54 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
Constructive Equivariant Observer Design for Inertial Velocity-Aided Attitude
Inertial Velocity-Aided Attitude (VAA) is an important problem in the control
of Remotely Piloted Aerial Systems (RPAS), and involves estimating the velocity
and attitude of a vehicle using gyroscope, accelerometer, and inertial-frame
velocity (e.g. GPS velocity) measurements. Existing solutions tend to be
complex and provide limited stability guarantees, relying on either high gain
designs or assuming constant acceleration of the vehicle. This paper proposes a
novel observer for inertial VAA that exploits Lie group symmetries of the
system dynamics, and shows that the observer is synchronous with the system
trajectories. This is achieved by adding a virtual state of only three
dimensions, in contrast to the larger virtual states typically used in the
literature. The error dynamics of the observer are shown to be almost globally
asymptotically and locally exponentially stable. Finally, the observer is
verified in simulation, where it is shown that the estimation error converges
to zero even with an extremely poor initial condition.Comment: 11 pages, 2 figures, submitted to NOLCOS 202
Constructive Equivariant Observer Design for Inertial Navigation
Inertial Navigation Systems (INS) are algorithms that fuse inertial
measurements of angular velocity and specific acceleration with supplementary
sensors including GNSS and magnetometers to estimate the position, velocity and
attitude, or extended pose, of a vehicle. The industry-standard extended Kalman
filter (EKF) does not come with strong stability or robustness guarantees and
can be subject to catastrophic failure. This paper exploits a Lie group
symmetry of the INS dynamics to propose the first nonlinear observer for INS
with error dynamics that are almost-globally asymptotically and locally
exponentially stable, independently of the chosen gains. The observer is aided
only by a GNSS measurement of position. As expected, the convergence guarantee
depends on persistence of excitation of the vehicle's specific acceleration in
the inertial frame. Simulation results demonstrate the observer's performance
and its ability to converge from extreme errors in the initial state estimates.Comment: 10 pages, 2 figures, to appear in Proceedings of IFAC World Congress
202
Event Blob Tracking: An Asynchronous Real-Time Algorithm
Event-based cameras have become increasingly popular for tracking fast-moving
objects due to their high temporal resolution, low latency, and high dynamic
range. In this paper, we propose a novel algorithm for tracking event blobs
using raw events asynchronously in real time. We introduce the concept of an
event blob as a spatio-temporal likelihood of event occurrence where the
conditional spatial likelihood is blob-like. Many real-world objects generate
event blob data, for example, flickering LEDs such as car headlights or any
small foreground object moving against a static or slowly varying background.
The proposed algorithm uses a nearest neighbour classifier with a dynamic
threshold criteria for data association coupled with a Kalman filter to track
the event blob state. Our algorithm achieves highly accurate tracking and event
blob shape estimation even under challenging lighting conditions and high-speed
motions. The microsecond time resolution achieved means that the filter output
can be used to derive secondary information such as time-to-contact or range
estimation, that will enable applications to real-world problems such as
collision avoidance in autonomous driving.Comment: 17 pages, 8 figures, preprint versio
Exploiting Different Symmetries for Trajectory Tracking Control with Application to Quadrotors
High performance trajectory tracking control of quadrotor vehicles is an
important challenge in aerial robotics. Symmetry is a fundamental property of
physical systems and offers the potential to provide a tool to design
high-performance control algorithms. We propose a design methodology that takes
any given symmetry, linearises the associated error in a single set of
coordinates, and uses LQR design to obtain a high performance control; an
approach we term Equivariant Regulator design. We show that quadrotor vehicles
admit several different symmetries: the direct product symmetry, the extended
pose symmetry and the pose and velocity symmetry, and show that each symmetry
can be used to define a global error. We compare the linearised systems via
simulation and find that the extended pose and pose and velocity symmetries
outperform the direct product symmetry in the presence of large disturbances.
This suggests that choices of equivariant and group affine symmetries have
improved linearisation error
Nonlinear constructive observer design for direct homography estimation
Feature-based homography estimation approaches rely on extensive image
processing for feature extraction and matching, and do not adequately account
for the information provided by the image. Therefore, developing efficient
direct techniques to extract the homography from images is essential. This
paper presents a novel nonlinear direct homography observer that exploits the
Lie group structure of and its action on the space of image
maps. Theoretical analysis demonstrates local asymptotic convergence of the
observer. The observer design is also extended for partial measurements of
velocity under the assumption that the unknown component is constant or slowly
time-varying. Finally, simulation results demonstrate the performance of the
proposed solutions on real images.Comment: 11 pages, 3 figures, to appear in Proceedings of IFAC World Congress
202
MSCEqF: A Multi State Constraint Equivariant Filter for Vision-aided Inertial Navigation
This letter re-visits the problem of visual-inertial navigation system (VINS)
and presents a novel filter design we dub the multi state constraint
equivariant filter (MSCEqF, in analogy to the well known MSCKF). We define a
symmetry group and corresponding group action that allow specifically the
design of an equivariant filter for the problem of visual-inertial odometry
(VIO) including IMU bias, and camera intrinsic and extrinsic calibration
states. In contrast to state-of-the-art invariant extended Kalman filter (IEKF)
approaches that simply tack IMU bias and other states onto the
group, our filter builds upon a symmetry that properly
includes all the states in the group structure. Thus, we achieve improved
behavior, particularly when linearization points largely deviate from the truth
(i.e., on transients upon state disturbances). Our approach is inherently
consistent even during convergence phases from significant errors without the
need for error uncertainty adaptation, observability constraint, or other
consistency enforcing techniques. This leads to greatly improved estimator
behavior for significant error and unexpected state changes during, e.g.,
long-duration missions. We evaluate our approach with a multitude of different
experiments using three different prominent real-world datasets.Comment: Accepted for publication in the IEEE Robotics and Automation Letters
(RA-L), 202
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