11,435 research outputs found
Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs
This paper provides a new observer design methodology for invariant systems
whose state evolves on a Lie group with outputs in a collection of related
homogeneous spaces and where the measurement of system input is corrupted by an
unknown constant bias. The key contribution of the paper is to study the
combined state and input bias estimation problem in the general setting of Lie
groups, a question for which only case studies of specific Lie groups are
currently available. We show that any candidate observer (with the same state
space dimension as the observed system) results in non-autonomous error
dynamics, except in the trivial case where the Lie-group is Abelian. This
precludes the application of the standard non-linear observer design
methodologies available in the literature and leads us to propose a new design
methodology based on employing invariant cost functions and general gain
mappings. We provide a rigorous and general stability analysis for the case
where the underlying Lie group allows a faithful matrix representation. We
demonstrate our theory in the example of rigid body pose estimation and show
that the proposed approach unifies two competing pose observers published in
prior literature.Comment: 11 page
Local observers on linear Lie groups with linear estimation error dynamics
This paper proposes local exponential observers for systems on linear Lie
groups. We study two different classes of systems. In the first class, the full
state of the system evolves on a linear Lie group and is available for
measurement. In the second class, only part of the system's state evolves on a
linear Lie group and this portion of the state is available for measurement. In
each case, we propose two different observer designs. We show that, depending
on the observer chosen, local exponential stability of one of the two
observation error dynamics, left- or right-invariant error dynamics, is
obtained. For the first class of systems these results are developed by showing
that the estimation error dynamics are differentially equivalent to a stable
linear differential equation on a vector space. For the second class of system,
the estimation error dynamics are almost linear. We illustrate these observer
designs on an attitude estimation problem
On sensor fusion for airborne wind energy systems
A study on filtering aspects of airborne wind energy generators is presented.
This class of renewable energy systems aims to convert the aerodynamic forces
generated by tethered wings, flying in closed paths transverse to the wind
flow, into electricity. The accurate reconstruction of the wing's position,
velocity and heading is of fundamental importance for the automatic control of
these kinds of systems. The difficulty of the estimation problem arises from
the nonlinear dynamics, wide speed range, large accelerations and fast changes
of direction that the wing experiences during operation. It is shown that the
overall nonlinear system has a specific structure allowing its partitioning
into sub-systems, hence leading to a series of simpler filtering problems.
Different sensor setups are then considered, and the related sensor fusion
algorithms are presented. The results of experimental tests carried out with a
small-scale prototype and wings of different sizes are discussed. The designed
filtering algorithms rely purely on kinematic laws, hence they are independent
from features like wing area, aerodynamic efficiency, mass, etc. Therefore, the
presented results are representative also of systems with larger size and
different wing design, different number of tethers and/or rigid wings.Comment: This manuscript is a preprint of a paper accepted for publication on
the IEEE Transactions on Control Systems Technology and is subject to IEEE
Copyright. The copy of record is available at IEEEXplore library:
http://ieeexplore.ieee.org
Output Regulation for Systems on Matrix Lie-group
This paper deals with the problem of output regulation for systems defined on
matrix Lie-Groups. Reference trajectories to be tracked are supposed to be
generated by an exosystem, defined on the same Lie-Group of the controlled
system, and only partial relative error measurements are supposed to be
available. These measurements are assumed to be invariant and associated to a
group action on a homogeneous space of the state space. In the spirit of the
internal model principle the proposed control structure embeds a copy of the
exosystem kinematic. This control problem is motivated by many real
applications fields in aerospace, robotics, projective geometry, to name a few,
in which systems are defined on matrix Lie-groups and references in the
associated homogenous spaces
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