mechanical systems is based on application of variational principles from mechanics, to state estimation of mechanical systems evolving on configuration manifolds. If the configuration manifold is a symmetric space, then the overlying connected Lie group of which it is a quotient space, can be used to design nonlinearly stable observers for estimation of configuration and velocity states from measurements. If the configuration manifold is a sphere, then it can be globally represented by an unit vector. We illustrate the design of variational observers for mechanical systems evolving on spheres, through its application to estimation of pointing directions (reduced attitude) on the regular sphere S^2.
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This content will become publicly available on December 16, 2025
Variational Observer Designs on Lie Groups, with Applications to Rigid Body Motion Estimation
Variational estimation of a mechanical system is based on the application of variational principles from mechanics to state estimation of the system evolving on its configuration manifold. If the configuration manifold is a Lie group, then the underlying group structure can be used to design nonlinearly stable observers for estimation of configuration and velocity states from measurements. Measured quantities are on a vector space on which the Lie group acts smoothly. We formulate the design of variational observers on a general finite-dimensional Lie group, followed by the design and experimental evaluation of a variational observer for rigid body motions on the Lie group SE(3).
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- Award ID(s):
- 2343062
- PAR ID:
- 10574416
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 979-8-3503-1633-9
- Page Range / eLocation ID:
- 8690 to 8695
- Subject(s) / Keyword(s):
- Manifolds Motion estimation Lie groups Observers Cameras Vectors Motion capture Velocity measurement Mechanical systems
- Format(s):
- Medium: X
- Location:
- Milan, Italy
- Sponsoring Org:
- National Science Foundation
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