Autopilot to Maintain Movement of a Drone in a Vertical Plane at a Constant Height in the Presence of Vision-Based Navigation

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.

[1]  Oleg Kupervasser,et al.  A navigation filter for fusing DTM/correspondence updates , 2011, 2011 IEEE International Conference on Robotics and Biomimetics.

[2]  Ehud Rivlin,et al.  Pose and Motion from Omnidirectional Optical Flow and a Digital Terrain Map , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[3]  N. Azbelev,et al.  Stability of Differential Equations with Aftereffect , 2002 .

[4]  Alexander Domoshnitsky,et al.  W-transform for exponential stability of second order delay differential equations without damping terms , 2017, Journal of inequalities and applications.

[5]  James U. Korein,et al.  Robotics , 2018, IBM Syst. J..

[6]  Philip David,et al.  SoftPOSIT: Simultaneous Pose and Correspondence Determination , 2002, ECCV.

[7]  Igor Sazonov,et al.  Precision improvement of MEMS gyros for indoor mobile robots with horizontal motion inspired by methods of TRIZ , 2014, The 9th IEEE International Conference on Nano/Micro Engineered and Molecular Systems (NEMS).

[8]  Oleg Kupervasser,et al.  Robust positioning of drones for land use monitoring in strong terrain relief using vision-based navigation , 2018, ArXiv.

[9]  Marcos A. Rodrigues,et al.  Statistical image analysis for pose estimation without point correspondences , 2001, Pattern Recognit. Lett..

[10]  Oleg Kupervasser,et al.  Correction of inertial navigation system's errors by the help of video-based navigator based on Digital Terrarium Map , 2013, ArXiv.

[11]  Ehud Rivlin,et al.  Pose and motion recovery from feature correspondences and a digital terrain map , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  R. Agarwal,et al.  On exponential stability of second order delay differential equations , 2015 .

[13]  Emilia Fridman,et al.  A positivity-based approach to delay-dependent stability of systems with large time-varying delays , 2016, Syst. Control. Lett..

[14]  Ehud Rivlin,et al.  Error analysis for a navigation algorithm based on optical-flow and a digital terrain map , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[15]  Alexander Domoshnitsky.  Nonoscillation, maximum principles, and exponential stability of second order delay differential equations without damping term , 2014 .