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doi: 10.3934/jimo.2020180
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Energy management method for an unpowered landing

Xiaoxiao Li , Yingjing Shi , , Rui Li and  Shida Cao

School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

* Corresponding author: Yingjing Shi (shiyingjing@uestc.edu.cn)

Received  June 2020 Revised  September 2020 Early access December 2020

Fund Project: This work is supported in part by the National Natural Science Foundation of China under grant (No. 61973055), the Fundamental Research Funds for the Central Universities (No. ZYGX2019J062) and a grant from the applied basic research programs of Sichuan province (No. 2019YJ0206).

The unpowered landing of unmanned aerial vehicle (UAV) is a critical stage, which affects the safety of flight. To solve the problem of the unpowered landing of UAV, an energy management scheme is proposed. After the cruise is over, the aircraft shuts down the engine and begins to land. When the aircraft is in the high altitude, the dynamic pressure is too large, and it is difficult to open the speed brake. When the aircraft is in the low altitude, it is close to the runway. The method of S-turn may make the aircraft veer off the runway and may be unable to land. So two different schemes of high altitude and low altitude are designed to control energy. In the high altitude, when the energy is too high, it takes the S-turn scheme to consume excess energy. At the same time, the availability and reasonability of the S-turn scheme is demonstrated. In the low altitude, the open angle of speed brake is controlled to adjust the energy consumption. Finally, the simulation results are given to illustrate the availability of energy management.

Keywords: unpowered landing, energy management, S-turn, speed brake, UAV.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Xiaoxiao Li, Yingjing Shi, Rui Li, Shida Cao. Energy management method for an unpowered landing. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020180
References:
[1]

V. Artale, C. L. R. Milazzo and C. Orlando, Comparison of GA and PSO approaches for the direct and LQR tuning of a multirotor PD controller, Journal of Industrial and Management Optimization, 13 (2017), 2067-2091.  doi: 10.3934/jimo.2017032.  Google Scholar

[2]

A. R. Babaei and M. Mortazavi, Three-dimensional curvature-constrained trajectory planning based on in-flight waypoints, Journal of Aircraft, 47 (2010), 1391-1398.  doi: 10.2514/1.47711.  Google Scholar

[3]

J. Benasher and D. K. Maya, Pseudo-spectral-method based optimal glide in the event of engine cut-off, in Navigation, and Control Conference, (2011), Tel-Aviv and Haifa, Israel, 1201–1218. doi: 10.2514/6.2011-6596.  Google Scholar

[4]

P. Eng, L. Mejias and X. Liu, Automating human thought processes for a uav forced landing, Journal of Intelligent and Robotic Systems, 57 (2010), 329-349.  doi: 10.1007/978-90-481-8764-5_17.  Google Scholar

[5]

D. L. Fitzgerald, R. A. Walker and D. A. Campbell, A vision based forced landing site selection system for an autonomous UAV, in 2005 International Conference on Intelligent Sensors, Sensor Networks and Information Processing, (2005), Melbourne, Australia, 397–402. Google Scholar

[6]

R. Frezza and C. Altafini, Autonomous landing by computer vision: An application of path following in SE, in Proceedings of the 39th IEEE Conference on Decision and Control, (2000), Sydney, NSW, Australia, 2527–2532. doi: 10.1109/CDC.2000.914183.  Google Scholar

[7]

R. Ghanem and B. Zireg, Numerical solution of bilateral obstacle optimal control problem, where the controls and the obstacles coincide, Numerical Algebra, Control and Optimization, 10 (2020), 275-300.   Google Scholar

[8]

D. Gu and D. W. Zhang, Parametric control to second-order linear time-varying systems based on dynamic compensator and multi-objective optimization, Applied Mathematics and Computation, 365 (2020), 124681, 25pp. doi: 10.1016/j.amc.2019.124681.  Google Scholar

[9]

D. Gu and D. W. Zhang, A parametric method to design dynamic compensator for high-order quasi-linear systems, Nonlinear Dynamics, 100 (2020), 1379-1400.  doi: 10.1007/s11071-020-05555-0.  Google Scholar

[10]

X. Guo, S. Denman and C. Fookes, et al., Automatic UAV forced landing site detection using machine learning, in 2014 International Conference on Digital Image Computing: Techniques and Applications (DICTA), (2014), Wollongong, NSW, Australia, 1–7. doi: 10.1109/DICTA.2014.7008097.  Google Scholar

[11]

