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Coordinate Descent Optimization for Winged-UAV Design

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Abstract

In this paper, a powerful optimization framework is proposed to design highly efficient winged unmanned aerial vehicle (UAV) that is powered by electric motors. In the proposed approach, the design of key UAV parameters including both aerodynamic configurations, (e.g. wing span, sweep angle, chord, taper ratio, cruise speed and angle of attack) and the propulsion systems (e.g. propeller, motor and battery) are cast into an unified optimization problem, where the optimization objective is the design goal (e.g. flight range, endurance). Moreover, practical constraints are naturally incorporated into the design procedures as constraints of the optimization problem. These constraints may arise from the preliminary UAV shape and layout determined by industrial design, weight constraints, etc. The backend of the optimization based UAV design framework are highly accurate aerodynamic models and propulsion system models proposed in this paper and verified by actual experiment data. The optimization framework is inherently non-convex and involves both continuous variables (e.g. the aerodynamic configuration parameters) and discrete variables (e.g. propulsion system combinations). To solve this problem, a novel coordinate descent method is proposed. Trial designs show that the proposed method works rather efficiently, converging in a few iterations. And the returned solution is rather stable with different initial conditions. Finally, the entire approach is applied to design a quadrotor tail-sitter VTOL UAV. The designed UAV is validated by both CFD simulations and intensive real-world flight tests.

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References

  1. Kuchemann, D.: The aerodynamic design of aircraft. Progress in aeronautical sciences, 1965, 6, 271 (Pergamon, London) (1978)

  2. Niu, C.: Airframe Structural Design: Practical Design Information and Data on Aircraft Structures. Conmilit Press (1988)

  3. Oates, G.C.: Aircraft propulsion systems technology and design Aiaa (1989)

  4. Vatistas, G.H., Lin, S., Kwok, C.K.: Reverse flow radius in vortex chambers. AIAA J. 24(11), 1872, 1873 (1986). https://doi.org/10.2514/3.13046

    Article  Google Scholar 

  5. Goraj, Z., Cisowski, J., Frydrychewicz, A., Grendysa, W., Jonas, M.: Mini UAV design and optimization for long endurance mission. In: Proceedings of ICAS Congress (2008)

  6. Gu, H., Lyu, X., Li, Z., Shen, S., Zhang, F.: Development and experimental verification of a hybrid vertical take-off and landing (vtol) unmanned aerial vehicle (UAV). In: 2017 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 160–169. IEEE (2017)

  7. Martins, J.R., Lambe, A.B.: Multidisciplinary design optimization: a survey of architectures. AIAA J. 51 (9), 2049–2075 (2013)

    Article  Google Scholar 

  8. Ebrahimi, M., Farmani, M.R., Roshanian, J.: Multidisciplinary design of a small satellite launch vehicle using particle swarm optimization. Struct. Multidiscip. Optim. 44(6), 773–784 (2011)

    Article  Google Scholar 

  9. Hwang, J.T., Lee, D.Y., Cutler, J.W., Martins, J.R.: Large-scale multidisciplinary optimization of a small satellite’s design and operation. J. Spacecr. Rocket. 51(5), 1648–1663 (2014)

    Article  Google Scholar 

  10. Ashuri, T., Zaaijer, M.B., Martins, J.R., Van Bussel, G.J., Van Kuik, G.A.: Multidisciplinary design optimization of offshore wind turbines for minimum levelized cost of energy. Renew. Energy 68, 893–905 (2014)

    Article  Google Scholar 

  11. Zi, B., Ding, H., Cao, J., Zhu, Z., Kecskeméthy, A.: Integrated mechanism design and control for completely restrained hybrid-driven based cable parallel manipulators. J. Intell. Robot. Syst. 74(3-4), 643–661 (2014)

    Article  Google Scholar 

  12. Artoni, A.: A methodology for simulation-based, multiobjective gear design optimization. Mech. Mach. Theory 133, 95–111 (2019)

