Browsing by Author "Mouton, Hendrik D"

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    Comparison of body rotations using Euler angles and quaternions
    (2021) Mouton, Hendrik D
    Many comparisons between Euler angle and quaternion representations of body rotations have been done in the past, but what are additionally investigated in this article are the handling of the generally important non-zero starting conditions, and a demonstration of the correctness of the Euler to quaternion and quaternion to Euler conversions despite giving remarkably different Euler angle and quaternion values for the same set of starting values. Two Euler configurations are also investigated and compared to demonstrate that the findings are generally valid. The first is the often-used yaw-pitch-roll (inner) and the second the less known roll-yaw-pitch (inner) configuration. Some of the test scenarios were chosen such that both the Euler angle configurations had to move through their gimbal lock positions. All transformation matrices, using two sets of Euler angles, and three sets of quaternion values, gave the same projections in an inertial axes system of a point fixed to the rotating body doing a chosen set of rotations, but there are accuracy differences. Therefore there is an optimal solution for each Euler configuration. The findings of this paper are also important in tracking loops where these types of transformations are used in the relative geometry calculations where the angles, for example, between the target and the camera sightline, must be determined accurately.
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    The Exodus Route considering all Biblical Information, Part 1
    (2021) Mouton, Hendrik D
    All biblical information, geographic information mostly with Google Earth Pro and some archaeological evidence were investigated to determine the exodus routes of Israel as accurately as possible. The plural “routes” is sometimes used because of the distinctive phases of the 40-year journey. Some archaeological evidence points to the Red Sea crossing to be in the Gulf of Aqaba and the mountain of Horeb or Sinai to be in Saudi Arabia, which are not only consistent with biblical information but is strongly suggested by the Bible. Comparing the exodus route information in different books in the Bible and with some identified Google Earth Pro locations also indicates the disobedience of Israel in the last year before entering Canaan by wanting to go their own route, but God forced them by calamities to ask for rescue and to turn around and travel along the border between Edom and Moab eventually to the east of the Jordan river. This article is divided in two parts.
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    The Exodus Route considering all Biblical Information, Part 1.0
    (OpenUCT, 2023) Mouton, Hendrik D
    All biblical information, geographic information mostly with Google Earth Pro and some archaeological evidence was investigated to determine the exodus routes of Israel as accurately as possible. The plural “routes” is sometimes used because of the distinctive phases of the 40-year journey. Evidence points strongly to the Red Sea crossing to be in the Gulf of Suez and the mountain of Horeb or Sinai to be in Saudi Arabia. Comparing the exodus route information in different books in the Bible and with some identified Google Earth Pro locations also indicates the disobedience of Israel in the last year before entering Canaan by wanting to go their own route. But God forced them by calamities to ask for rescue and to turn around and travel along the border between Edom and Moab eventually to the east of the Jordan river. This article is divided in two parts.
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    The Exodus Route considering all Biblical Information, Part 2
    (2021) Mouton, Hendrik D
    All biblical information, geographic information mostly with Google Earth Pro and some archaeological evidence were investigated to determine the exodus routes of Israel as accurately as possible. The plural “routes” is sometime used because of the distinctive phases of the 40-year journey. Some archaeological evidence points to the Red Sea crossing in the Gulf of Aqaba and the mountain of Horeb or Sinai to be in Saudi Arabia, which are not only consistent with biblical information but is strongly suggested by the Bible. Comparing the exodus route information in different books in the Bible and with some identified Google Earth Pro locations also indicates the disobedience of Israel in the last year before entering Canaan by wanting to go their own route, but God forced them by calamities to ask for rescue and to turn around and travel along the border between Edom and Moab eventually to the east of the Jordan river. This is Part 2 of the article.
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    Open Access
    The Exodus Route considering all Biblical Information, Part 2.0
    (OpenUCT, 2023) Mouton, Hendrik D
    All biblical information, geographic information mostly with Google Earth Pro and some archaeological evidence was investigated to determine the exodus routes of Israel as accurately as possible. The plural “routes” is sometimes used because of the distinctive phases of the 40-year journey. Evidence points strongly to the Red Sea crossing to be in the Gulf of Suez and the mountain of Horeb or Sinai to be in Saudi Arabia. Comparing the exodus route information in different books in the Bible and with some identified Google Earth Pro locations also indicates the disobedience of Israel in the last year before entering Canaan by wanting to go their own route. But God forced them by calamities to ask for rescue and to turn around and travel along the border between Edom and Moab eventually to the east of the Jordan river. This is Part 2 of the article.
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    Inductive Coupled Transfer Functions for Four Major Topologies, and their Relevant Design Equations
    (2021) Mouton, Hendrik D
    The four major topologies for inductive couplers (such as transformers with air gaps used for wireless power transfer), are discussed in many articles widely available. In this article all the relevant transfer functions and design equations for all four topologies are given and derived. It contains Bode plots showing gain and phase characteristics against frequency with different load resistances, demonstrating clearly that each topology has its own specific characteristics so that the best one for a particular application can be selected. The author used the Laplace s-parameter in all derivations, and only convert later to the frequency domain when required. The concept of reflected impedances due to the transformer in all the designs is used, because it simplifies the derivations significantly, though care must be taken to apply it correctly. Therefore, the basic der-ivation of reflected impedances is also given. A novel set of formulas is derived for calculating the capacitance of the capacitor on the secondary side of the transformer. It is demonstrated to give satisfactory results even though the resultant formulas are relatively simple.
