scholarly journals A Moving Frame Trajectory Tracking Method of a Flying-Wing UAV Using the Differential Geometry

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Yi Zhu ◽  
Xin Chen ◽  
Chuntao Li
Keyword(s):  
Flight Control ◽  
Trajectory Tracking ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Dynamic Equations ◽  
Moving Frame ◽  
Moving Frames ◽  
Tracking Method ◽  
Tracking Process

The problem of UAV trajectory tracking is a difficult issue for scholars and engineers, especially when the target curve is a complex curve in the three-dimensional space. In this paper, the coordinate frames during the tracking process are transformed to improve the tracking result. Firstly, the basic concepts of the moving frame are given. Secondly the transfer principles of various moving frames are formulated and the Bishop frame is selected as a final choice for its flexibility. Thirdly, the detailed dynamic equations of the moving frame tracking method are formulated. In simulation, a moving frame of an elliptic cylinder helix is formulated precisely. Then, the devised tracking method on the basis of the dynamic equations is tested in a complete flight control system with 6 DOF nonlinear equations of the UAV. The simulation result shows a satisfactory trajectory tracking performance so that the effectiveness and efficiency of the devised tracking method is proved.

Production and Analytics of a Multi-Linked Robotic System

2019 ◽  
Author(s):  
Thorstein R. Rykkje ◽  
Eystein Gulbrandsen ◽  
Andreas Fosså Hettervik ◽  
Morten Kvalvik ◽  
Daniel Gangstad ◽  
...  
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Robotic System ◽  
Moving Frame ◽  
Moving Frames ◽  
New Approach ◽  
Lie Group Theory ◽  
Senior Design ◽  
Moving Frame Method ◽  
Frame Method

Abstract This paper extends research into flexible robotics through a collaborative, interdisciplinary senior design project. This paper deploys the Moving Frame Method (MFM) to analyze the motion of a relatively high multi-link system, driven by internal servo engines. The MFM describes the dynamics of the system and enables the construction of a general algorithm for the equations of motion. Lie group theory and Cartan’s moving frames are the foundation of this new approach to engineering dynamics. This, together with a restriction on the variation of the angular velocity used in Hamilton’s principle, enables an effective way of extracting the equations of motion. The result is a dynamic 3D analytical model for the motion of a snake-like robotic system, that can take the physical sizes of the system and return the dynamic behavior. Furthermore, this project builds a snake-like robot driven by internal servo engines. The multi-linked robot will have a servo in each joint, enabling a three-dimensional movement. Finally, a test is performed to compare if the theory and the measurable real-time results match.

Computation of Rigid-Body Rotation in Three-Dimensional Space From Body-Fixed Linear Acceleration Measurements

1979 ◽  
Vol 46 (4) ◽  
pp. 925-930 ◽  
Author(s):  
N. K. Mital ◽  
A. I. King
Keyword(s):  
Rigid Body ◽  
High Speed ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Angular Acceleration ◽  
Linear Acceleration ◽  
Field Measurements ◽  
Moving Frame ◽  
Accelerometer Data ◽  
Hypothetical Data

The angular acceleration of a rigid body with respect to a body-fixed (moving) frame can be reliably computed from nine acceleration field measurements. Noncommutativity of finite rotations causes computational problems during numerical integration to obtain the transformation matrix, especially when the rotation is three-dimensional and there are errors in the measured linear accelerations. A method based on the orientation vector concept is formulated and tested against hypothetical data. The rigid-body rotations computed from linear accelerometer data from impact acceleration tests are compared against those obtained from three-dimensional analysis of high speed movie films.

scholarly journals Trajectory Tracking Method of Volleyball Player’s Arm Hitting Image Based on D-P Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Hao Qin
Keyword(s):  
Trajectory Tracking ◽  
Three Dimensional ◽  
Feature Points ◽  
Tracking Accuracy ◽  
Tracking Method ◽  
Feature Extraction Method ◽  
Image Tracking ◽  
Volleyball Players ◽  
Long Time ◽  
Tracking Time

Aiming at the problems of poor image tracking effect, low precision, and long time in the process of image tracking of volleyball player’s arm hitting, a volleyball player's arm hitting image tracking method based on D-P algorithm is proposed. This paper analyzes the basic concept, basic principle, and basic equation of D-P algorithm and collects the arm stroke trajectory image of volleyball players under the three-dimensional visual model. Using wavelet multiscale decomposition method, the arm stroke trajectory of volleyball players is filtered, and the edge contour feature points of the arm stroke image of volleyball players are extracted. Using the gray histogram feature extraction method, the gray information of volleyball player's arm hitting trajectory image is enhanced. Combined with pixel adaptive enhancement technology, the key action feature points of volleyball player's arm hitting image trajectory are located. Based on D-P algorithm, the volleyball player's arm hitting image trajectory is adjusted and modified to realize the correct tracking of volleyball player's arm hitting image trajectory. The experimental results show that the trajectory tracking effect of volleyball player's arm hitting image is better, which can effectively improve the tracking accuracy and shorten the tracking time.

