Quaternion Research Papers - Academia.edu (original) (raw)

A new spacecraft attitude estimation approach based on the Unscented Filter is derived. For nonlinear systems the Unscented Filter uses a carefully selected set of sample points to more accurately map the probability distribution than the... more

A new spacecraft attitude estimation approach based on the Unscented Filter is derived. For nonlinear systems the Unscented Filter uses a carefully selected set of sample points to more accurately map the probability distribution than the linearization of the standard Extended Kalman Filter, leading to faster convergence from inaccurate initial conditions in attitude estimation problems. The filter formulation is based on standard attitude-vector measurements using a gyro-based model for attitude propagation. The global attitude parameterization is given by a quaternion, while a generalized three-dimensional attitude representation is used to define the local attitude error. A multiplicative quaternion-error approach is derived from the local attitude error, which guarantees that quaternion normalization is maintained in the filter. Simulation results indicate that the Unscented Filter is more robust than the Extended Kalman Filter under realistic initial attitude-error conditions. ...

A new Hyperspherical trigonometry based on Quaternion's Algebra is introduced. Spatial curves on the surface of the unit-quaternion hypersphere are described in the parametric form. A draft of a new Continuous Quaternion Modulation System... more

A new Hyperspherical trigonometry based on Quaternion's Algebra is introduced. Spatial curves on the surface of the unit-quaternion hypersphere are described in the parametric form. A draft of a new Continuous Quaternion Modulation System is presented, in which two modulation signals are used to drive paths in the normalized 4D-hypersphere. The outline of a PLL-based demodulation is also sketched.

The paper deals with the issue of developing an attitude control system for a remotely operated vehicle (ROV) for large inclination angles (pitch, roll). The construction of the orientation control system is considered based on the... more

The paper deals with the issue of developing an attitude control system for a remotely operated vehicle (ROV) for large inclination angles (pitch, roll). The construction of the orientation control system is considered based on the traditional approach using Euler angles (yaw, pitch and roll). A transfer matrix general form of the ROV attitude control system was obtained. It was shown that with the increase of inclination angles the transfer matrix of the system becomes multivariable. Algorithms of disturbances compensation and a methodology for parameters selection for decomposition algorithm were proposed. The obtained results were verified during the in situ tests of the ROV “Iznos”, developed in Bauman Moscow State Technical University (BMSTU). The proposed decomposition algorithms allow to expand the ranges of working angles and to improve the quality of the control system performance without significant re-engineering of its structure.

The developed y4 copter is an Unmanned Aerial Vehic le with autonomous subsystems which reports the fully automated y4 copter for the first time. Autom ation is implemented through maintaining the desire d roll, pitch and yaw therefore... more

The developed y4 copter is an Unmanned Aerial Vehic
le with autonomous subsystems which reports the
fully automated y4 copter for the first time. Autom
ation is implemented through maintaining the desire
d
roll, pitch and yaw therefore the flight stability
as well as in case of controlling elevation. An imp
roved and
efficient algorithm that uses Quaternion is impleme
nted to determine Euler angles avoiding Gimbal lock
in
case of developing an inertial measurement unit. It
has a self-stabilization system powered by Proport
ional
Integral Derivative control system which is computa
tionally affordable by an ordinary 8 bit
microcontroller capable of performing only integer
operations. A remote is designed to communicate wit
h
the y4 copter from the base station using XBee tran
sceiver modules which come with secured
communication with long range. The developed system
demonstrates simple design offering lower cost and
secured means of control.

For most autonomous robots it is crucial to know where the robot is located and where it is heading to, so it can plan its next steps. Especially for stabilizing the attitude of an unmanned aerial vehicle (UAV), a high degree of precision... more

For most autonomous robots it is crucial to know where the robot is located and where it is heading to, so it can plan its next steps. Especially for stabilizing the attitude of an unmanned aerial vehicle (UAV), a high degree of precision and accuracy is required.
The goal of this work was to enable the UAV to hover and land safely without relying on optical sensors.
Therefore, we introduce a state estimation algorithm for a quadrotor using an inertial measurement unit (IMU), a barometer and a sonar sensor.
We have developed an Extended Kalman Filter (EKF) that uses rigid body dynamics for the prediction, while transforming the information of the sensor signals to information about the states for the correction.
We tested the algorithm using real sensor data in a specifically developed Matlab framework, where direct and indirect variations of an EKF, as well as a non-linear Unscented Kalman Filter (UKF), are compared. Furthermore, we evaluated the implementation on the PX4FMU micro-controller of the pixhawk project.
The algorithm outlined in this work produces a state estimate for the height and attitude of a rotorcraft with any number of rotors that are fixed pitch.

