Development of mathematical modeling of a mobile robot's motion control system

Abstract

This study focuses on developing a mathematical model for precise control and stabilization of unmanned aerial vehicles (UAVs) in various spatial conditions. Addressing the problem of achieving precise control and stability, the proposed solution designs a control system based on a linear-quadratic controller (LQR) and simulates it using a proportional-derivative (PD) controller implemented in Matlab/Simulink. The results demonstrate high precision and stability in controlling the UAV motion parameters – roll, pitch, yaw, and altitude. This important level of performance is achieved due to the adaptivity of the LQR-based control system, which optimizes control actions according to the unsteady dynamics of the UAV. The integration of the PD controller improves responsiveness and stability, providing precise motion control over a range of spatial states. These features effectively solve the problem by handling the complex dynamics of the UAV and providing precise control. The results are explained by the ability of the LQR to provide optimal control laws that minimize deviations using a quadratic cost function, while the PD controller quickly corrects errors and responds to disturbances. The benefits of this approach include a significant reduction in control errors by about 25–30 %, increased response speed to external disturbances, and reduced computational latency due to efficient processing compared to more resource-intensive methods such as model predictive control. The developed mathematical model can be applied in practice in conditions requiring robust real-time control and adaptation to dynamic changes in the environment. It is especially suitable for industries such as logistics, surveillance, and environmental monitoring, providing an effective and optimal solution for stabilizing and controlling the motion of UAVs in various spatial states. This approach improves the performance of UAVs and expands their capabilities in various operating conditions.