50 research outputs found
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
A Global Asymptotic Convergent Observer for SLAM
This paper examines the global convergence problem of SLAM algorithms, an
issue that faces topological obstructions. This is because the state-space of
attitude dynamics is defined on a non-contractible manifold: the special
orthogonal group of order three SO(3). Therefore, this paper presents a novel,
gradient-based hybrid observer to overcome these topological obstacles. The
Lyapunov stability theorem is used to prove the globally asymptotic convergence
of the proposed algorithm. Finally, comparative analyses of two simulations
were conducted to evaluate the performance of the proposed scheme and to
demonstrate the superiority of the proposed hybrid observer to a smooth
observer.Comment: 7 pages, 8 figures, conferenc
Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation with Online Calibration
Stochastic filters for on-line state estimation are a core technology for
autonomous systems. The performance of such filters is one of the key limiting
factors to a system's capability. Both asymptotic behavior (e.g.,~for regular
operation) and transient response (e.g.,~for fast initialization and reset) of
such filters are of crucial importance in guaranteeing robust operation of
autonomous systems.
This paper introduces a new generic formulation for a gyroscope aided
attitude estimator using N direction measurements including both body-frame and
reference-frame direction type measurements. The approach is based on an
integrated state formulation that incorporates navigation, extrinsic
calibration for all direction sensors, and gyroscope bias states in a single
equivariant geometric structure. This newly proposed symmetry allows modular
addition of different direction measurements and their extrinsic calibration
while maintaining the ability to include bias states in the same symmetry. The
subsequently proposed filter-based estimator using this symmetry noticeably
improves the transient response, and the asymptotic bias and extrinsic
calibration estimation compared to state-of-the-art approaches. The estimator
is verified in statistically representative simulations and is tested in
real-world experiments.Comment: to be published in Robotics and Automation Letter
Equivariant Filter (EqF): A General Filter Design for Systems on Homogeneous Spaces
The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing
attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold
equipped with a transitive Lie-group symmetry. This paper
shows that any system posed in a homogeneous space can
be extended to a larger system that is equivariant under a
symmetry action. The equivariant structure of the system is
exploited to propose a novel new filter, the Equivariant Filter
(EqF), based on linearisation of global error dynamics derived
from the symmetry action. The EqF is applied to an example
of estimating the positions of stationary landmarks relative to
a moving monocular camera that is intractable for previously
proposed symmetry based filter design methodologie
PEBO-SLAM: Observer design for visual inertial SLAM with convergence guarantees
This paper introduces a new linear parameterization to the problem of visual
inertial simultaneous localization and mapping (VI-SLAM) -- without any
approximation -- for the case only using information from a single monocular
camera and an inertial measurement unit. In this problem set, the system state
evolves on the nonlinear manifold , on which we
design dynamic extensions carefully to generate invariant foliations, such that
the problem can be reformulated into online \emph{constant parameter}
identification, then interestingly with linear regression models obtained. It
demonstrates that VI-SLAM can be translated into a linear least squares
problem, in the deterministic sense, \emph{globally} and \emph{exactly}. Based
on this observation, we propose a novel SLAM observer, following the recently
established parameter estimation-based observer (PEBO) methodology. A notable
merit is that the proposed observer enjoys almost global asymptotic stability,
requiring neither persistency of excitation nor uniform complete observability,
which, however, are widely adopted in most existing works with provable
stability but can hardly be assured in many practical scenarios
Sensor-based formation control using a generalised rigidity framework and passivity techniques
The research in this thesis addresses the subject of sensor-based
formation control for a network of autonomous agents.
The task of formation control involves the stabilisation of the
agents to a desired set of relative states, with the possible
additional objective of manoeuvring the agents while maintaining
this formation.
Although the formation control challenge has been widely studied
in the literature, many existing control strategies are based on
full state information, and give little consideration to the
sensor modalities available for the task.
The focus of this thesis lies in the use of a generic arrangement
of partial state measurements as can commonly be acquired by
onboard sensors; for example, time-of-flight sensors can be used
to measure the distances between vehicles, and onboard cameras
can provide the bearing from one vehicle to each of the others.
Particular aspects of the problem that are addressed in this
thesis include (i) ways of modelling the formation control task,
(ii) methods of analysing the system's behaviour, and (iii) the
design of a formation control scheme based on generic
arrangements of sensors that provide only partial position
information.
A key contribution in this thesis is a generalisation of the
classical notion of rigidity, which considers the use of distance
constraints between agents in R^2 or R^3 to specify a rigid body
(or formation).
This enables the concept of rigidity to be applied to agent
networks involving a variety of (possibly non-Euclidean)
state-spaces, with a generic set of state constraints that may,
for example, include bearings between agents as well as
distances.
I demonstrate that this framework is very well-suited for
modelling a wide variety of formation control problems
(addressing goal (i) above), and I extend several fundamental
results from classical rigidity theory in order to provide
significant insight for system analysis (addressing goal (ii)
above).
To design a formation control scheme that uses generic partial
position measurements (addressing goal (iii) above), I employ a
modular passivity-based approach that is developed using the
bondgraph modelling formalism.
I illustrate how adaptive compensation can be incorporated into
this design approach in order to account for the unknown position
information that is not available from the onboard sensors.
Although formation control is the subject of this thesis, it
should be noted that the rigidity-based and passivity-based
frameworks developed here are quite general and may be applied to
a wide range of other problems