MATHEMATICAL MODEL OF UNMANNED AERIAL VEHICLES’ DYNAMICS

Abstract

The article solves the current scientific and applied problem of increasing the accuracy and robustness of autonomous guidance systems of unmanned aerial vehicles (UAVs) under the influence of non-stationary external disturbances and limited resources of on-board computers. The authors have conducted a thorough analysis of the modern scientific and technical contradiction between the need to implement complex intelligent control algorithms and strict SWaP constraints of embedded real-time systems, where excessive computational complexity leads to critical time delays and loss of stability. The scientific novelty of the study lies in the development of a refined mathematical model of the dynamics of a four-rotor UAV, which for the first time takes into account the vector configuration of additional horizontal thrusters (HST). Such a constructive scheme with redundant actuation allows for independent control of the linear position of the device without changing its angular orientation, which is crucial for the precision maneuvering stage. For the first time, a complete algorithmic decoupling of positioning and orientation channels has been mathematically substantiated and implemented, which creates conditions for parallel execution of computational flows on modern multi-core systems on a crystal. Particular attention is paid to computational efficiency: it has been proven that the use of a full-rank actuation matrix guarantees a single analytical solution to the control effort distribution problem with constant complexity O(1), excluding iterative methods and unpredictable delays. The choice of Euler angles for describing orientation within small tilt angles has been justified, which reduces the load on the processor and provides high linguistic interpretability for intelligent algorithms. The practical significance of the work is confirmed by the implementation of the RSEFNN neural network for online identification of nonlinear forces and external disturbances, which allows replacing cumbersome analytical expressions of Coriolis forces and aerodynamic drag with a single adaptive block. The proposed approach radically simplifies the architecture of the flight software, increases its robustness to parametric uncertainties and minimizes the amount of required program memory. The formed intelligent-robust architecture provides precision UAV guidance without the risk of computational singularities, while maintaining the high performance of the digital twin in hard real-time systems.