1 Autopilot to maintain movement of a drone in a vertical plane at a constant height in the presence of vision-based navigation Corresponding Author's E-mail: olegkup@yahoo.com Shiran Avasker 1 , Alexander Domoshnitsky 1 , Max Kogan 1 , Oleg Kupervaser 1,2 , Hennadii Kutomanov 1 , Yonatan Rofsov 1 , Irina Volinsky 1 , Roman Yavich 1 1 Department of Mathematics, Ariel University, Israel; 2 TRANSIST VIDEO LLC, Skolkovo, Russia Abstract The main finding this paper is nontrivial and implicit possibility to use well developed mathematical theory of differential equations with delays for solving actual engineering problem of a drone autonomous flight. In this paper we describe correct operation of autopilot for supply correct drone flight. There exists noticeable delay in getting information about position and orientation of a drone to autopilot in the presence of vision-based navigation. In spite of this fact, we demonstrate that it is possible to provide stable flight at a constant height in a vertical plane. We describe how to form relevant controlling signal for autopilot in the case of the navigation information delay and provide control parameters for particular case of flight. Keywords—visual navigation; drones;UAV; autopilot; prototype; vision-based navigation; delay 1. Introduction The main finding this paper is possibility to use well developed mathematical theory of differential equations with delays for solving actual engineering problem of a drone autonomous flight. It is a nontrivial problem, because it cannot be made directly and explicitly. Indeed, we need to make some nontrivial mathematical transform of the physical differential equations and to find nontrivial solution for relevant parameters of the differential equations if we want to use known methods of the mathematical theory of differential equations with delays. This paper is engineering application of stability theory for differential equations with delays described in [1- 5]. In this paper we describe correct operation of autopilot for supply desirable drone flight (movement of a drone in a vertical plane at a constant height). For the finding drone flight parameters was used vision-based navigation [6-15]. For realization vision-based navigation was developed the computer program “Video-navigation of UAV over relief” [6]. This program was tested in Zhejiang Province in east China near the capital Hangzhou using Google Earth data [12]. There always exists noticeable delay in getting information about position and orientation of a drone to autopilot for vision-based navigation because of computer processing image’s big data. In spite of this fact, we demonstrate that it is possible to provide stable flight at a constant height in a vertical plane. We want to describe how to form relevant controlling signal for autopilot in the case of the navigation information delay. For this purpose we use theory of stability for differential equations with delays described in [1-5]. We plan to use the autopilot described in the paper for controlling flight parameters found from vision-based navigation.