2,753 research outputs found
Geometric State Observers for Autonomous Navigation Systems
The development of reliable state estimation algorithms for autonomous navigation systems is of great interest in the control and robotics communities. This thesis studies the state estimation problem for autonomous navigation systems. The first part of this thesis is devoted to the pose estimation on the Special Euclidean group \SE(3). A generic globally exponentially stable hybrid estimation scheme for pose (orientation and position) and velocity-bias estimation on \SE(3)\times \mathbb{R}^6 is proposed. Moreover, an explicit hybrid observer, using inertial and landmark position measurements, is provided.
The second part of this thesis is devoted to the problem of simultaneous estimation of the attitude, position and linear velocity for inertial navigation systems (INSs). Three different types of nonlinear observers are developed to handle the following cases: continuous landmark position measurements, intermittent landmark position measurements and continuous stereo bearing measurements. First, a class of nonlinear geometric hybrid observers on the Lie group \SE_2(3), with GES guarantees, using continuous IMU and landmark position measurements is developed. Then, a class of nonlinear state observers, with strong stability guarantees, using intermittent landmark measurements is proposed. Finally, a class of state observers, with strong stability guarantees, directly incorporating body-frame stereo-bearing measurements, is proposed
An Equivariant Observer Design for Visual Localisation and Mapping
This paper builds on recent work on Simultaneous Localisation and Mapping
(SLAM) in the non-linear observer community, by framing the visual localisation
and mapping problem as a continuous-time equivariant observer design problem on
the symmetry group of a kinematic system. The state-space is a quotient of the
robot pose expressed on SE(3) and multiple copies of real projective space,
used to represent both points in space and bearings in a single unified
framework. An observer with decoupled Riccati-gains for each landmark is
derived and we show that its error system is almost globally asymptotically
stable and exponentially stable in-the-large.Comment: 12 pages, 2 figures, published in 2019 IEEE CD
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
Gradient-like observer design on the Special Euclidean group SE(3) with system outputs on the real projective space
A nonlinear observer on the Special Euclidean group for full
pose estimation, that takes the system outputs on the real projective space
directly as inputs, is proposed. The observer derivation is based on a recent
advanced theory on nonlinear observer design. A key advantage with respect to
existing pose observers on is that we can now incorporate in a
unique observer different types of measurements such as vectorial measurements
of known inertial vectors and position measurements of known feature points.
The proposed observer is extended allowing for the compensation of unknown
constant bias present in the velocity measurements. Rigorous stability analyses
are equally provided. Excellent performance of the proposed observers are shown
by means of simulations
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