Homozkova I. Models and methods of research of orientation algorithms for high-dynamic objects

The aim of the dissertation work is an improvement of the mathematical modeling of the rotational motion of a rigid body due to the generalization of the method of analytical reference models, which is based on the heuristic representation of the orientation quaternion in the form of a superposition of trigonometric functions of linear angles. The object of research is determination in strapdown inertial orientation systems. The subject of research is the simulation of the rotational motion of a rigid body using the quaternion apparatus and analytical mechanics. The introduction proves the relevance of developing models that reproduce specific types of angular movement and optimizing algorithms for determining the orientation for such movement of objects. The connection of the work with scientific programs, plans and topics is given, scientific novelty is given, the practical significance of the obtained results is presented, information is provided about the personal contribution of the recipient, a list of publications on the topic of the dissertation is presented. The first chapter describes in detail the principles of operation of the computing unit of platformless inertial navigation systems, the way of their development and comparison with other types of navigation systems. The classification of existing orientation determination algorithms is presented. Sources of errors that occur in such systems and methods of their compensation are listed. The existing methods of modeling and testing the operation of the computing unit are analyzed. The expediency of optimizing platformless navigation systems for the characteristics of the movement of modern objects is substantiated, the numerical implementation of models in the form of trajectories in the configuration space and time dependencies is given. The second chapter describes the principles by which mathematical modeling of the computing unit of platformless navigation systems is performed. The requirements for such models are listed, taking into account their dependence on the degrees of freedom of the rotating object. The main tasks of the dissertation have been formulated. New reference models have been built that realize the rotational motion of the object, and it has been proven through numerical simulation that each of them realizes unique characteristics of angular motion, different from the classical ones. The solutions of the corresponding kinematic equations and the Euler system of dynamic equations were obtained. The latter play an important role in the management and reorientation of objects. In the third section, the accuracy of two algorithms for determining the orientation of the 4th order of accuracy is evaluated. Based on the obtained result, Miller's algorithm was chosen for further implementation. New values of the parameters of this algorithm were found, for which the drift error is smaller than for classical values. The factors that lead to a decrease in the actual accuracy of the algorithm compared to the mathematical one are described. The values of the angular velocity modules, which achieve the chosen accuracy of the orientation determination algorithm, were studied for the developed angular motion models. In the fourth chapter, clear characteristics of a highly maneuverable object are formed and it is proved that one of the developed models allows to reproduce this type of movement. For this model, another set of parameters of the Miller algorithm was found, which in the case of a high rotation speed of the device give a drift error smaller compared to the classical parameter values . It has been proven that the new four-frequency models take into account the influence of the vibrating environment in the form of harmonic oscillations. The fifth chapter describes the software application developed for the numerical implementation of the models. The program was written in the C++ language using elements of object-oriented programming. The output data is automatically saved to an Excel file. In the same file, construction of the corresponding graphs of dependencies is performed. The basic requirements for installing the application on each specific device are listed. The characteristics and limitations of the input conditions necessary for the implementation of calculations are described. The conclusions list the main results of the scientific work, which are solutions to the formed theoretical and applied research problems.