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Trajectory optimisation of six degree of freedom aircraft using differential flatness

Published online by Cambridge University Press:  15 November 2018

P. Elango  and
R. Mohan
P. Elango*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, India
R. Mohan
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, India
*
*[email protected]
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Abstract

The flatness of a six-degree-of-freedom (6DoF) aircraft model with conventional control surfaces – aileron, flap, rudder and elevator, along with thrust vectoring ability is established in this work. Trajectory optimisation of an aircraft can be cast as an inverse problem where the solution for control inputs that yield desired trajectories for certain states is sought. The solution to the inverse problems for certain systems is made tractable when they exhibit differential flatness. Flatness-based trajectory optimisation has a significant advantage over an equivalent collocation-based method in terms of computational efficiency and viability for real-time implementation. An application for the flatness of 6DoF aircraft is shown in the trajectory optimisation for dynamic soaring, and its connection with an equivalent 3DoF flatness-based implementation is also brought out. The results are compared with that from a collocation-based approach.

Keywords

Differential flatnessTrajectory optimisation6DoF aircraftDynamic soaring
Type
Research Article
Information
The Aeronautical Journal , Volume 122 , Issue 1257 , November 2018 , pp. 1788 - 1810
Copyright
© Royal Aeronautical Society 2018 

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References

1. Thomson, D. and Bradley, R. Inverse simulation as a tool for flight dynamics research principles and applications, Progress in Aerospace Sciences, 2006, 42, (3), pp 174–210.Google Scholar
2. Rouchon, P., Martin, P. and Murray, R.M. Flat systems, equivalence and trajectory generation, Tech. Rep. CDS 2003-008, California Institute of Technology, Pasadena, California, USA, 2003.Google Scholar
3. Fliess, M., Lévine, J., Martin, P. and Rouchon, P. Flatness and defect of non-linear systems: introductory theory and examples, International J of control, 1995, 61, (6), pp 1327–1361.Google Scholar
4. Nieuwstadt, M.J.V. and Murray, R.M. Real-time trajectory generation for differentially flat systems, Int J of Robust and Nonlinear Control, 1998, 8, (11), pp 995–1020.Google Scholar
5. Petit, N., Milam, M.B. and Murray, R.M. Inversion based constrained trajectory optimisation, IFAC Proceedings Volumes, 2001, 34, (6), pp 1211–1216.Google Scholar
6. Yakimenko, O.A. Direct method for rapid prototyping of near-optimal aircraft trajectories, J of Guidance, Control, and Dynamics, 2000, 23, (5), pp 865–875.Google Scholar
7. Deittert, M., Richards, A., Toomer, C.A. and Pipe, A. Engineless unmanned aerial vehicle propulsion by dynamic soaring, J of Guidance, Control, and Dynamics, 2009, 32, (5), pp 1446–1457.Google Scholar
8. Akhtar, N., Whidborne, J.F. and Cooke, A.K. Real-time optimal techniques for unmanned air vehicles fuel saving, Proceedings of the Institution of Mechanical Engineers, Part G: J of Aerospace Engineering, 2011, 226, (10), pp 1315–1328.Google Scholar
9. Boslough, M. Autonomous dynamic soaring platform for distributed mobile sensor arrays, Sandia National Laboratories, Sandia National Laboratories, Tech. Rep. SAND2002-1896, 2002.Google Scholar
10. Lawrance, N.R.J. and Sukkarieh, S. A guidance and control strategy for dynamic soaring with a gliding uav, In IEEE International Conference on Robotics and Automation, 2009. ICRA’09., 2009, pp 3632-3637.Google Scholar
11. Sukumar, P.P. and Selig, M.S. Dynamic soaring of sailplanes over open fields, J of Aircraft, 2013, 50, (5), pp 1420–1430.Google Scholar
12. Flanzer, T.C., Bunge, R.A. and Kroo, I.M. Efficient six degree of freedom aircraft trajectory optimisation with application to dynamic soaring, In 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSM, 2012, p 5622.Google Scholar
13. Liu, D.N., Hou, Z.X. and Gao, X.Z. Flight modeling and simulation for dynamic soaring with small unmanned air vehicles, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2017, 231, (4), pp 589–605.Google Scholar
14. Martin, P. Contribution à l’étude des systèmes différentiellement plats, PhD Thesis, École Nationale Supérieure des Mines de Paris, 1992.Google Scholar
15. Stevens, B.L., Lewis, F.L. and Johnson, E.N. Aircraft Control and Simulation: Dynamics, Controls Design, and Autonomous Systems, John Wiley & Sons, New Jersey, US, 2015.Google Scholar
16. Cazaurang, F., Bergeon, B. and Lavigne, L. Modeling of a longitudinal disturbed aircraft model by flatness approach, In Proceedings of AIAA Conference, Guidance, Navigation and Control, 2003, pp 5478-5482.Google Scholar
17. Hines, G.H. Nonlinear Three-Dimensional Trajectory Following: Simulation and Application, PhD Thesis, California Institute of Technology, 2008.Google Scholar
18. Cooke, J.M., Zyda, M.J., Pratt, D.R. and McGhee, R.B. Npsnet: flight simulation dynamic modeling using quaternions, Presence: Teleoperators & Virtual Environments, 1992, 1, (4), pp 404–420.Google Scholar
19. Berndt, J.S. Jsbsim: An open source flight dynamics model, in C++. In AIAA Modeling and Simulation Technologies Conference and Exhibit, 2004, p 4923.Google Scholar
20. Sequeira, C.J., Willis, D.J. and Peraire, J. Comparing aerodynamic models for numerical simulation of dynamics and control of aircraft, In 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2006, p 1254.Google Scholar
21. Bower, G.C. Boundary Layer Dynamic Soaring for Autonomous Aircraft: Design and Validation, PhD Thesis, Stanford University Stanford, 2011.Google Scholar
22. Drela, M. and Youngren, H. Athena vortex lattice 3.36 user primer, 2017.Google Scholar
23. Liu, D.N., Hou, Z.X., Guo, Z., Yang, X.X. and Gao, X.Z. Optimal patterns of dynamic soaring with a small unmanned aerial vehicle, Proceedings of the Institution of Mechanical Engineers, Part G: J of Aerospace Engineering, 2017, 231, (9), pp 1593–1608.Google Scholar
24. Sachs, G. and Bussotti, P. Application of optimal control theory to dynamic soaring of seabirds , Springer, Massachusetts, US, 2005.Google Scholar
25. Rigatos, G.G. Nonlinear Control and Filtering Using Differential Flatness Approaches: Applications to Electromechanical Systems, Springer, Switzerland, 2015.Google Scholar
26. Fahroo, F. and Ross, I.M. Direct trajectory optimisation by a Chebyshev pseudospectral method, J of Guidance, Control, and Dynamics, 2002, 25, (1), pp 160–166.Google Scholar