MATHEMATICAL MODELS OF ANGULAR MOTION OF SPACE VEHICLES AND THEIR USE IN ORIENTATION CONTROL PROBLEMS

2021 ◽  
Vol 5 ◽  
pp. 124-139
Author(s):  
Viktor Volosov ◽  
◽  
Vladimir Shevchenko ◽  
Keyword(s):  
Coordinate System ◽  
Attitude Control ◽  
Evolution Equations ◽  
General Structure ◽  
Control Synthesis ◽  
Space Vehicles ◽  
Direct Lyapunov Method ◽  
Coordinate Systems ◽  
Advantages And Disadvantages ◽  
Modified Rodrigues Parameters

A general structure of the kinematic equations for attitude evolution of a spacecraft (SC) (coordinate system associated with a spacecraft (SCS)) relative to the reference coordinate system (RCS) is proposed. It is assumed that the origins of the coordinate systems coincide and are located at an arbitrary point of the spacecraft. Each of the coordinate systems rotates at an arbitrary absolute angular velocity (relative to the inertial space) specified by the projections on their axes. Attitude parameters can be the Euler–Krylov angles, Rodrigues–Hamilton parameters, and modified Rodrigues parameters. It is shown that the well-known representations of the attitude evolution equations of the SCS relative to the RCS using the Rodrigues-Hamilton parameters (components of normalized quaternions) can be simply obtained from the solution of the Erugin problem of finding the entire set of differential equations with a given integral of motion. The advantages and disadvantages of use for each of the specified attitude parameters are considered. A method of attitude control synthesis is proposed which is common for all these equations and based on the decomposition of the original problem into kinematic and dynamic ones and the use of well-known generalizations of the direct Lyapunov method for their solution. The property of structural roughness according to Andronov–Pontryagin [27–29] of the obtained algorithm is illustrated with the help of computer simulation. Particularly, a specific example illustrates the possibility for even a structurally simplified algorithm of stabilizing a specified constant spacecraft attitude to track the program of its change with sufficient accuracy. The tracking task is typical for the control of spacecraft docking, spacecraft de-orbiting, and performing route surveys of the Earth's surface.

Reference Coordinate System Requirements for Geophysics

1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender
Keyword(s):  
Coordinate System ◽  
Polar Motion ◽  
Main Part ◽  
Measurement Techniques ◽  
Reference Points ◽  
Angular Motion ◽  
Coordinate Systems ◽  
Axis Of Rotation ◽  
The Earth ◽  
Fixed System

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Technique for relation global reference system and local realization of global reference system by continuously operated reference stations

2020 ◽  
Vol 962 (8) ◽  
pp. 24-37
Author(s):  
V.E. Tereshchenko
Keyword(s):  
Coordinate System ◽  
Russian Federation ◽  
Reference System ◽  
Main Part ◽  
Precise Point Positioning ◽  
Global Coordinate System ◽  
Coordinate Systems ◽  
Novosibirsk Region ◽  
The Russian Federation

The article suggests a technique for relation global kinematic reference system and local static realization of global reference system by regional continuously operated reference stations (CORS) network. On the example of regional CORS network located in the Novosibirsk Region (CORS NSO) the relation parameters of the global reference system WGS-84 and its local static realization by CORS NSO network at the epoch of fixing stations coordinates in catalog are calculated. With the realization of this technique, the main parameters to be determined are the speed of displacement one system center relativly to another and the speeds of rotation the coordinate axes of one system relatively to another, since the time evolution of most stations in the Russian Federation is not currently provided. The article shows the scale factor for relation determination of coordinate systems is not always necessary to consider. The technique described in the article also allows detecting the errors in determining the coordinates of CORS network in global coordinate system and compensate for them. A systematic error of determining and fixing the CORS NSO coordinates in global coordinate system was detected. It is noted that the main part of the error falls on the altitude component and reaches 12 cm. The proposed technique creates conditions for practical use of the advanced method Precise Point Positioning (PPP) in some regions of the Russian Federation. Also the technique will ensure consistent PPP method results with the results of the most commonly used in the Russian Federation other post-processing methods of high-precision positioning.

scholarly journals The Celestial Reference System in Relativistic Framework

1990 ◽  
Vol 141 ◽  
pp. 99-110
Author(s):  
Han Chun-Hao ◽  
Huang Tian-Yi ◽  
Xu Bang-Xin
Keyword(s):  
Coordinate System ◽  
Reference Frame ◽  
Reference System ◽  
Light Deflection ◽  
Coordinate Systems ◽  
Definition Of ◽  
Celestial Sphere ◽  
Celestial Reference System ◽  
Relativistic Framework

The concept of reference system, reference frame, coordinate system and celestial sphere in a relativistic framework are given. The problems on the choice of celestial coordinate systems and the definition of the light deflection are discussed. Our suggestions are listed in Sec. 5.