The paper deals with the issue of developing an attitude control system for a remotely operated vehicle (ROV) for large inclination angles (pitch, roll). The construction of the orientation control system is considered based on the... more

The paper deals with the issue of developing an attitude control system for a remotely operated vehicle (ROV) for large inclination angles (pitch, roll). The construction of the orientation control system is considered based on the traditional approach using Euler angles (yaw, pitch and roll). A transfer matrix general form of the ROV attitude control system was obtained. It was shown that with the increase of inclination angles the transfer matrix of the system becomes multivariable. Algorithms of disturbances compensation and a methodology for parameters selection for decomposition algorithm were proposed. The obtained results were verified during the in situ tests of the ROV “Iznos”, developed in Bauman Moscow State Technical University (BMSTU). The proposed decomposition algorithms allow to expand the ranges of working angles and to improve the quality of the control system performance without significant re-engineering of its structure.

Vertices of the 4-dimensional semi-regular polytope, snub 24-cell and its symmetry group (W(D4)/C2):S3(W(D4)/C2):S3 of order 576 are represented in terms of quaternions with unit norm. It follows from the icosian representation of E8E8... more

Vertices of the 4-dimensional semi-regular polytope, snub 24-cell and its symmetry group (W(D4)/C2):S3(W(D4)/C2):S3 of order 576 are represented in terms of quaternions with unit norm. It follows from the icosian representation of E8E8 root system. A simple method is employed to construct the E8E8 root system in terms of icosians which decomposes into two copies of the quaternionic root system of the Coxeter group W(H4)W(H4), while one set is the elements of the binary icosahedral group the other set is a scaled copy of the first. The quaternionic root system of H4H4 splits as the vertices of 24-cell and the snub 24-cell under the symmetry group of the snub 24-cell which is one of the maximal subgroups of the group W(H4)W(H4) as well as W(F4)W(F4). It is noted that the group is isomorphic to the semi-direct product of the proper rotation subgroup of the Weyl group of D4D4 with symmetric group of order 3 denoted by (W(D4)/C2):S3(W(D4)/C2):S3, the Coxeter notation for which is [3,4,3+][3,4,3+]. We analyze the vertex structure of the snub 24-cell and decompose the orbits of W(H4)W(H4) under the orbits of (W(D4)/C2):S3(W(D4)/C2):S3. The cell structure of the snub 24-cell has been explicitly analyzed with quaternions by using the subgroups of the group (W(D4)/C2):S3(W(D4)/C2):S3. In particular, it has been shown that the dual polytopes 600-cell with 120 vertices and 120-cell with 600 vertices decompose as 120=24+96120=24+96 and 600=24+96+192+288600=24+96+192+288 respectively under the group (W(D4)/C2):S3(W(D4)/C2):S3. The dual polytope of the snub 24-cell is explicitly constructed. Decompositions of the Archimedean W(H4)W(H4) polytopes under the symmetry of the group (W(D4)/C2):S3(W(D4)/C2):S3 are given in the appendix.

In the past, Kepler painstakingly derived laws of planetary motion using difficult to understand and hard to follow techniques. In 1843 William Hamilton created and described the quaternions, which extend the complex numbers and can... more

In the past, Kepler painstakingly derived laws of planetary motion using difficult to understand and hard to follow techniques. In 1843 William Hamilton created and described the quaternions, which extend the complex numbers and can easily describe rotations in three dimensional space. In this article, we will harness this system to provide a new and intuitive way to derive Kepler’s laws. This will include using a quaternionic version of the spatial Kepler problem differential equation, and using the general solution to describe the motion of planets orbiting a central body. We use the standard method for regularizing celestial mechanics, but this article will be solely focused on showing the validity of Kepler’s laws.

A novel quaternion color representation tool is proposed to the images and videos efficiently. In this work, we consider a full model for representation and processing color images in the quaternion algebra. Color images are presented in... more

A novel quaternion color representation tool is proposed to the images and videos efficiently. In this work, we consider a full model for representation and processing color images in the quaternion algebra. Color images are presented in the threefold complex plane where each color component is described by a complex image. Our preliminary experimental results show significant performance improvements of the proposed approach over other well-known color image processing techniques. Moreover, we have shown how a particular image enhancement of the framework leads to excellent color enhancement (better than other algorithms tested). In the framework of the proposed model, many other color processing algorithms, including filtration and restoration, can be expressed.

La introducción de piezas metálicas como tornillos, arandelas, pequeñas herramientas con partes metálicas, etc., en el proceso de molienda fina en la empresa minera Buena Vista del Cobre® genera pérdidas económicas y accidentes laborales... more

La introducción de piezas metálicas como tornillos,
arandelas, pequeñas herramientas con partes metálicas,
etc., en el proceso de molienda fina en la empresa
minera Buena Vista del Cobre® genera pérdidas
económicas y accidentes laborales derivados del paro
de maquinaria. Por este motivo en el presente trabajo
de investigación se propone el diseño de un dispositivo
de extracción de materiales metálicos magnéticos
utilizando la teoría del diseño mecatrónico. Con esta
finalidad se realiza una investigación de los diversos
dispositivos existentes donde se analizan las ventajas y
desventajas de los mismos, éstos a su vez se comparan
con una serie de diseños propuestos mediante el
método de lluvia de ideas donde al final se determina
el dispositivo ideal basando su elección mediante el
empleo de una matriz morfológica. Con este diseño es
posible ahorrar al grupo hasta un día de producción
al mes por banda transportadora, al reducir el paro de
maquinaria ocasionado por detección de metales y la
reducción de muertes y accidentes relacionados
con el mismo aspecto. El diseño y empleo de tecnologías
adecuadas en los procesos de producción reduce
los costos por fallos en los sistemas y los derivados
de los procesos de exportación, mantenimiento e
implementación de dispositivos comerciales los cuales
no son diseñados específicamente para la solución de
un problema particular de la empresa.

