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Low thrust inclined circular trajectories for airplanes

  • Labonte, Gilles (Department of Mathematics and Computer Science and Department of Electrical Engineering and Computer Engineering, Royal Military College of Canada)
  • 투고 : 2016.06.17
  • 심사 : 2016.07.08
  • 발행 : 2017.05.25

초록

Automatic trajectory re-planning is an integral part of unmanned aerial vehicle mission planning. In order to be able to perform this task, it is necessary to dispose of formulas or tables to assess the flyability of various typical flight segments. Notwithstanding their importance, there exist such data only for some particularly simple segments such as rectilinear and circular sub-trajectories. This article presents an analysis of a new, very efficient, way for an airplane to fly on an inclined circular trajectory. When it flies this way, the only thrust required is that which cancels the drag. It is shown that, then, much more inclined trajectories are possible than when they fly at constant speed. The corresponding equations of motion are solved exactly for the position, the speed, the load factor, the bank angle, the lift coefficient and the thrust and power required for the motion. The results obtained apply to both types of airplanes: those with internal combustion engines and propellers, and those with jet engines. Conditions on the trajectory parameters are derived, which guarantee its flyability according to the dynamical properties of a given airplane. An analytical procedure is described that ensures that all these conditions are satisfied, and which can serve for producing tables from which the trajectory flyability can be read. Sample calculations are shown for the Cessna 182, a Silver Fox like unmanned aerial vehicle, and an F-16 jet airplane.