K. R. Horneman and C. A. Kluever, Terminal area energy management trajectory planning for an unpowered reusable launch vehicle, in Collection of Technical Papers - AIAA Atmospheric Flight Mechanics Conference, (2004), Providence, RI, United States, 1103–1120. doi: 10.2514/6.2004-5183.  Google Scholar

[12]

D. Jung and P. Tsiotras, On-line path generation for unmanned aerial vehicles using B-spline path templates, Journal of Guidance, 36 (2013), 1642-1653.  doi: 10.2514/1.60780.  Google Scholar

[13]

R. Li and Y. J. Shi, The fuel optimal control problem of a hypersonic aircraft with periodic cruising mode, J Mathematical and Computer Modelling, 55 (2012), 2141-2150.  doi: 10.1016/j.mcm.2011.12.052.  Google Scholar

[14]

B. Li, X. Guo, X. Zeng, S. Dian and M. Guo, An optimal PID tuning method for a single link manipulator based on the control parametrization technique, Discrete and Continuous Dynamical Systems Series S, 13 (2020), 1813-1823.  doi: 10.3934/dcdss.2020107.  Google Scholar

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R. Li, Y. J. Shi and K. L. Teo, Coordination arrival control for multi-agent systems, International Journal of Robust and Nonlinear Control, 26 (2016), 1456-1474.  doi: 10.1002/rnc.3359.  Google Scholar

[16]

L. Mejias and D. L. Fitzgerald, A multi-layered approach for site detection in UAS emergency landing scenarios using geometry-based image segmentation, in 2013 International Conference on Unmanned Aircraft Systems (ICUAS), (2013), Atlanta, GA, USA, 366–372. doi: 10.1109/ICUAS.2013.6564710.  Google Scholar

[17]

T. E. Moore, Space shuttle entry terminal area energy management, Houston, TX, United States [Online]. Available: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920010688.pdf Google Scholar

[18]

H. Niu, Z. J. Feng, Q. J. Xiao and Y. J. Zhang, A PID control method based on optimal control strategy, Numerical Algebra, Control and Optimization, (2020). Google Scholar

[19]

M. Ohno, Y. Yamaguchi and T. Hata, Robust flight control law design for an automatic landing flight experiment, Control Engineering Practice, 7 (1999), 1143-1151.   Google Scholar

[20]

D. Orfanus, E. D. Freitas and F. Eliassen, Self-organization as a supporting paradigm for military UAV relay networks, IEEE Communications Letters, 20 (2016), 804-807.  doi: 10.1109/LCOMM.2016.2524405.  Google Scholar

[21]

R. K. Rangel, C. A. D. Oliveira and K. H. Kienitz, Development of a multipurpose tactical surveillance system using UAV's, in 2014 IEEE Aerospace Conference, (2014), Big Sky, MT, USA, 1–9. doi: 10.1109/AERO.2014.6836300.  Google Scholar

[22]

S. D. Ridder and E. Mooij, Terminal area trajectory planning using the energy-tube concept for reusable launch vehicles, Acta Astronautica, 68 (2011), 915-930.  doi: 10.1016/j.actaastro.2010.08.032.  Google Scholar

[23]

S. D. Ridder and E. Mooij, Optimal longitudinal trajectories for reusable space vehicles in the terminal area, Journal of Spacecraft and Rockets, 48 (2011), 642-653.  doi: 10.2514/1.51083.  Google Scholar

[24]

S. D. Ridder and E. Mooij, Terminal area trajectory planning using the energy-tube concept for reusable launch, Acta Astronautica, 68 (2011), 915-930.  doi: 10.1016/j.actaastro.2010.08.032.  Google Scholar

[25]

M. Senpheng and M. Ruchanurucks, Automatic landing assistant system based on stripe lines on runway using computer vision, in 2015 International Conference on Science and Technology (TICST), (2015), Pathum Thani, Thailand, 35–39. doi: 10.1109/TICST.2015.7369336.  Google Scholar

[26]

I. Shapira and J. Ben-Asher, Range maximization for emergency landing after engine cut-off, Journal of Guidance, 42 (2005), 1296-1306.   Google Scholar

[27]

Y. F. Shen, Z. Rahman and D. Krusienski, A vision-based automatic safe landing-site detection system, IEEE Transactions on Aerospace and Electronic Systems, 49 (2013), 294-311.   Google Scholar

[28]