Reaction wheel attitude control for space vehicles

1959 ◽  
Vol 4 (3) ◽  
pp. 139-149 ◽  
Author(s):  
R. Froelich ◽  
H. Papapoff
Keyword(s):  
Attitude Control ◽  
Space Vehicles ◽  
Reaction Wheel

Quaternion Algorithm for Initial Alignment of Strapdown INS Using the A. N. Tikhonov Regularization Method

2021 ◽  
Vol 22 (4) ◽  
pp. 217-224
Author(s):  
Yu. N. Chelnokov ◽  
A. V. Molodenkov
Keyword(s):  
Angular Velocity ◽  
Coordinate System ◽  
Regularization Method ◽  
Numerical Experiments ◽  
Tikhonov Regularization Method ◽  
Coordinate Systems ◽  
Initial Alignment ◽  
Unknown Variable ◽  
Absolute Angular Velocity ◽  
Acceleration Vector

For the functioning of algorithms of inertial orientation and navigation of strapdown inertial navigation system (SINS), it is necessary to conduct a mathematical initial alignment of SINS immediately before the operation of these algorithms. An efficient method of initial alignment (not calibration!) of SINS is the method of vector matching. Its essence is to determine the relative orientation of the instrument trihedron Y (related to the unit of SINS sensors) and the reference trihedron X according to the results of measuring the projections of at least two non-collinear vectors of the axes on both trihedrons. We address the estimation of the initial orientation of the object using the method of gyrocompassing, which is a form of vector matching method. This initial alignment method is based upon using the projections of the apparent acceleration vector a and the absolute angular velocity vector ω of the object in the coordinate systems X and Y. It is assumed that the three single-axis accelerometers and the three gyroscopes (generally speaking, the three absolute angular velocity sensors of any type), which measure the projections of the vectors a and ω, are installed along the axes of the instrument coordinate system Y. If the projections of the same vectors on the axes of the base coordinate system X are known, then it is possible to estimate the mutual orientation of X and Y trihedrons. We are solving the problem of the initial alignment of SINS for the case of a fixed base, when the accelerometers measure the projection gi (i = 1, 2, 3) of the gravity acceleration vector g, and the gyroscopes measure the projections u i of the vector u of angular velocity of Earth’s rotation on the body-fixed axes. The projections of the same vectors on the axes of the normal geographic coordinate system X are also estimated using the known formulas. The correlation between the projections of the vectors u and g in X and Y coordinate system is given by known quaternion relations. In these relations the unknown variable is the orientation quaternion of the object in the X coordinate system. By separating the scalar and vector parts in the equations, we obtain an overdetermined system of linear algebraic equations (SLAE), where the unknown variable is the finite rotation vector θ, which aligns the X and Y coordinate systems (it is assumed that there is no half-turn of the X coordinate system with respect to the Y coordinate system). Thus, the mathematical formulation of the problem of SINS initial alignment by means of gyrocompassing is to find the unknown vector θ from the derived overdetermined SLAE. When finding the vector θ directly from the SLAE (algorithm 1) and data containing measurement errors, the components of the vector q are also determined with errors (especially the component of the vector θ, which is responsible for the course ψ of an object). Depending on the pre-defined in the course of numerical experiments values of heading ψ, roll ϑ, pitch γ angles of an object and errors of the input data (measurements of gyroscopes and accelerometers), the errors of estimating the heading angle Δψ of an object may in many cases differ from the errors of estimating the roll Δϑ and pitch Δγ angles by two-three (typically) or more orders. Therefore, in order to smooth out these effects, we have used the A. N. Tikhonov regularization method (algorithm 2), which consists of multiplying the left and right sides of the SLAE by the transposed matrix of coefficients for that SLAE, and adding the system regularization parameter to the elements of the main diagonal of the coefficient matrix for the newly derived SLAE (if necessary, depending on the value of the determinant of this matrix). Analysis of the results of the numerical experiments on the initial alignment shows that the errors of estimating the object’s orientation angles Δψ, Δϑ, Δγ using algorithm 2 are more comparable (more consistent) regarding their order.

The structure and application of an automated system for monitoring passenger traffic

2021 ◽  
Vol 14 (3) ◽  
pp. 4-11
Author(s):  
Evgeniy Anikeev
Keyword(s):  
Data Collection ◽  
General Structure ◽  
Automated System ◽  
Passenger Transport ◽  
Service Levels ◽  
Passenger Traffic ◽  
Advantages And Disadvantages ◽  
Transport Services ◽  
Transport Control

Various methods of collecting data on passenger traffic, their advantages and disadvantages are considered. It is shown that in order to improve the quality of transport services, it is necessary to regularly collect and refine data on passenger traffic. The goals and methods of obtaining information about passenger traffic in the system of municipal passenger transport are indicated. All currently existing methods are divided into three categories: data collection using technical means, data collection with the help of censors and volunteers, and interpretation of fare payments. All the methods presented in the article were compared in terms of labor intensity, costs and accuracy of the results obtained. The advantages and disadvantages of each method are considered. The general structure of an automated system for collecting data on passenger traffic is presented. The necessity of creating a centralized system for collecting and processing data associated with all passenger transport control systems has been substantiated. The tasks solved by this system at all levels of transport services for passengers are shown. Each of the tasks is assigned to one of three service levels: pre-transport, transport and post-transport. It is shown that only solving problems at all levels can ensure high-quality operation of the municipal passenger transport system.