    Article  Google Scholar 

  13. Cramer, E.J., Dennis, Jr, J.E., Frank, P.D., Lewis, R.M., Shubin, G.R.: Problem formulation for multidisciplinary optimization. SIAM J. Optim. 4(4), 754–776 (1994)

    Article  MathSciNet  Google Scholar 

  14. Balling, R.J., Sobieszczanski-Sobieski, J.: Optimization of coupled systems-a critical overview of approaches. AIAA J. 34(1), 6–17 (1996)

    Article  Google Scholar 

  15. Braun, R., Gage, P., Kroo, I., Sobieski, I.: Implementation and performance issues in collaborative optimization. In: 6th Symposium on Multidisciplinary Analysis and Optimization, p. 4017 (1996)

  16. Manning, V.M.: Large-scale design of supersonic aircraft via collaborative optimization (1999)

  17. Dunning, P.D., Brampton, C.J., Kim, H.A.: Multidisciplinary level set topology optimization of the internal structure of an aircraft wing. In: 10th World Congress on Structural and Multidisciplinary Optimization, pp. 19–24 (2013)

  18. Raymer, D.: Enhancing Aircraft Conceptual Design Using Multidisciplinary Optimization. Ph.D. thesis, Institutionen för flygteknik (2002)

    Google Scholar 

  19. Leifsson, L., Ko, A., Mason, W.H., Schetz, J.A., Grossman, B., Haftka, R.T.: Multidisciplinary design optimization of blended-wing-body transport aircraft with distributed propulsion. Aerosp. Sci. Technol. 25 (1), 16–28 (2013)

    Article  Google Scholar 

  20. Alonso, J.J., Colonno, M.R.: Multidisciplinary optimization with applications to sonic-boom minimization. Annu. Rev. Fluid Mech. 44, 505–526 (2012)

    Article  MathSciNet  Google Scholar 

  21. Antoine, N.E., Kroo, I.M.: Framework for aircraft conceptual design and environmental performance studies. AIAA J. 43(10), 2100–2109 (2005)

    Article  Google Scholar 

  22. Ganguli, R., Rajagopal, S.: Multidisciplinary design optimization of an UAV wing using kriging based multi-objective genetic algorithm. In: 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 17th AIAA/ASME/AHS Adaptive Structures Conference 11th AIAA No, p. 2219 (2009)

  23. Batill, S.M., Stelmack, M.A., Yu, X.Q.: Multidisciplinary design optimization of an electric-powered unmanned air vehicle. Aircr. Des. 2(1), 1–18 (1999)

    Article  Google Scholar 

  24. Gu, H., Cai, X., Zhou, J., Li, Z., Shen, S., Zhang, F.: A coordinate descent method for multidisciplinary design optimization of electric-powered winged UAVs. In: 2018 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 1189–1198. IEEE (2018)

  25. Stengel, R.F.: Flight Dynamics. Princeton University Press (2015)

  26. Zhang, X., et al.: Aircraft Design Manual, vol. VI. Aerodynamic design China Aviation Publishing & Media (2002)

  27. Anderson, J.D.: Aircraft Performance and Design. McGraw-Hill Science/Engineering/Math (1999)

  28. Drela, M.: Xfoil: An analysis and design system for low Reynolds number airfoils. In: Low Reynolds Number Aerodynamics, pp. 1–12. Springer (1989)

  29. Gur, O., Mason, W.H., Schetz, J.A.: Full-configuration drag estimation. J. Aircr. 47(4), 1356–1367 (2010)

    Article  Google Scholar 

  30. Pennycuick, C.: Mechanics of flight. In: Avian Biology, vol. V, pp. 1–75. Elsevier (1975)

  31. Paterson, J., MacWilkinson, D., Blackerby, W.: A survey of drag prediction techniques applicable to subsonic and transonic aircraft design. AGARD Aerodyn. Drag 38, SEE N 74-14709 06–01 (1973)

