14,543 research outputs found
Symmetry-preserving Observers
This paper presents three non-linear observers on three examples of
engineering interest: a chemical reactor, a non-holonomic car, and an inertial
navigation system. For each example, the design is based on physical
symmetries. This motivates the theoretical development of invariant observers,
i.e, symmetry-preserving observers. We consider an observer to consist in a
copy of the system equation and a correction term, and we give a constructive
method (based on the Cartan moving-frame method) to find all the
symmetry-preserving correction terms. They rely on an invariant frame (a
classical notion) and on an invariant output-error, a less standard notion
precisely defined here. For each example, the convergence analysis relies also
on symmetries consideration with a key use of invariant state-errors. For the
non-holonomic car and the inertial navigation system, the invariant
state-errors are shown to obey an autonomous differential equation independent
of the system trajectory. This allows us to prove convergence, with almost
global stability for the non-holonomic car and with semi-global stability for
the inertial navigation system. Simulations including noise and bias show the
practical interest of such invariant asymptotic observers for the inertial
navigation system.Comment: To be published in IEEE Automatic Contro
Invariant length scale in relativistic kinematics - Lessons from Dirichlet branes
We show that Dirac-Born-Infeld theory possesses a hidden invariance that
enhances the local O(1,p) Lorentz symmetry on a Dirichlet p-brane to an O(1,p)
x O(1,p) gauge group, encoding both an invariant velocity and acceleration (or
length) scale. This enlarged gauge group predicts consequences for the
kinematics of observers on Dirichlet branes, with admissible accelerations
being bounded from above. An important lesson beyond string theory is that a
fundamental length scale can be implemented into the kinematics of general
relativity, whilst preserving both space-time as a smooth manifold and local
Lorentz symmetry, contrary to common belief. We point out consequences for
string phenomenology, classical gravity and atomic physics.Comment: 4 pages, to be published in Phys Lett
Non-linear Symmetry-preserving Observer on Lie Groups
In this paper we give a geometrical framework for the design of observers on
finite-dimensional Lie groups for systems which possess some specific
symmetries. The design and the error (between true and estimated state)
equation are explicit and intrinsic. We consider also a particular case:
left-invariant systems on Lie groups with right equivariant output. The theory
yields a class of observers such that error equation is autonomous. The
observers converge locally around any trajectory, and the global behavior is
independent from the trajectory, which reminds of the linear stationary case.Comment: 12 pages. Submitted. Preliminary version publicated in french in the
CIFA proceedings and IFAC0
The Invariant Unscented Kalman Filter
International audienceThis article proposes a novel approach for nonlinear state estimation. It combines both invariant observers theory and unscented filtering principles whitout requiring any compatibility condition such as proposed in the -IUKF algorithm. The resulting algorithm, named IUKF (Invariant Unscented Kalman Filter), relies on a geometrical-based constructive method for designing filters dedicated to nonlinear state estimation problems while preserving the physical invariances and systems symmetries. Within an invariant framework, this algorithm suggests a systematic approach to determine all the symmetry- preserving terms without requiring any linearization and highlighting remarkable invariant properties. As a result, the estimated covariance matrices of the IUKF converge to quasi-constant values due to the symmetry-preserving property provided by the invariant framework. This result enables the development of less conservative robust control strategies. The designed IUKF method has been successfully applied to some relevant practical problems such as the estimation of attitude for aerial vehicles using low-cost sensors reference systems. Typical experimental results using a Parrot quadrotor are provided in this pape
A Separation Principle on Lie Groups
For linear time-invariant systems, a separation principle holds: stable
observer and stable state feedback can be designed for the time-invariant
system, and the combined observer and feedback will be stable. For non-linear
systems, a local separation principle holds around steady-states, as the
linearized system is time-invariant. This paper addresses the issue of a
non-linear separation principle on Lie groups. For invariant systems on Lie
groups, we prove there exists a large set of (time-varying) trajectories around
which the linearized observer-controler system is time-invariant, as soon as a
symmetry-preserving observer is used. Thus a separation principle holds around
those trajectories. The theory is illustrated by a mobile robot example, and
the developed ideas are then extended to a class of Lagrangian mechanical
systems on Lie groups described by Euler-Poincare equations.Comment: Submitted to IFAC 201
A general symmetry-preserving observer for aided attitude heading reference systems
International audienceWe generalize several recent works on nonlinear observers for aided attitude heading reference systems: we propose a symmetry-preserving nonlinear observer which merges the most common measurements available on an aircraft (altitude, Earth-fixed and body-fixed velocity, inertial and magnetic sensors). It can be seen as an alternative to the Extended Kalman Filter, but easier to tune and computationally much more economic. Moreover it has by design a nice geometrical structure appealing from an engineering viewpoint. We illustrate its good performance on simulation and experimental results
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