Mathematical Modeling of a Tethered Platform's Controlled Vertical Flight

Abstract

There is a problem of quickly obtaining reliable and sufficient information about the environment, including in hard-to-reach areas where there is no communication or long-term stationary monitoring is required in order to ensure the safety or security of important objects. The paper discusses the issues of mathematical modeling of automated cable parking of an unmanned aerial vehicle (platform) in a vertical plane. The aim of the research is to create tools for the design of tethered flying platforms equipped with an automated cable restraint system, taking into account external random atmospheric disturbances during vertical flight. To achieve this aim, it is necessary to carry out mathematical modeling of the flight of tethered unmanned aerial platforms, taking into account external active and reactive forces, as well as disturbing forces – random air flows, which can be significant in strength and variable in direction, which undoubtedly affects the stable position tethered platform. The use of the extended Kalman filter algorithm as an observer of the tethered flying platform state in mathematical modeling of the platform's flight makes it possible to take into account random disturbances of the atmosphere as a partially deterministic environment in order to reduce the position error of the aircraft during its control. To solve the problem, methods of classical mechanics, motion stability theory, optimal control, estimation theory, and parametric optimization were used. The results of mathematical modeling of a tethered flying platform – a tethered copter – flight are presented, taking into account random atmospheric disturbances. The results of computational experiments made it possible to establish that random atmospheric disturbances can have a significant impact on the position control of an aircraft.