    Google Scholar 

  32. Mason, W.: Boundary layer analysis methods. Aerodynamic Calculation Methods for Programmable Calculators & Personal Computers (1981)

  33. Shevell, R.S.: Fundamentals of flight (1989)

  34. Torenbeek, E.: Synthesis of Subsonic Airplane Design. Springer, Delft (1982)

    Book  Google Scholar 

  35. Blackwell, J.A. Jr.: Numerical method to calculate the induced drag or optimum loading for arbitrary non-planar aircraft (1976)

  36. Falkner, V.: The solution of lifting-plane problems by vortex-lattice theory. Ministry of Supply, Aeronautical Research Council (1947)

  37. Prandtl, L.: Tragflügeltheorie. I. Mitteilung. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse 1918, 451–477 (1918)

    Google Scholar 

  38. Finck, R., Hoak, D.: USAF stability and control DATCOM. Engineering Documents (1978)

  39. Lyu, X., Gu, H., Wang, Y., Li, Z., Shen, S., Zhang, F.: Design and implementation of a quadrotor tail-sitter vtol UAV. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), pp. 3924–3930. IEEE (2017)

  40. Zhang, F., Lyu, X., Wang, Y., Gu, H., Li, Z.: Modeling and flight control simulation of a quadrotor tailsitter vtol UAV. In: AIAA Modeling and Simulation Technologies Conference, p. 1561 (2017)

  41. Brandt, J., Selig, M.: Propeller performance data at low Reynolds numbers. In: 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, p. 1255 (2011)

  42. John, B.B., Robert, W.D., Gavin, K.A., Michael, S.S.: Apc propeller. http://m-selig.ae.illinois.edu/props/prop{DB}.html (1999)

  43. Traub, L.: Validation of endurance estimates for battery powered UAVs. Aeronaut. J. 117(1197), 1155–1166 (2013)

    Article  Google Scholar 

  44. Kannan, R., Monma, C.L.: On the computational complexity of integer programming problems. In: Optimization and Operations Research, pp. 161–172. Springer (1978)

  45. Powell, M.J.: A fast algorithm for nonlinearly constrained optimization calculations. In: Numerical Analysis, pp. 144–157. Springer (1978)

  46. Byrd, R.H., Gilbert, J.C., Nocedal, J.: A trust region method based on interior point techniques for nonlinear programming. Math. Program. 89(1), 149–185 (2000)

    Article  MathSciNet  Google Scholar 

  47. Wright, S.J.: Coordinate descent algorithms. Math. Program. 151(1), 3–34 (2015)

    Article  MathSciNet  Google Scholar 

  48. Grippo, L., Sciandrone, M.: On the convergence of the block nonlinear Gauss–Seidel method under convex constraints. Oper. Res. Lett. 26(3), 127–136 (2000)

    Article  MathSciNet  Google Scholar 

  49. Saeed, A.S., Younes, A.B., Islam, S., Dias, J., Seneviratne, L., Cai, G.: A review on the platform design, dynamic modeling and control of hybrid UAVs. In: 2015 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 806–815. IEEE (2015)

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Acknowledgments

Research supported by Hong Kong ITF Foundation (ITS/334/15FP).

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    Authors and Affiliations

    1. Electronic & Computer Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

      Haowei Gu, Ximin Lyu & Zexiang Li

    2. Mechanical Engineering, University of Hong Kong, HW7-18, Pokfulam, Hong Kong

      Fu Zhang

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    1. Haowei Gu
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    Correspondence to Fu Zhang.

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    Haowei Gu and Ximin Lyu contributed equally to this work.

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    Gu, H., Lyu, X., Li, Z. et al. Coordinate Descent Optimization for Winged-UAV Design. J Intell Robot Syst 97, 109–124 (2020). https://doi.org/10.1007/s10846-019-01020-2

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