A Robust and Optimal Visual Tracking Method With Blocking Obstacles and Water Reflection Noises

2018 ◽  
Author(s):  
Xiongfeng Yi ◽  
Zheng Chen
Keyword(s):  
Visual Tracking ◽  
Water Surface ◽  
Optimal Algorithm ◽  
Dimensional Space ◽  
The Body ◽  
Moving Object ◽  
Tracking Method ◽  
The Real ◽  
Tracking Process ◽  
Image Pixels

Image-based tracking has been widely used to obtain the position and velocity information of a moving object in a 2-dimensional or 3-dimensional space. However, the tracking process is always affected by reflection noises and blocking obstacles in the environment. This paper provides a robust and optimal algorithm for tracking a moving object on the surface of water. First, we create a matrix to project the image pixels back to the real world coordinate. Second, color and shape tests are used to recognize the object and a vector is used to represent the object. If the object is partially blocked by the obstacles or the reflection from the water surface, the vector is used to predict the position of the body. In the real-time tracking, a Kalman filter is used to optimize the prediction. We tested our algorithm by tracking a submarine on the water surface of a tank. Experimental results show that the visual tracking method is robust to reflection noises and blocking obstacles.

MPU6050 MODULE CONTROL UNIT ON THE IC BUS BASED ON A MICROCONTROLLER

2021 ◽  
pp. 65-69
Author(s):  
А.Б. Буслаев ◽  
Н.Н. Кошелева ◽  
С.С. Белокопытов
Keyword(s):  
Flight Control ◽  
Temperature Sensor ◽  
Dimensional Space ◽  
Low Cost ◽  
Assembly Language ◽  
Three Dimensional ◽  
Control Unit ◽  
Control Flight ◽  
Micromechanical Systems ◽  
Simultaneous Reading

Рассматривается модуль GY-521, на котором установлена микросхема MPU6050, объединяющая в одном корпусе акселерометр, гироскоп и температурный датчик. Такие датчики изготовлены на основе микромеханических систем (МЭМС), основным преимуществом которых является малый размер, низкое энергопотребление и небольшая стоимость. Одновременное использование акселерометра и гироскопа позволяет определить изменение движения тела в трехмерном пространстве. Рассмотрены основные характеристики используемого модуля. Управление микросхемы осуществляется с помощью архитектуры интерфейса IC «ведущий-ведомый». В работе ведомым является MPU6050, а ведущим (производит запрос на чтение или запись данных) является микроконтроллер, имеющий в своем составе аппаратную шину передачи данных IC. Показана возможная программная реализация алгоритма подключения нескольких ведомых устройств (шести микросхем MPU6050). Представлена принципиальная схема подключения к одному порту ввода-вывода микроконтроллера. Рассмотрен алгоритм работы микроконтроллера с подключенными микросхемами (шестью) MPU6050. Приведены пример программы (с использованием языка ассемблер) инициализации связи с MPU6050, а также программа считывания данных для снятия последних измерений акселерометра, гироскопа, температурного датчика. Применение нескольких модулей с одновременным считыванием с них информации позволяет осуществлять контроль систем управления полетом, имеющих совокупность нескольких управляющих поверхностей и устройств The paper considers the GY-521 module, which is equipped with the MPU6050 chip, which combines an accelerometer, a gyroscope and a temperature sensor in one housing. Such sensors are made on the basis of micromechanical systems (MEMS), the main advantages of which are small size, low power consumption and low cost. The simultaneous use of an accelerometer and a gyroscope allows you to determine the change in the movement of a body in three-dimensional space. We considered the main characteristics of the module used. The control of the chip is carried out using the architecture of the IC interface "master-slave". In operation, the MPU6050 is the host, and the master (makes a request to read or write data) is a microcontroller that has an IC hardware data bus. We show a possible software implementation of the algorithm for connecting multiple slave devices (six MPU6050 chips). We present a schematic diagram of the connection to a single I/O port of the microcontroller. We consider the algorithm of operation of the microcontroller with connected chips (six) MPU6050. We give an example of a program (using the assembly language) for initializing communication with the MPU6050, as well as a program for reading data for taking the latest measurements of the accelerometer, gyroscope, and temperature sensor. The use of several modules with simultaneous reading of information from them allows you to control flight control systems that have a set of several control surfaces and devices

Modeling Crane-Induced Ship Motion Using the Moving Frame Method

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Paulo Alexander Jacobsen Jardim ◽  
Jan Tore Rein ◽  
Øystein Haveland ◽  
Thorstein R. Rykkje ◽  
Thomas J. Impelluso
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Moving Frame ◽  
Integration Scheme ◽  
Moving Frames ◽  
Offshore Installations ◽  
Numerical Integration Scheme ◽  
Moving Frame Method ◽  
Frame Method ◽  
The Masses