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참고문헌

  1. Aeronautics Learning Laboratory for Science Technology and Research (ALLSTAR) of the Florida International University, (2011), Propeller Aircraft Performance and The Bootstrap Approach, Miami, FL, USA, http://www.allstar.fiu.edu/aero/BA-Background.htm.
  2. Airliners.net (2015), Santa Monica, CA, USA, http://www.airliners.net/aircraft-data/stats.main?id=145
  3. Ambrosino, G., Ariola, M., Ciniglio, U., Corraro, F., De Lellis, E. and Pironti, A. (2009), "Path generation and tracking in 3-D for UAVs", IEEE Tran. Control Syst. Technol., 17(4), 980-988. https://doi.org/10.1109/TCST.2009.2014359
  4. Anderson, E.P. (2002), "Extremal control and unmanned air vehicle trajectory generation", MSc Dissertation, Brigham Young University, Utah, USA.
  5. Anderson, E.P., Beard, R.W. and McLain, T.W. (2005),"Real-Time dynamic trajectory smoothing for unmanned air vehicles", IEEE Tran. Control Syst. Technol., 13(3), 471-477. https://doi.org/10.1109/TCST.2004.839555
  6. Anderson, J.D. Jr. (2000), Introduction to Flight, Fourth Edition, McGraw-Hill Series in Aeronautical and Aerospace Engineering, Toronto, Ontario, Canada.
  7. Babaei, A.R. and Mortazavi, M. (2010), "Three-dimensional curvature-constrained trajectory planning based on in-flight waypoints", J. Aircraft, 47(4), 1391-1398. https://doi.org/10.2514/1.47711
  8. Bottasso,C.L., Leonello, D. and Savini, B. (2008) "Path planning for autonomous vehicles by trajectory smoothing using motion primitives", IEEE Tran. Control Syst. Technol., 16(6), 1152-1168. https://doi.org/10.1109/TCST.2008.917870
  9. Cavcar, M. (2004), Propeller, Anadolu University, School of Civil Aviation, Eskisehir, Turkey. http://home.anadolu.edu.tr/-mcavcar/common/Propeller.pdf
  10. Chandler, P., Rasmussen, S. and Pachter, M. (2000), "UAV cooperative path planning", Proceedings of the AIAA Guidance, Navigation, and Control Conference, Denver, Colorado, USA, August.
  11. Chitsaz, H. and LaValle, S.M. (2007), "Time-optimal paths for a Dubins airplane", Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, December.
  12. Cowley, W.L. and Levy, H. (1920), Aeronautics Theory and Experiment, 2nd Edition, Edward Arnold, London, England.
  13. Currawong Engineering (2016), UAV Engines, Kingston, Australia. http://www.currawongeng.com/products/uav_engines/
  14. Dubins, L.E. (1957), "On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents", Am. J. Math., 79, 497-516. https://doi.org/10.2307/2372560
  15. Faculty of Engineering, University of Porto (2013), SilverFox Block B-3 Specifications, Porto, Portugal. http://whale.fe.up.pt/asasf/images/f/f8/UAV_SF_Specs.pdf
  16. Filippone, A. (2000), "Data and performances of selected aircraft and rotorcraft", Prog. Aerospace Sci., 36, 629-654. https://doi.org/10.1016/S0376-0421(00)00011-7
  17. Gradshteyn, I.S. and Ryzhik, I.M. (1965), Table of Integrals Series and Products, Academic Press, New York, NY, USA.
  18. Hota, S. and Ghose, D. (2010), "Optimal geometrical path in 3D with curvature constraint", Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan, October.
  19. Hwangbo, M., Kuffner, J. and Kanade, T. (2007), "Efficient two-phase 3D motion planning for small fixedwing UAVs", Proceedings of the IEEE International Conference on Robotics and Automation, Rome, Italy, April.
  20. Jeyaraman, S., Tsourdos, A., Zbikowski, R. and White, B. (2005), "Formal techniques for the modelling and validation of a co-operating UAV team that uses Dubins set for path planning", Proceedings of the 2005 American Control Conference, Portland, OR, USA, June.
  21. Jia, D. and Vagners, J. (2004), "Parallel evolutionary algorithms for UAV path planning", Proceedings of the AIAA 1st Intelligent Systems Technical Conference, Chicago, IL, September.
  22. Judd, K.B. (2001), "Trajectory planning strategies for unmanned air vehicles", MSc Dissertation, Brigham Young University, Utah, USA.
  23. Jun, M. and D'Andrea, R (2003), Path Planning for Unmanned Aerial Vehicles in Uncertain and Adversarial Environments, Chapter 6, "Cooperative control: models, applications and algorithms", Eds. Butenko, S., Murphey, R. and Pardalos, P., Kluwer Academic Publishers, Norwell, MA, USA.
  24. Korkan, K.D., Gregorek, G.M. and Mikkelson, D.C. (1980), "A theoretical and experimental investigation of propeller performance methodologies", Proceedings of the AIAA-80-1240, AIAA / SAE / ASME 16th Joint Propulsion Conference, Hartford, CT, USA, June.
  25. Labonte, G. (2011), "Formulas for the fuel of climbing propeller driven planes", Aircraft Eng. Aerosp. Tech., 84(1), 23-36. https://doi.org/10.1108/00022661211194951
  26. Labonte, G. (2015a), "Simple formulas for the fuel of climbing propeller driven airplanes", Adv. Aircraft Spacecraft Sci., 2(4), 367-389. https://doi.org/10.12989/aas.2015.2.4.367
  27. Labonte, G. (2015b), "Airplanes at constant speeds on inclined circular trajectories", Adv. Aircraft Spacecraft Sci., 3(4), 399-425. https://doi.org/10.12989/AAS.2016.3.4.399
  28. Li, X., Xie, J., Cai, M., Xie, M. and Wang, Z. (2009), "Path planning for UAV based on improved A* algorithm", Proceedings of the 9th International Conference on Electronic Measurement & Instruments, ICEMI '09, Beijing, China, August.
  29. Lin, Y. and Saripalli, S. (2014), "Path planning using 3D Dubins curve for unmanned aerial vehicles", Proceedings of the 2014 International Conference on Unmanned Aircraft Systems (ICUAS), Orlando, FL, USA, May.
  30. Lockheed-Martin (2015), F-16 Specifications, Bethesda, MD, USA, http://lockheedmartin.com/us/products/f16/F-16Specifications.html
  31. Lugo-Cardenas, I., Flores, G., Salazar, S. and Lozano, R. (2014), "Dubins path generation for a fixed wing UAV", Proceedings of the 2014 International Conference on Unmanned Aircraft Systems (ICUAS), Orlando, FL, USA, May.
  32. Mair, W.A. and Birdsall, D.L. (1992), Aircraft Performance, Cambridge Aerospace Series 5, Cambridge University Press, Cambridge, GB.
  33. Marion, J.B. (1970), Classical Dynamics of Particles and Systems, 2nd Edition, Academic Press, New York, NY, USA.
  34. McIver, J. (2003), Cessna Skyhawk II /100, Performance Assessment, Temporal Images, Melbourne, Australia. http://www.temporal.com.au/c172.pdf
  35. Phillips, W.F. (2004), Mechanics of Flight, John Wiley & Sons, Inc., Hoboken, New Jersey, USA
  36. Rathbun, D., Kragelund, S., Pongpunwattan, A. and Capozzi, B. (2002), "An evolution based path planning algorithm for autonomous motion of a UAV through uncertain environments", Proceedings of the 21st Digital Avionics Systems Conference, 8D2-1-8D2-12, Irvine, CA, USA, October.
  37. Roud, O. and Bruckert D. (2006), Cessna 182 Training Manual, Red Sky Ventures and Memel CATS, Second Edition 2011, Windhoek, Namibia.
  38. Sadraey, M. (2009), Aircraft Performance Analysis, VDM Verlag Dr. Muller, Saarbrucken, Germany.
  39. Shanmugavel, M., Tsourdos, A. and White, B.A. (2010), "Collision avoidance and path planning of multiple UAVs using flyable paths in 3D", Proceedings of the 15th International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland, August.
  40. Singh, S. and Padhi, R. (2009), "Automatic path planning and control design for autonomous landing of UAVs using dynamic inversion", Proceedings of the 2009 American Control Conference, St. Louis, MO, USA, June.
  41. Stengel, R.F. (2004), Flight Dynamics, Princeton University Press, Princeton, NJ, USA.
  42. Torroella, J.C. (2004) "Long range evolution-based path planning for UAVs through realistic weather environments", MSc Dissertation, University of Washington, Washington, USA.
  43. Von Mises, R. (1945), Theory of Flight, Dover Publications Inc., New York, NY, USA.
  44. Wang Zhong and Li Yan (2014), "A target visiting path planning algorithm for the fixed-wing UAV in obstacle environment", Proceedings of the 2014 IEEE Chineese Guidance, Navigation and Control Conference (CGNCC), Yantai, China, August.
  45. Yang, K. and Sukkarieh, S. (2010), "An analytical continuous-curvature path-smoothing algorithm", IEEE Tran. Robot., 26(3), 561-568. https://doi.org/10.1109/TRO.2010.2042990
  46. Zheng, C., Ding, M. and Zhou, C. (2003), "Real-Time route planning for unmanned air vehicle with an evolutionary algorithm", Int. J. Patt. Recog. Artif. Intel., 17(1), 63-81. https://doi.org/10.1142/S021800140300223X

피인용 문헌

  1. Recent advances in unmanned aerial vehicles real-time trajectory planning vol.7, pp.4, 2017, https://doi.org/10.1139/juvs-2017-0004
  2. Point de référence pour la planification de trajectoires d’UAV à voilure fixe vol.9, pp.1, 2021, https://doi.org/10.1139/juvs-2019-0022