Using the natural connection equivalent to the SU(2) Yang-Mills instanton on the quaternionic Hopf fibration of S7over the quaternionic projective space HP1 sime S4 with an SU(2) sime S3 fibre, the geometry of entanglement for two qubits... more

Using the natural connection equivalent to the SU(2) Yang-Mills instanton on the quaternionic Hopf fibration of S7over the quaternionic projective space HP1 sime S4 with an SU(2) sime S3 fibre, the geometry of entanglement for two qubits is investigated. The relationship between base and fibre i.e. the twisting of the bundle corresponds to the entanglement of the qubits. The measure

A simple algorithm is developed and implemented to eliminate ambiguities, in both statistical analyses of orientation data (e.g., orientation averaging) and electron backscattered diffraction (EBSD) orientation map visualization, caused... more

A simple algorithm is developed and implemented to eliminate ambiguities, in both statistical analyses of orientation data (e.g., orientation averaging) and electron backscattered diffraction (EBSD) orientation map visualization, caused by symmetrically equivalent orientations and the wrap-around or umklapp effect. Using crystal symmetry operators and the lowest Euclidian-distance criterion, the orientation of each pixel within a grain is redefined. An advantage of this approach is demonstrated for direct determination of the representative orientation of a grain within an EBSD map by mean, median, or quaternion-based averaging methods that can be further used within analyses or visualization of misorientation or geometrically necessary dislocation (GND) density. If one also considers the lattice curvature tensor, five components of the dislocation density tensor—corresponding to a part of the GND content—may be inferred. The methodology developed is illustrated using EBSD orientation data obtained from the fatigue crack-tips/wakes in aerospace aluminum alloys 2024-T351 and 7050-T7451.

The orientation of body in space is defined 3 by angles. The step by step rotation process and chain of three-dots multiplication give an easy way to compute pile of rotations in 3D and high dimensional space and give a general... more

The orientation of body in space is defined 3 by angles. The step by step rotation process and chain of three-dots multiplication give an easy way to compute pile of rotations in 3D and high dimensional space and give a general orientation system. A visualization of quaternion is proposed.

In the design of attitude control, rotational motion of the spacecraft is usually considered as a rotation of rigid body. Rotation matrix parameterization using quaternion can represent globally attitude of a rigid body rotational... more

In the design of attitude control, rotational motion of the spacecraft is usually considered as a rotation of rigid body. Rotation matrix parameterization using quaternion can represent globally attitude of a rigid body rotational motions. However, the representation is not unique hence implies difficulties on the stability guarantee. This paper presents asymptotically stable analysis of a continuous scheme of quaternion-based control system that has saturation function. Simulations run show that the designed system applicable for a zero initial angular velocity case and a non-zero initial angular velocity case due to utilization of deadzone function as an element of the defined constraint in the stability analysis. 1. INTRODUCTION Design of a spacecraft or satellite attitude control by analyzing rotational motion of a rigid body remains become a challenging research field until recent years. Ashok et al proposed control moment gyros based attitude control system to achieve time-optimal maneuver for agile (rigid) satellite [1]. Chabot and Schaub presented a spherical actuator for satellite attitude control that covers modeling, simulation of attitude control of a rigid body system motion as well as comparison with a configuration of three reaction wheels [2]. in [3], Stevenson and Schaub used rigid body approach in the attitude control development prior to do testbed experiment of remote electrostatic charge control. Rezanezhad in [4] presented Takagi-Sugeno fuzzy-based attitude controller in order to reduce thruster fuel consumption and increase longevity of satellite. Particle swarm optimization algorithm is used to reduce limit cycle on the fuzzy system. Pirouzmand in [5] proposed a model reference adaptive system-based robust model predictive controller for three degree of freedom satellite attitude control system. Whilst the controller gain is obtained through solving a convex optimization problem using linear matrix inequality approach. The kinematics of a rigid body rotational motion is represented by rotation matrix that is member of

The parameterization of a rigid-body motion can be done using multiple algebraic entities. A very important criterion when choosing a parameterization method is the number of algebraic equations and variables. Recently, orthogonal dual... more

The parameterization of a rigid-body motion can be done using multiple algebraic entities. A very important criterion when choosing a parameterization method is the number of algebraic equations and variables. Recently, orthogonal dual tensors and dual quaternion proved to be a complete tool for computing rigid body displacement and motion parameters. The present research is focused on developing new methods for recovering kinematic data when the state of features attached to a body during a rigid displacement is available. The proof of concept is sustained by computational solutions both for the singularity-free extraction of a dual quaternion from feature-based representation of motion and for the recovery algorithms of the dual quaternion.