Y. J. Shi, R. Li and K. L. Teo, Design of a band-stop filter for a space shuttle vehicle, IEEE Transactions on Circuits and Systems-II: Express Briefs, 62 (2015), 1174-1178.  doi: 10.1109/TCSII.2015.2468922.  Google Scholar

[29]

Y. J. Shi, R. Li and H. L. Xu, Control augmentation design of UAVs based on deviation modification of aerodynamic focus, Journal of Industrial and Management Optimization, 11 (2015), 231-240.  doi: 10.3934/jimo.2015.11.231.  Google Scholar

[30]

D. G. Ward, J. F. Monaco and J. D. Schierman, Reconfigurable control for VTOL UAV shipboard landing, in Guidance, Navigation, and Control Conference and Exhibit, Portland, OR, United States, (1999), 499–509. doi: 10.2514/6.1999-4045.  Google Scholar

[31]

F. Yang, K. L. Teo, R. Loxton, V. Rehbock, B. Li, C. Yu and L. Jennings, VISUAL MISER: An efficient user-friendly visual program for solving optimal control problems, Journal of Industrial and Management Optimization, 12 (2016), 781-810.  doi: 10.3934/jimo.2016.12.781.  Google Scholar

[32]

J. F. Zhang and C. J. Jia, Automatic landing controller design and simulation of flying-wing unmanned aerial vehicle, in Proceedings of 2013 2nd International Conference on Measurement, Information and Control, 2 (2013), Harbin, China, 893–896. doi: 10.1109/MIC.2013.6758104.  Google Scholar

[33]

M. Zhou, J. Zhou and J. G. Guo, Terminal area energy management trajectory planning for an unpowered reusable launch vehicle with gliding limitations, Applied Mechanics and Materials, 446 (2014), 611-615.  doi: 10.4028/www.scientific.net/AMM.446-447.611.  Google Scholar

show all references

References:
[1]

V. Artale, C. L. R. Milazzo and C. Orlando, Comparison of GA and PSO approaches for the direct and LQR tuning of a multirotor PD controller, Journal of Industrial and Management Optimization, 13 (2017), 2067-2091.  doi: 10.3934/jimo.2017032.  Google Scholar

[2]

A. R. Babaei and M. Mortazavi, Three-dimensional curvature-constrained trajectory planning based on in-flight waypoints, Journal of Aircraft, 47 (2010), 1391-1398.  doi: 10.2514/1.47711.  Google Scholar

[3]

J. Benasher and D. K. Maya, Pseudo-spectral-method based optimal glide in the event of engine cut-off, in Navigation, and Control Conference, (2011), Tel-Aviv and Haifa, Israel, 1201–1218. doi: 10.2514/6.2011-6596.  Google Scholar

[4]

P. Eng, L. Mejias and X. Liu, Automating human thought processes for a uav forced landing, Journal of Intelligent and Robotic Systems, 57 (2010), 329-349.  doi: 10.1007/978-90-481-8764-5_17.  Google Scholar

[5]

D. L. Fitzgerald, R. A. Walker and D. A. Campbell, A vision based forced landing site selection system for an autonomous UAV, in 2005 International Conference on Intelligent Sensors, Sensor Networks and Information Processing, (2005), Melbourne, Australia, 397–402. Google Scholar

[6]

R. Frezza and C. Altafini, Autonomous landing by computer vision: An application of path following in SE, in Proceedings of the 39th IEEE Conference on Decision and Control, (2000), Sydney, NSW, Australia, 2527–2532. doi: 10.1109/CDC.2000.914183.  Google Scholar

[7]

R. Ghanem and B. Zireg, Numerical solution of bilateral obstacle optimal control problem, where the controls and the obstacles coincide, Numerical Algebra, Control and Optimization, 10 (2020), 275-300.   Google Scholar

[8]

D. Gu and D. W. Zhang, Parametric control to second-order linear time-varying systems based on dynamic compensator and multi-objective optimization, Applied Mathematics and Computation, 365 (2020), 124681, 25pp. doi: 10.1016/j.amc.2019.124681.  Google Scholar

[9]

D. Gu and D. W. Zhang, A parametric method to design dynamic compensator for high-order quasi-linear systems, Nonlinear Dynamics, 100 (2020), 1379-1400.  doi: 10.1007/s11071-020-05555-0.  Google Scholar

[10]

X. Guo, S. Denman and C. Fookes, et al., Automatic UAV forced landing site detection using machine learning, in 2014 International Conference on Digital Image Computing: Techniques and Applications (DICTA), (2014), Wollongong, NSW, Australia, 1–7. doi: 10.1109/DICTA.2014.7008097.  Google Scholar