scholarly journals How visual experience and task context modulate the use of internal and external spatial coordinate for perception and action

2018 ◽  
Author(s):  
Virginie Crollen ◽  
Tiffany Spruyt ◽  
Pierre Mahau ◽  
Roberto Bottini ◽  
Olivier Collignon
Keyword(s):  
Coordinate System ◽  
Visual Experience ◽  
Simon Task ◽  
Frame Of Reference ◽  
The Body ◽  
Blind People ◽  
Coordinate Systems ◽  
Task Instructions ◽  
Congenitally Blind ◽  
External Frame

Recent studies proposed that the use of internal and external coordinate systems may be more flexible in congenitally blind when compared to sighted individuals. To investigate this hypothesis further, we asked congenitally blind and sighted people to perform, with the hands uncrossed and crossed over the body midline, a tactile TOJ and an auditory Simon task. Crucially, both tasks were carried out under task instructions either favoring the use of an internal (left vs. right hand) or an external (left vs. right hemispace) frame of reference. In the internal condition of the TOJ task, our results replicated previous findings (Röder et al., 2004) showing that hand crossing only impaired sighted participants’ performance, suggesting that blind people did not activate by default a (conflicting) external frame of reference. However, under external instructions, a decrease of performance was observed in both groups, suggesting that even blind people activated an external coordinate system in this condition. In the Simon task, and in contrast with a previous study (Roder et al., 2007), both groups responded more efficiently when the sound was presented from the same side of the response (‘‘Simon effect’’) independently of the hands position. This was true under the internal and external conditions, therefore suggesting that blind and sighted by default activated an external coordinate system in this task. All together, these data comprehensively demonstrate how visual experience shapes the default weight attributed to internal and external coordinate systems for action and perception depending on task demand.

scholarly journals Denavit-Hartenberg Coordinate System for Robots with Tree-like Kinematic Structure

2016 ◽  
Vol 5 (4) ◽  
pp. 244
Author(s):  
Alexander Kovalchuk ◽  
F. Akhmetova
Keyword(s):  
Graph Theory ◽  
Coordinate System ◽  
Kinematic Chain ◽  
Kinematics And Dynamics ◽  
Kinematic Structure ◽  
Coordinate Systems ◽  
Reachability Graph ◽  
Joint Application ◽  
Linear Chains ◽  
Use Efficiency

<p class="MDPI17abstract"><span lang="EN-US">The paper presents a modified Denavit-Hartenberg coordinate system resulted from joint application of graph theory and the Denavit-Hartenberg coordinate system, which was developed to describe the kinematics of robot actuators with a linear open kinematic chain. It allows forming mathematical models of actuating mechanisms for the robots with tree-like kinematic structures. The work introduces the concept of primary and auxiliary coordinate systems. It considers an example of making the links’ reachability matrix and reachability graph for the tree-like actuating mechanism of a robotic mannequin. The use efficiency of the proposed modified Denavit-Hartenberg coordinate system is illustrated by the examples giving the mathematical description of the kinematics and dynamics of specific robots’ tree-like actuating mechanisms discussed in the previously published papers. It is shown that the proposed coordinate system can also be successfully applied to describe the actuating mechanisms of robots with a linear open kinematic chain, which is a particular case of the tree-like kinematic structure. The absence of branching joints in it does not require introducing auxiliary coordinate systems and the parameters f(i) and ns(i) are necessary only for the formal notation of equations, which have similar forms for the tree-like and linear chains. In this case, the modified and traditional coordinate systems coincide.</span></p>

scholarly journals Identity and compatibility of reference genome resources

2021 ◽  
Author(s):  
Michał Stolarczyk ◽  
Bingjie Xue ◽  
Nathan C. Sheffield
Keyword(s):  
Coordinate System ◽  
Genome Analysis ◽  
Reference Genome ◽  
Reference Data ◽  
Coordinate Systems ◽  
Link Type ◽  
Novel Approach ◽  
Many Sources ◽  
Parent Child Relationships ◽  
Parent Child

Genome analysis relies on reference data like sequences, feature annotations, and aligner indexes. These data can be found in many versions from many sources, making it challenging to identify and assess compatibility among them. For example, how can you determine which indexes are derived from identical raw sequence files, or which annotations share a compatible coordinate system? Here, we describe a novel approach to establish identity and compatibility of reference genome resources. We approach this with three advances: First, we derive unique identifiers for each resource; second, we record parent-child relationships among resources; and third, we describe recursive identifiers that determine identity as well as compatibility of coordinate systems and sequence names. These advances facilitate portability, reproducibility, and re-use of genome reference data.Availabilityhttps://refgenie.databio.org

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