# V P Kharchenko, S I Ilnytska - Analysis of unmanned aerial vehicle kinematic equations integration algorithms - страница 2

Below (fig. 3) the result of roll angle determination under conditions of high UAV dynamics is represented.

It was decided to choose here the result for roll angle since the longitudinal axis has the lowest inertia and roll calculation error according the given algorithm is the highest.

For example, at conditions of normal UAV dynamics the standard deviation (STD) of roll angle determination is 0,0101°, pitch and yaw -0,0046° and 0,0077° correspondently, and at conditions of high UAV dynamics STD of roll angle determination is 0,0635°, pitch and yaw -0,0123° and 0,0156° correspondently.

a

t, s

b

Fig. 3. Roll angle: reference values (a) and calculation error (b) at conditions of high UAV dynamics

For UAV translational motions integration algorithm verification and computational errors determination the following steps have been performed. In MATLAB circle motions at XY-plane were simulated to get the reference data of accelerations, velocities and positions.

Therefore, the results of comparison of reference values of velocities and position coordinates with the defined with the help of equations (8)-(9) are represented at fig. 4.

It is seen from figure that velocity errors are bounded in time and position errors are not.

Besides, sampling frequency influence at navigation parameters definition has been investigated. Both algorithms, for rotational and translational motions, have been checked at frequencies from 20 to 300 Hz at conditions of normal and high UAV dynamics.

The results for rotational motions are represented at fig. 5, and for translational motions - at fig. 6.

From fig. 5, 6 it's seen that the revealed dependencies are of hyperbolic nature.

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And frequency increasing up to 100 Hz greatly improves navigation parameters determination accuracy, but the further frequency increasing doesn't influence essentially.

Conclusion

At work the analysis of UAV kinematic equations integration algorithms has been performed.

The software in MATLAB has been developed based on proposed algorithms. It has been verified at conditions of normal and high UAV dynamics.

As a result the algorithms efficiency has been approved, since the acceptable values of STDs has been got for all cases.

Also sampling frequency influence at navigation parameters definition has been investigated.

As a result the dependence of hyperbolic nature has been revealed. In further investigations it would be interesting to study this dependence.

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Fig. 4. Velocity (a) and position (b) calculation errors

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Fig. 5. Dependence of Euler angles definition errors STD on sampling frequency: a - normal dynamics; b - high dynamics

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Fig. 6. Dependence of Velocity (a) and Position (b) definition errors STD on sampling frequency

References

1. Конин В.В. Системы спутниковой радионавигации / В.В. Конин, В.П. Харченко. - К.: Холтех, 2010. - 520 с.

2. Grewall M.S. Global Positioning Systems, Inertial Navigation, and Integration / M.S. Grewall, L.P. Weill, A.P. Andrews. -A John Wiley & Sons, Inc. Publ., New York, Chichester, Brisbane, Singapore, Toronto,

2001. - 392 p.

3. Siouris George M. Aerospace Avionics Systems: a modern synthesis / George M. Siouris. - Academic Press, Inc., 2007. - 466 p.

4. Bennett M. Development of Technologies for Low-cost Oceanographic Unmanned Aeronautical Vehicles: Doct. of Engineer. thesis / M. Bennett. - University of Southampton, USA, 2009. - 218 p.

5. Coopmans C. Design and implementation of sensing and estimation software in AGIENAV, a small UAV navigation platform / C. Coopmans, H. Chao, Y. Chen // Proceedings of the ASME IDETC/CIE 2009. - 2009. - P. 2- 8.

6. Yang Y. Tightly Coupled MEMS INS/GPS Integration with INS Aided Receiver Tracking Loops: PhD thesis / Y. Yang. - Department of Geomatics Engineering. - University of Calgary, Canada, 2008. - 205 p.

7. Larin V.B. Attitude-determination problems for a rigid body / V.B. Larin // Int. App. Mechanics. - 2001. - 37, № 7. - P. 870-898.

8. Shin E.H. Estimation techniques for low-cost inertical navigation: PhD thesis / E.H Shin. - Department of Geomatics Engineering. - University of Calgary, Canada, 2005. - 206 p.

9. Бранец В.Н. Применение кватернионов в задаче ориентации твёрдого тела / В.Н. Бранец, И.П. Шмыглевский. - М.: Наука, 1973. - 320 с.

The editors received the article on 09 June 2010.