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    Long term orbital inclination and eccentricity oscillations of the planets in our solar system
    (University of Cape Town, 2016) Mouton, Hendrik D
    The orbits of the planets in our solar system are not in the same plane, therefore natural torques stemming from Newton’s gravitational forces exist to pull them all back to the same plane. This causes the inclinations of the planet orbits to oscillate with potentially long periods and very small damping, because the friction in space is very small. Orbital inclination changes are known for some planets in terms of current rates of change, but the oscillation periods are not well published. They can however be predicted with proper dynamic simulations of the solar system. A three-dimensional dynamic simulation was developed for our solar system capable of handling 12 objects, where all objects affect all other objects. Each object was considered to be a point mass which proved to be an adequate approximation for this study. Initial orbital radii, eccentricities and speeds were set according to known values. The validity of the simulation was demonstrated in terms of short term characteristics such as sidereal periods of planets as well as long term characteristics such as the orbital inclination and eccentricity oscillation periods of Jupiter and Saturn. A significantly more accurate result, than given on approximate analytical grounds in a well-known solar system dynamics textbook, was found for the latter period. Empirical formulas were developed from the simulation results for both these periods for three-object solar type systems. They are very accurate for the Sun, Jupiter and Saturn as well as for some other comparable systems.
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    Mathematical Modelling and Control System Development of a Remote Controlled, IMU Stabilised Hexapod Robot
    (2020) Christopher, Ross; Mouton, Hendrik D
    Walking robots are useful in search and rescue applications due to their ability to navigate uneven and complex terrain. A hexapod robot has been developed by the Robotics and Agents Research Lab at UCT, however multiple inadequacies have become evident. This work aims to produce a mathematical model of the hexapod and using this model, implement an effective control algorithm to achieve a smooth walking motion and overcome the original flaws. The mathematical model was integrated with the mechanical structure of the hexapod and controlled by a micro-controller. This micro-controller allows for a rapid start-up and low power consumption when compared to previous iterations of the hexapod. Using a path generation algorithm sets of foot positions and velocities are generated. Generating these points in real time allows for walking in any direction without any pre-defined foot positions. To enable attitude control of the hexapod body, an inertial measurement unit was added to the hexapod. By using a PID controller the IMU pitch and roll data was used to control a height offset of each foot of the hexapod, allowing for stabilisation of the hexapod body. An improved wireless remote control was developed to facilitate communication with a host computer. The remote system has a graphical user interface allowing for walking control and status information feedback, such as error information and current battery voltage. Walking tests have shown that the hexapod walks successfully with a smooth tripod gait using the path generation algorithm. Stabilisation tests have shown that the hexapod is capable of stabilising itself after a disturbance to its pitch and/or roll in ±2.5 seconds with a steady state error of ±0.001 radians. This proves that the hexapod robot can be controlled wirelessly while walking in any direction with a stabilised body. This is beneficial in search and rescue as the hexapod has a high degree of manoeuvrability to access areas too dangerous for rescuers to access. With cameras mounted on the stabilised body, it can be used to locate survivors in a disaster area and assist rescuers in recovering them with speed.
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    A Simplified Dynamics Block Diagram for a Four-Axis Stabilized Platform
    (2015-07) Mouton, Hendrik D
    It is relatively straight-forward to derive comprehensive dynamics block diagrams for two- and three-axis balanced stabilized platforms. But trying to do it for four and higher order systems is getting rapidly such an amount of work, and the resulting block diagrams so extensive, that sensible simplification from the start if feasible could be very beneficial. Those terms that are going to be insignificantly small relative to the other terms should be left out right from the start when deriving the equations. In this paper a method is shown to simplify the dynamics model of stabilized platforms, with the four-axis platform as the main example. The relevant equations are derived for the four-axis example, the block diagram is compiled from the equations after adding simple control loops around the dynamics model to get to the final expanded block diagram, and then some simulation results are shown. The method is validated by showing that the simulation results for a three-axis system are exactly the same for the comprehensive and simplified block diagrams, using the same method. It is proposed that it is therefore reasonable to expect similar findings for the four-axis case.
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    Systems Development of a Two-Axis Stabilised Platform to Facilitate Astronomical Observations
    (2018) Hepworth, James Haydn; Mouton, Hendrik D
    Inertially Stabilised Platforms (ISPs) aim to control the line-of-sight between a sensor and a target. They perform two distinct operations; keeping track of the target as the sensor host and the target move in inertial space and attenuating rotational disturbances incurred to the sensor by host vehicle motion. This project aimed to develop a two-axis ISP for use in astronomical applications. It represents the initial development of all systems of a low-cost ISP designed for a 3.5” compound telescope. To achieve this, relevant literature describing the various components of an ISP were reviewed to inform the design, implementation and testing cycle which comprised most of the project. A set of system specifications was developed to guide design decisions. The performance of the implemented system was compared against these specifications once the project was complete. During the project, the electro-mechanical structure of the ISP was designed and implemented, including a mechanical assembly designed to mount a camera and inertially and geometrically model the specified telescope. This allowed the ISP to be tested at a lower cost than with the telescope itself. The associated electrical systems were specified and configured. An image processing script capable of detecting and locating the centre of the Moon in the camera field of view was written in Python and implemented on a Raspberry Pi Computer. A complete simulation model for the system was written in the simulation language, Simul_C_EM, and used to design various controllers for the ISP control system and help verify certain estimated system parameters such as gimbal friction. For each gimbal, PI controllers were designed to allow manual orientation control of the telescope, compensated P controllers were designed to achieve target tracking, and compensated PI controllers were designed to reject rotational disturbances. These were implemented in C on an STM32F0 microcontroller tasked with managing the various control and communications tasks required by the system. Finally, a user interface was written in LabVIEW to facilitate intuitive user control of the system and perform datalogging of the system runtime data. Testing of the system showed good correlation between the hardware and the simulated results indicating an accurate simulation model that can be used to test future design developments.