V.Е. Pavlovsky - Dr. Sc. (Phys.-Math.), Professor, Chief Research Scientist, Keldysh Institute of Applied Mathematics of RAS, Moscow E-mail: vlpavl@mail.ru A.V. Savitskiy - Post-raduate Student, Lomonosov Moscow State University E-mail: as@ttorr.ru

This article is about a solution of the inverse problem of dynamics for an unmanned aerial vehicle quadrocopter. This article is based on the the system of differential equations describing the motion of the robot which was published previously. The rotor-flying robots are systems with deficit control actions. They have 6 degrees of freedom and no more than 4 degrees of control. Therefore, in the configuration space not any trajectory is achievable. Taking into account the limited control actions, we got the limits limits on the possible acceleration of the system. In this work we studied analytically such aerobatics as «dead loop», slide, flying in a vertical spiral and others. Besides a numerical si-mulation algorithm was described. Using this algorithm we obtained the graphics of quadrocopters motion and control actions for each trajectory. It is shown that using the solution of inverse dynamics problem we can find the control for complex trajectory, including aero-batics.

 

1. Pavlovskijj V.E., Savickijj A.V. Nejjrosetevojj algoritm upravlenija kvadrokopterom na tipovykh traektorijakh // Nelinejjnyjj mir. 2015. № 6. S. 47-51. 
2. Belinskaja JU.S., CHetverikov V.N. Upravlenie chetyrekhvintovym vertoletom // Nauka i obrazovanie. 2012. № 5. S. 157-171.
3. Kanatnikov A.N., Akopjan K.R. Upravlenie ploskim dvizheniem kvadrokomptera // Matematika i matematicheskoe modelirovanie. MGTU im. N.EH. Baumana. EHlektronnyjj zhurnal. 2015. № 2. S. 23-36.
4. Kanatnikov A.N., Krishhenko A.P., Tkachev S.B. Dopustimye prostranstvennye traektorii bespilotnogo letatelnogo apparata v vertikalnojj ploskosti // Nauka i obrazovanie. 2012. № 3. S. 1-15.
5. Fantoni I., Lozano R. Nelinejjnoe upravlenie mekhanicheskimi sistemami s deficitom upravljajushhikh vozdejjstvijj. M.-Izhevsk: OOO «Kompjuternaja dinamika». 2012. 312 s.
6. Bresciani T. Modelling, Identification and Control of a Quadrotor Helicopter, Department of Automatic Control. Lund University. 2008.
7. Dzul P. A., Lozano R. Real-time stabilization and tracking of a four-rotor mini rotorcraft // IEEE Transaction on Control System Technology. July 2004. V. 12. № 4. P. 510-516.
8. Pounds P., Mahony R., Corke P. Modelling and Control of a Quad-Rotor Robot. Canberra: Australian National University. 2008. 10 p.
9. Dierks T., Jagannathan S. Neural Network Control and Wireless Sensor Network-based Localization of Quadrotor UAV Formations // Aerial Vehicles. 2009. P. 601-620.
10. Munoz R.S.M., Rossi C., Cruz A.B. Modelling and Identification of Flight Dynamics in Mini-Helicopters Using Neural Networks // Aerial Vehicles. 2009. P. 287-312.
11. Lavi B. An Adaptive Neuro PID for Controlling the Altitude of quadcopter Robot // International Conference on Methods and Models in Automation and Robotics. Poland. 2014. V. 18. P. 662-665.