[11]

K. R. Horneman and C. A. Kluever, Terminal area energy management trajectory planning for an unpowered reusable launch vehicle, in Collection of Technical Papers - AIAA Atmospheric Flight Mechanics Conference, (2004), Providence, RI, United States, 1103–1120. doi: 10.2514/6.2004-5183.  Google Scholar

[12]

D. Jung and P. Tsiotras, On-line path generation for unmanned aerial vehicles using B-spline path templates, Journal of Guidance, 36 (2013), 1642-1653.  doi: 10.2514/1.60780.  Google Scholar

[13]

R. Li and Y. J. Shi, The fuel optimal control problem of a hypersonic aircraft with periodic cruising mode, J Mathematical and Computer Modelling, 55 (2012), 2141-2150.  doi: 10.1016/j.mcm.2011.12.052.  Google Scholar

[14]

B. Li, X. Guo, X. Zeng, S. Dian and M. Guo, An optimal PID tuning method for a single link manipulator based on the control parametrization technique, Discrete and Continuous Dynamical Systems Series S, 13 (2020), 1813-1823.  doi: 10.3934/dcdss.2020107.  Google Scholar

[15]

R. Li, Y. J. Shi and K. L. Teo, Coordination arrival control for multi-agent systems, International Journal of Robust and Nonlinear Control, 26 (2016), 1456-1474.  doi: 10.1002/rnc.3359.  Google Scholar

[16]

L. Mejias and D. L. Fitzgerald, A multi-layered approach for site detection in UAS emergency landing scenarios using geometry-based image segmentation, in 2013 International Conference on Unmanned Aircraft Systems (ICUAS), (2013), Atlanta, GA, USA, 366–372. doi: 10.1109/ICUAS.2013.6564710.  Google Scholar

[17]

T. E. Moore, Space shuttle entry terminal area energy management, Houston, TX, United States [Online]. Available: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920010688.pdf Google Scholar

[18]

H. Niu, Z. J. Feng, Q. J. Xiao and Y. J. Zhang, A PID control method based on optimal control strategy, Numerical Algebra, Control and Optimization, (2020). Google Scholar

[19]

M. Ohno, Y. Yamaguchi and T. Hata, Robust flight control law design for an automatic landing flight experiment, Control Engineering Practice, 7 (1999), 1143-1151.   Google Scholar

[20]

D. Orfanus, E. D. Freitas and F. Eliassen, Self-organization as a supporting paradigm for military UAV relay networks, IEEE Communications Letters, 20 (2016), 804-807.  doi: 10.1109/LCOMM.2016.2524405.  Google Scholar

[21]

R. K. Rangel, C. A. D. Oliveira and K. H. Kienitz, Development of a multipurpose tactical surveillance system using UAV's, in 2014 IEEE Aerospace Conference, (2014), Big Sky, MT, USA, 1–9. doi: 10.1109/AERO.2014.6836300.  Google Scholar

[22]

S. D. Ridder and E. Mooij, Terminal area trajectory planning using the energy-tube concept for reusable launch vehicles, Acta Astronautica, 68 (2011), 915-930.  doi: 10.1016/j.actaastro.2010.08.032.  Google Scholar

[23]

S. D. Ridder and E. Mooij, Optimal longitudinal trajectories for reusable space vehicles in the terminal area, Journal of Spacecraft and Rockets, 48 (2011), 642-653.  doi: 10.2514/1.51083.  Google Scholar

[24]

S. D. Ridder and E. Mooij, Terminal area trajectory planning using the energy-tube concept for reusable launch, Acta Astronautica, 68 (2011), 915-930.  doi: 10.1016/j.actaastro.2010.08.032.  Google Scholar

[25]

M. Senpheng and M. Ruchanurucks, Automatic landing assistant system based on stripe lines on runway using computer vision, in 2015 International Conference on Science and Technology (TICST), (2015), Pathum Thani, Thailand, 35–39. doi: 10.1109/TICST.2015.7369336.  Google Scholar

[26]

I. Shapira and J. Ben-Asher, Range maximization for emergency landing after engine cut-off, Journal of Guidance, 42 (2005), 1296-1306.   Google Scholar

[27]

Y. F. Shen, Z. Rahman and D. Krusienski, A vision-based automatic safe landing-site detection system, IEEE Transactions on Aerospace and Electronic Systems, 49 (2013), 294-311.   Google Scholar

