In this article the unmanned aerial vehicle of the tricopter type is described, the scheme of constructing its mathematical model as a controlled dynamic object using the controls installed on the device, which is based on four basic models of behavior, is demonstrated. The interest in such devices is caused by the fact that, in comparison with devices of the whole class of multi-rotor UAVs, the use of tricopters is often the most reasonable due to their compactness, good maneuverability (especially in the angles of pitch and yaw), and good field repairability. In order to further develop the prototype of the UAV of the discussed type, which will be able to perform all the tasks assigned to it, such as aerial survey, exploration of the territory, interception of other drones, the paper provides a rather detailed description of the process of constructing a mathematical model of object dynamics in space. The constructed mathematical model is described by a system of ordinary nonlinear differential equations of the 12th order and can be used to investigate the behavior of the tricopter depending on possible changes in its design, optimize the parameters of the device during its design, and formulate sufficiently flexible and effective laws for automatic control.