998 research outputs found
On the integration of singularity-free representations of SO(3) for direct optimal control
In this paper we analyze the performance of different combinations of: (1) parameterization of the rotational degrees of freedom (DOF) of multibody systems, and (2) choice of the integration scheme, in the context of direct optimal control discretized according to the direct multiple-shooting method. The considered representations include quaternions and Direction Cosine Matrices, both having the peculiarity of being non-singular and requiring more than three parameters to describe an element of the Special Orthogonal group SO(3). These representations yield invariants in the dynamics of the system, i.e., algebraic conditions which have to be satisfied in order for the model to be representative of physical reality. The investigated integration schemes include the classical explicit Rungeâ\u80\u93Kutta method, its stabilized version based on Baumgarteâ\u80\u99s technique, which tends to reduce the drift from the underlying manifold, and a structure-preserving alternative, namely the Rungeâ\u80\u93Kutta Munthe-Kaas method, which preserves the invariants by construction. The performances of the combined choice of representation and integrator are assessed by solving thousands of planning tasks for a nonholonomic, underactuated cart-pendulum system, where the pendulum can experience arbitrarily large 3D rotations. The aspects analyzed include success rate, average number of iterations and CPU time to convergence, and quality of the solution. The results reveal how structure-preserving integrators are the only choice for lower accuracies, whereas higher-order, non-stabilized standard integrators seem to be the computationally most competitive solution when higher levels of accuracy are pursued. Overall, the quaternion-based representation is the most efficient in terms of both iterations and CPU time to convergence, albeit at the cost of lower success rates and increased probability of being trapped by higher local minima
Geometry-Aware Learning of Maps for Camera Localization
Maps are a key component in image-based camera localization and visual SLAM
systems: they are used to establish geometric constraints between images,
correct drift in relative pose estimation, and relocalize cameras after lost
tracking. The exact definitions of maps, however, are often
application-specific and hand-crafted for different scenarios (e.g. 3D
landmarks, lines, planes, bags of visual words). We propose to represent maps
as a deep neural net called MapNet, which enables learning a data-driven map
representation. Unlike prior work on learning maps, MapNet exploits cheap and
ubiquitous sensory inputs like visual odometry and GPS in addition to images
and fuses them together for camera localization. Geometric constraints
expressed by these inputs, which have traditionally been used in bundle
adjustment or pose-graph optimization, are formulated as loss terms in MapNet
training and also used during inference. In addition to directly improving
localization accuracy, this allows us to update the MapNet (i.e., maps) in a
self-supervised manner using additional unlabeled video sequences from the
scene. We also propose a novel parameterization for camera rotation which is
better suited for deep-learning based camera pose regression. Experimental
results on both the indoor 7-Scenes dataset and the outdoor Oxford RobotCar
dataset show significant performance improvement over prior work. The MapNet
project webpage is https://goo.gl/mRB3Au.Comment: CVPR 2018 camera ready paper + supplementary materia
Wing and body motion during flight initiation in Drosophila revealed by automated visual tracking
The fruit fly Drosophila melanogaster is a widely used model organism in studies of genetics, developmental biology and biomechanics. One limitation for exploiting Drosophila as a model system for behavioral neurobiology is that measuring body kinematics during behavior is labor intensive and subjective. In order to quantify flight kinematics during different types of maneuvers, we have developed a visual tracking system that estimates the posture of the fly from multiple calibrated cameras. An accurate geometric fly model is designed using unit quaternions to capture complex body and wing rotations, which are automatically fitted to the images in each time frame. Our approach works across a range of flight behaviors, while also being robust to common environmental clutter. The tracking system is used in this paper to compare wing and body motion during both voluntary and escape take-offs. Using our automated algorithms, we are able to measure stroke amplitude, geometric angle of attack and other parameters important to a mechanistic understanding of flapping flight. When compared with manual tracking methods, the algorithm estimates body position within 4.4±1.3% of the body length, while body orientation is measured within 6.5±1.9 deg. (roll), 3.2±1.3 deg. (pitch) and 3.4±1.6 deg. (yaw) on average across six videos. Similarly, stroke amplitude and deviation are estimated within 3.3 deg. and 2.1 deg., while angle of attack is typically measured within 8.8 deg. comparing against a human digitizer. Using our automated tracker, we analyzed a total of eight voluntary and two escape take-offs. These sequences show that Drosophila melanogaster do not utilize clap and fling during take-off and are able to modify their wing kinematics from one wingstroke to the next. Our approach should enable biomechanists and ethologists to process much larger datasets than possible at present and, therefore, accelerate insight into the mechanisms of free-flight maneuvers of flying insects
Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard
We derive the statistics of the time-delay matrix (energy derivative of the
scattering matrix) in an ensemble of superconducting quantum dots with chaotic
scattering (Andreev billiards), coupled ballistically to conducting modes
(electron-hole modes in a normal metal or Majorana edge modes in a
superconductor). As a first application we calculate the density of states
at the Fermi level. The ensemble average
deviates
from the bulk value by an amount depending on the
Altland-Zirnbauer symmetry indices . The divergent average for
in symmetry class D (, ) originates from the
mid-gap spectral peak of a closed quantum dot, but now no longer depends on the
presence or absence of a Majorana zero-mode. As a second application we
calculate the probability distribution of the thermopower, contrasting the
difference for paired and unpaired Majorana edge modes.Comment: 13 pages, 6 figure
Support Vector Machines for Anatomical Joint Constraint Modelling
The accurate simulation of anatomical joint models is becoming increasingly important for both realistic animation and diagnostic medical applications. Recent models have
exploited unit quaternions to eliminate singularities when modeling orientations between limbs at a joint. This has led to
the development of quaternion based joint constraint validation and correction methods. In this paper a novel method for implicitly modeling unit quaternion joint
constraints using Support Vector Machines (SVMs) is proposed which attempts to address the limitations of current constraint validation approaches. Initial results show that the resulting SVMs are capable of modeling regular spherical constraints on the rotation of the limb
Self Organising Maps for Anatomical Joint Constraint
The accurate simulation of anatomical joint models is becoming increasingly important for both realistic animation and diagnostic medical applications. Recent models have exploited unit quaternions to eliminate ingularities when
modelling orientations between limbs at a joint. This has led to
the development of quaternion based joint constraint
validation and correction methods. In this paper a novel
method for implicitly modelling unit quaternion joint
constraints using Self Organizing Maps (SOMs) is proposed
which attempts to address the limitations of current constraint validation and correction approaches. Initial results show that the resulting SOMs are capable of modelling regular spherical constraints on the orientation of the limb
- …