Advanced Mathematical Modeling and Control Strategies for Autonomous Drone Systems

This paper explores the mathematical modelling and simulation of drones, focusing on both low-level and high-level control aspects. The low-level control involves altitude maintenance and stabilization, alongside disturbance compensation, essential for ensuring stable flight. At the high-level control, the research addresses compensating for air currents, drift correction, obstacle avoidance, localization, mapping, navigation to predefined points, returning to the take-off position (return to home), and person tracking. Additionally, it highlights the inherent limitations in drone usage, including restricted weight capacity, limited processing power, a constrained number of sensors, short battery life, rapid dynamics requiring electronic stabilization, continuous motion of the drone, and safety concerns. The study emphasizes the intricate interplay between mathematical models and control strategies to manage these control objectives and constraints. It delves into the development of mathematical models representing drone dynamics and sensor data fusion techniques. Simulation environments are utilized to validate and optimize control algorithms, replicating real-world scenarios to ensure reliable and robust drone performance. The paper aims to address these challenges by proposing mathematical modelling techniques and control strategies. By integrating sophisticated algorithms with limited hardware resources, it seeks to improve the efficiency and autonomy of drones while overcoming constraints. Ultimately, the research endeavours to contribute to the advancement of drone technology, enabling enhanced capabilities for various applications while ensuring safety and reliability.