[28]

Y. J. Shi, R. Li and K. L. Teo, Design of a band-stop filter for a space shuttle vehicle, IEEE Transactions on Circuits and Systems-II: Express Briefs, 62 (2015), 1174-1178.  doi: 10.1109/TCSII.2015.2468922.  Google Scholar

[29]

Y. J. Shi, R. Li and H. L. Xu, Control augmentation design of UAVs based on deviation modification of aerodynamic focus, Journal of Industrial and Management Optimization, 11 (2015), 231-240.  doi: 10.3934/jimo.2015.11.231.  Google Scholar

[30]

D. G. Ward, J. F. Monaco and J. D. Schierman, Reconfigurable control for VTOL UAV shipboard landing, in Guidance, Navigation, and Control Conference and Exhibit, Portland, OR, United States, (1999), 499–509. doi: 10.2514/6.1999-4045.  Google Scholar

[31]

F. Yang, K. L. Teo, R. Loxton, V. Rehbock, B. Li, C. Yu and L. Jennings, VISUAL MISER: An efficient user-friendly visual program for solving optimal control problems, Journal of Industrial and Management Optimization, 12 (2016), 781-810.  doi: 10.3934/jimo.2016.12.781.  Google Scholar

[32]

J. F. Zhang and C. J. Jia, Automatic landing controller design and simulation of flying-wing unmanned aerial vehicle, in Proceedings of 2013 2nd International Conference on Measurement, Information and Control, 2 (2013), Harbin, China, 893–896. doi: 10.1109/MIC.2013.6758104.  Google Scholar

[33]

M. Zhou, J. Zhou and J. G. Guo, Terminal area energy management trajectory planning for an unpowered reusable launch vehicle with gliding limitations, Applied Mechanics and Materials, 446 (2014), 611-615.  doi: 10.4028/www.scientific.net/AMM.446-447.611.  Google Scholar

Figure 1.  The full ground track of S-turn scheme
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Figure 2.  Flow chart of terminal energy management at various phase
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Figure 3.  The prediction of range in acquisition phase
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Figure 4.  The prediction of range in HAC-Turn phase
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Figure 5.  Track angle of aircraft
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Figure 6.  The judgment nominal line of aircraft in pre-approach phase
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Figure 7.  The force direction of the aircraft
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Figure 8.  The high energy change of the S-turning scheme
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Figure 9.  The range of the S-turning scheme at high energy
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Figure 10.  The low energy change of the S-turning scheme
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Figure 11.  The range of the S-turning scheme at low energy
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Figure 12.  The angle of speed brake in the nominal case
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Figure 13.  The angle of speed brake at high energy
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Figure 14.  The angle of speed brake at low energy
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Table 1.  The resistance of closed speed brake and opened speed brake
h(m) $ \rho(kg/m^3) $ $ \alpha (^\circ) $ $ D_c $(N) $ D_o $(N)
4500 0.7768 4.86 5541 7565
4000 0.8191 4.74 5643 7782
3500 0.8632 4.46 5769 8028
3000 0.9091 4.36 5913 8296
2500 0.9569 4.12 6071 8558
2000 1.0065 3.76 11760 14290
1500 1.0580 3.60 12290 14950
1000 1.1116 3.44 12840 15630
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h(m) $ \rho(kg/m^3) $ $ \alpha (^\circ) $ $ D_c $(N) $ D_o $(N)
4500 0.7768 4.86 5541 7565
4000 0.8191 4.74 5643 7782
3500 0.8632 4.46 5769 8028
3000 0.9091 4.36 5913 8296
2500 0.9569 4.12 6071 8558
2000 1.0065 3.76 11760 14290
1500 1.0580 3.60 12290 14950
1000 1.1116 3.44 12840 15630
Table 2.  The control effect of the speed brake
Speed brake Glide angle (high/low) Touchdown velocity
Closed $ -9^{\circ}/-15^{\circ}/-19^{\circ} $ 293.4km/h
Fully opened $ -29^{\circ}/-15^{\circ}/-19^{\circ} $ 290.2km/h
Table Options

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Speed brake Glide angle (high/low) Touchdown velocity
Closed $ -9^{\circ}/-15^{\circ}/-19^{\circ} $ 293.4km/h
Fully opened $ -29^{\circ}/-15^{\circ}/-19^{\circ} $ 290.2km/h
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