# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2022026
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## Real-time online trajectory planning and guidance for terminal area energy management of unmanned aerial vehicle

 1 State Key Laboratory of Satellite Navigation System and Equipment Technology, Shijiazhuang, 050081, China 2 School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China 3 Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China

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

Received  October 2021 Revised  December 2021 Early access February 2022

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 the Key Research Development Program of HeBei (No. 19210906D)

Aiming at the energy management problem of unmanned aerial vehicles (UAVs) in the terminal area energy management (TAEM) phase, a real-time online trajectory planning and guidance strategy based on judging energy is proposed. The trajectory planning strategy estimates the flight profile online in real time by judging the energy and changing the radius of the heading alignment circle. In addition, guidance instructions are also obtained at once. In the S-turn stage, the lateral guidance adopts a closed loop control mode with a fixed bank angle. In the remaining stage, the lateral guidance adopts a closed loop control mode for tracking the azimuth angle. In all stages, the longitudinal guidance adopts a closed loop control mode for tracking the flight path angle and flight height. The trajectory planning strategy is able to quickly generate a reference trajectory for testing cases with large variations not only in the initial energy but also in the energy of the flight process. The simulation results show that the proposed trajectory planning and guidance strategy can effectively manage a UAV's energy in the TAEM phase, ensuring that the UAV lands safely.

Citation: Xiaoyong Mao, Baoguo Yu, Yingjing Shi, Rui Li. Real-time online trajectory planning and guidance for terminal area energy management of unmanned aerial vehicle. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022026
##### References:
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show all references

