A method for stabilization of drone flight controlled by autopilot with time delay

In this paper, the methods of the stability theory of differential equations with time delays are used in the study of an actual engineering problem of a drone (UAV) autonomous flight. We describe correct operation of autopilot for supply stability of desirable drone flight. There exists a noticeable delay in getting information about position and orientation of a drone to autopilot in the presence of vision-based navigation (visual 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]  Emilia Fridman,et al.  A positivity-based approach to delay-dependent stability of systems with large time-varying delays , 2016, Syst. Control. Lett..

[2]  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).

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

[4]  L. Berezansky,et al.  Nonoscillation Theory of Functional Differential Equations with Applications , 2012 .

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

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

[7]  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.

[8]  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.

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

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

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

[12]  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.

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

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

[15]  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..

[16]  A. Domoshnitsky.  Unboundedness of solutions and instability of differential equations of the second order with delayed argument , 2001, Differential and Integral Equations.