A decline in oil-related revenues challenges Norway to focus on new types of offshore installations. Often, ship-mounted crane systems transfer cargo or crew onto offshore installations such as floating windmills. This project analyzes the motion of a ship induced by an onboard crane in operation using a new theoretical approach to dynamics: the moving frame method (MFM). The MFM draws upon Lie group theory and Cartan's moving frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. While others have applied aspects of these mathematical tools, the notation presented here brings these methods together; it is accessible, programmable, and simple. In the MFM, the notation for multibody dynamics and single body dynamics is the same; for two-dimensional (2D) and three-dimensional (3D), the same. Most importantly, this paper presents a restricted variation of the angular velocity to use in Hamilton's principle. This work accounts for the masses and geometry of all components, interactive motor couples and prepares for buoyancy forces and added mass. This research solves the equations numerically using a relatively simple numerical integration scheme. Then, the Cayley–Hamilton theorem and Rodriguez's formula reconstruct the rotation matrix for the ship. Furthermore, this work displays the rotating ship in 3D, viewable on mobile devices. This paper presents the results qualitatively as a 3D simulation. This research demonstrates that the MFM is suitable for the analysis of “smart ships,” as the next step in this work.

Design and Implementation of Trajectory Tracking for 3-Axis Servo Table Using UMAC Based on Optimal Preview Controller

2012 ◽  
Vol 157-158 ◽  
pp. 165-170
Author(s):  
Mohammed M. Saleh All Bail ◽  
Yue Gang Tan
Keyword(s):  
Trajectory Tracking ◽  
Control Algorithm ◽  
Control Method ◽  
Simulation Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Experimental System ◽  
Driving Mechanism ◽  
Trajectory Tracking Control ◽  
Wide Range

This paper deals with the use of Programmable Multi-Axis Controller (UMAC) based on preview control method to give good trajectory tracking performance of 3-axis servo table. The paper consists of mathematical modeling, simulation, and an experimental work. Adopt the position coordinate method of three-dimensional space trajectory tracking. In this paper, based on previous research, it gives a trajectory tracking control algorithm, constructs an experimental system used to implement trajectory tracking, establishes its mathematical model, then uses the control algorithm to carry out simulation analysis, and finally uses the simulation results to carry out experimental study. In this paper, the experimental system, which decomposes object trajectory to various axes for tacking, is effective. It takes the best motion controller as the core, and takes servo motor as driving mechanism to drive precision positioning platform. It possesses of powerful real time and linkage performance, and the powerful hardware and software function enable it to have a wide range of applications.

Visual Synthesis of RRR- and RPR-Legged Planar Parallel Manipulators Using Constraint Manifold Geometry

2011 ◽  
Author(s):  
Anurag Purwar ◽  
Aditya Gupta
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Design Tool ◽  
Design Parameters ◽  
Moving Frames ◽  
Algebraic Manifold ◽  
Dimensional Synthesis ◽  
Geometric Transformations ◽  
Planar Parallel Manipulators

In this paper, we present our ongoing work on development of a visual design tool for designing planar parallel manipulators that satisfy a given rational motion. Although in this paper, we have restricted ourselves to RRR- and RPR-type legs, the approach presented here is general enough to accommodate other leg topologies. The basic idea is to represent the kinematic constraint of such parallel manipulators as an algebraic manifold and the given motion as a one-parameter curve in the image space of planar displacements. The algebraic manifold is projected in the three-dimensional space and a simple set of relationships are obtained that couple the geometry of the projected manifold to the design parameters of the parallel manipulators. Simple geometric transformations in the projected space allow a user to visually contain the image curve inside the manifold, thus satisfying the kinematic constraints. This interactive process, at the end, gives the dimensions of the links of the legs and the location of the fixed and moving frames. This is an extension of our previous work on the dimensional synthesis of planar 6R closed chains.

Three Dimensional structure and organization of diploid chromosomes by optical section microscopy

1987 ◽  
Vol 45 ◽  
pp. 633-635
Author(s):  
David A. Agard ◽  
Yasushi Hiraoka ◽  
John W. Sedat
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Developmental State ◽  
Mitotic Cell ◽  
Biological Properties ◽  
Dimensional Structure ◽  
Specific Gene ◽  
Three Dimensional Structure ◽  
Complementary Techniques ◽  
Dynamic Structures

In an effort to understand the complex relationship between structure and biological function within the nucleus, we have embarked on a program to examine the three-dimensional structure and organization of Drosophila melanogaster embryonic chromosomes. Our overall goal is to determine how DNA and proteins are organized into complex and highly dynamic structures (chromosomes) and how these chromosomes are arranged in three dimensional space within the cell nucleus. Futher, we hope to be able to correlate structual data with such fundamental biological properties as stage in the mitotic cell cycle, developmental state and transcription at specific gene loci.Towards this end, we have been developing methodologies for the three-dimensional analysis of non-crystalline biological specimens using optical and electron microscopy. We feel that the combination of these two complementary techniques allows an unprecedented look at the structural organization of cellular components ranging in size from 100A to 100 microns.

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