##### References:
 [1] R. K. Rangel, C. A. De Oliveira and K. H. Kienitz, Development of a multipurpose tactical surveillance system using UAV's, in 2014 IEEE Aerospace Conference, Big Sky, MT, United States, 2014, 6836300. doi: 10.1109/AERO.2014.6836300. [2] M. Seleck, J. Faigl and M. Rollo, Mixed reality simulation for incremental development of multi-UAV systems, in 2017 International Conference on Unmanned Aircraft Systems (ICUAS), Miami, FL, United States, 2017, 1530–1538. doi: 10.1109/ICUAS.2017.7991351. [3] T. Petrova and Z. Petrov, Long term development perspectives for UAV potential, International E-Journal of Advances in Social Sciences, 6 (2020), 45-53. [4] C. A. Kluever and D. A. Neal, Approach and landing range guidance for an unpowered reusable launch vehicle, Journal of Guidance, Control, and Dynamics, 38 (2015), 2057-2066.  doi: 10.2514/1.G000909. [5] M. J. Tahk, G. H. Moon and S. W. Shim, Augmented polynomial guidance with terminal speed constraints for unpowered aerial vehicles, International Journal of Aeronautical, 20 (2018), 183-194.  doi: 10.1007/s42405-018-0093-4. [6] S. Lim, S. Cho and E. Lee, Guidance to control arrival angle and altitude for an unpowered aerial vehicle, International Journal of Aeronautical and Space Sciences, 21 (2020), 1078-1091.  doi: 10.1007/s42405-020-00265-8. [7] T. E. Moore, Space shuttle entry terminal area energy management, NASA Technical Memorandum (104744), 1991. [8] K. Horneman and C. Kluever, Terminal area energy management trajectory planning for an unpowered reusable launch vehicle, in AIAA Atmospheric Flight Mechanics Conference and Exhibit, Providence, RI, United States, 2004, 1103–1120. doi: 10.2514/6.2004-5183. [9] L. Mu, X. Yu, Y. Zhang, P. Li and X. Wang, Trajectory planning for terminal area energy management phase of reusable launch vehicles, IFAC-PapersOnline, 49 (2016), 462-467.  doi: 10.1016/j.ifacol.2016.09.079. [10] W. Jiang and Z. Yang, Guidance law design for terminal area energy management of reusable launch vehicle by energy-to-range ratio, Mathematical Problems in Engineering, 2014 (2014), 929731.  doi: 10.1155/2014/929731. [11] C. Kluever, K. Horneman and J. Schierman, Rapid terminal-trajectory planner for an unpowered reusable launch vehicle, in AIAA Guidance, Navigation, and Control Conference, Chicago, IL, United States, 2009, 5766. doi: 10.2514/6.2009-5766. [12] S. De 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. [13] L. Mu, Y. Xiang, Y. Zhang, L. Ping and X. Wang, Onboard guidance system design for reusable launch vehicles in the terminal area energy management phase, Acta Astronautica, 143 (2018), 62-75.  doi: 10.1016/j.actaastro.2017.10.027. [14] X. Lan, L. Liu and Y. Wang, Online trajectory planning and guidance for reusable launch vehicles in the terminal area, Acta Astronautica, 118 (2016), 237-245.  doi: 10.1016/j.actaastro.2015.10.019. [15] X. Lan, W. Xu and Y. Wang, 3D profile reconstruction and guidance for the terminal area energy management phase of an unpowered RLV with aerosurface failure, Journal of Aerospace Engineering, 33 (2020), 04020003.  doi: 10.1061/(ASCE)AS.1943-5525.0001112. [16] B. T. Burchett, Fuzzy logic trajectory design and guidance for terminal area energy management, Journal of Spacecraft and Rockets, 41 (2004), 444-450.  doi: 10.2514/6.2004-700. [17] V. Morio, F. Cazaurang, A. Falcoz and P. Vernis, Robust terminal area energy management guidance using flatness approach, IET Control Theory & Applications, 4 (2010), 472-486.  doi: 10.1049/iet-cta.2008.0463. [18] Z. Min, J. Zhou and Z. Guo, Finite-time sliding mode based terminal area guidance with multiple constraints, in 2018 3rd International Conference on Control and Robotics Engineering (ICCRE), Nagpya, Japan, 2018, 60–64. doi: 10.1109/ICCRE.2018.8376434.
Forces acting on the UAV
Three predicted trajectories at TAEM phase
The strategy logic flowchart at TAEM phase
Predicted trajectory at separation state
Predicted trajectory at intersection state
The point A is below point D when two circles are tangent
The point A is above point D when two circles are tangent
Velocity-height profile with different heights
Ground track with different heights
Velocity-height profile with different velocities
Ground track with different velocities
Velocity-height profile with wind disturbances
Ground track with wind disturbances
The restrictions and terminal conditions
 State Maximum $q (KPa)$ $\leq$ 11 $|n_{z}|$ $\leq$ 10 $|V| (m/s)$ $\leq$ 310 $|h| (km)$ $\leq$ 5 $|\chi| (degrees)$ $\leq$ 30 $|y| (km)$ $\leq$ 10
 State Maximum $q (KPa)$ $\leq$ 11 $|n_{z}|$ $\leq$ 10 $|V| (m/s)$ $\leq$ 310 $|h| (km)$ $\leq$ 5 $|\chi| (degrees)$ $\leq$ 30 $|y| (km)$ $\leq$ 10
The values of initial state at TAEM phase
 Cases $H(km)$ $V(m/s)$ $\gamma(deg)$ $\chi(deg)$ $X(km)$ $Y(km)$ Case1 18.5 990 -8 0 -85 0 Case2 21.5 990 -8 0 -85 0 Case3 24.5 990 -8 0 -85 0 Case4 19.4 850 -8 0 -75 0 Case5 19.4 990 -8 0 -75 0 Case6 19.4 1100 -8 0 -75 0
 Cases $H(km)$ $V(m/s)$ $\gamma(deg)$ $\chi(deg)$ $X(km)$ $Y(km)$ Case1 18.5 990 -8 0 -85 0 Case2 21.5 990 -8 0 -85 0 Case3 24.5 990 -8 0 -85 0 Case4 19.4 850 -8 0 -75 0 Case5 19.4 990 -8 0 -75 0 Case6 19.4 1100 -8 0 -75 0
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