НЕЛІНІЙНЕ МОДЕЛЮВАННЯ КВАДРОКОПТЕРА: ВІД АНАЛІТИЧНОГО ВИВЕДЕННЯ ДО ФІЗИЧНОГО МОДЕЛЮВАННЯ
The subject matter of this study is the expansion of an H-frame quadrotor mathematical model to include nonlinearities and the implementation of its dynamics within the Simscape Multibody simulation environment. The goal is to develop a comprehensive nonlinear motion model and verify its accuracy by comparing analytical descriptions with physics-based component modeling. The tasks to be solved are: to analyze the challenges of describing and implementing nonlinear quadrotor models; to formulate a system of nonlinear differential equations using the Euler–Lagrange formalism; to conduct simulation experiments on the initial mathematical model; to develop and integrate a physical rigid-body model into the automatic control system; to perform a comparative analysis of the results. Methods are used: the Euler–Lagrange formalism, numerical methods, and comparative statistical analysis. The following results were obtained: a refined nonlinear mathematical model of an H-frame quadrotor was developed, accounting for cross-coupled gyroscopic effects and electromechanical actuator dynamics. A dynamic model based on physical constraints and inertia tensors was implemented in Simscape Multibody. Maneuvering scenarios for both the mathematical and multi-domain models indicate characteristic transients for orientation angles within the [11, 15] s interval. It was determined that the steady-state deviation for the mathematical model is 0.1° for yaw and roll and 0.12° for pitch, while the maximum error over the simulation interval reached 2.4° for yaw, 0.1° for roll, and 0.15° for pitch. Corresponding indicators for the multi-domain model were: a steady-state deviation of 1° for yaw, 0.9° for roll, and 1.3° for pitch, with maximum errors of 3°, 0.9°, and 1.3°, respectively. These values result from natural error accumulation due to different kinematic parameterization methods, gyroscopic moments, and electromechanical dynamics. Conclusions. The scientific novelty of the results obtained is as follows: the scientific and methodological approach to assessing the fidelity of complex dynamic systems was further developed, which, unlike existing ones, is based on the cross-platform verification of the analytical Euler–Lagrange formalism and multi-domain simulation; this allowed for the first time to establish the applicability limits of nonlinear models and to quantitatively determine the error in reproducing flight scenario caused by specific kinematic parameterization and cross-coupling dynamics. Quantitative evaluation confirmed the fidelity of both models. The steady-state deviations between the two models are 0.9° (yaw), 0.8° (roll), and 1.2° (pitch); at maximum error, they are 4.2° (yaw), 0.8° (roll), and 1.23° (pitch). Utilizing Simscape physical components significantly simplifies frame parameter modification, process visualization, and the formulation of coupling equations, as the tool handles part of the model implementation. The proposed approach provides a high-fidelity virtual prototype for testing robust control algorithms under conditions close to real-world operation