
-
Previous Article
Principal component analysis with drop rank covariance matrix
- JIMO Home
- This Issue
-
Next Article
A multi-objective decision-making model for supplier selection considering transport discounts and supplier capacity constraints
Multi-aircraft cooperative path planning for maneuvering target detection
AVIC LEIHUA Electronic Technology Institute, Wuxi 214063, China |
Multi-aircraft cooperative path planning is a key problem in modern and future air combat scenario. In this paper, this problem is studied in aspect of airborne radar detection to maintain a continuous tracking of a manoeuvring air target. Firstly, the objective function is established in combination with multiple constraints considered, including Doppler blind zone constraint, radar viewing aspect constraint, baseline constraint, and so on. Then, the above optimal control problem is transformed into a nonlinear programming problem with a series of algebraic constraints by hp-adaptive Gauss pseudospectral method (HPAGPM). And it is solved by GPOPS software package based on MATLAB. Simulation results show that the optimized cooperative paths can be got to achieve continuous tracking of maneuvering air target by HPAGPM.
References:
[1] |
D. Benson, Gauss Pseudospectral Transcription for Optimal Control, Massachusetts Institute of Technology, 2005. Google Scholar |
[2] |
J. T. Betts and W. P. Huffman,
Application of sparse nonlinear programming to trajectory optimization, Journal of Guidance, Control, and Dynamics, 15 (1992), 198-206.
doi: 10.2514/3.20819. |
[3] |
K. Bousson, Single gridpoint dynamic programming for trajectory optimization, in 2005 AIAA Atmospheric Flight Mechanics Conference and Exhibit, San Francisco, USA, (2005), 1–8.
doi: 10.2514/6.2005-5902. |
[4] |
X. T. Chen and J. Z. Wang,
Sliding-mode guidance for simultaneous control of impact time and angle, Journal of Guidance, Control, and Dynamics, 42 (2019), 394-401.
doi: 10.2514/1.G003893. |
[5] |
X. M. Cheng, H. F. Li and R. Zhang,
Efficient ascent trajectory optimization using convex models based on the Newton-Kantorovich/Pseudospectral approach, Aerospace Science and Technology, 66 (2017), 140-151.
doi: 10.1016/j.ast.2017.02.023. |
[6] |
Y. Cherfaoui and M. Moulai,
Biobjective optimization over the efficient set of multiobjective integer programming problem, Journal of Industrial and Management Optimization, 17 (2021), 117-131.
doi: 10.3934/jimo.2019102. |
[7] |
J. M. C. Clark, P. A. Kountouriotis and R. B. Vinter, A methodology for incorporating the Doppler blind zone in target tracking algorithms, in 2008 11th International Conference on Information Fusion, Cologne, Germany, (2008), 1–8. Google Scholar |
[8] |
H. B. Dan, X. X. Wei and Z. M. Dong,
Multiple UCAVs cooperative air combat simulation platform based on PSO, ACO, and game theory, IEEE Transactions on Aerospace and Electronic System Magazine, 28 (2013), 12-19.
doi: 10.1109/MAES.2013.6678487. |
[9] |
C. L. Darby, W. W. Hager and A. V. Rao, An improved adaptive hp algorithm using pseudospectral methods for optimal control, in 2010 AIAA Guidance, Navigation, and Control Conference, Reston, USA, 2012.
doi: 10.2514/6.2010-8272. |
[10] |
C. L. Darby, W. W. Hager and A. V. Rao,
An hp-adaptive pseudospectral method for solving optimal control problems, Optimal Control Applications and Methods, 32 (2011), 476-502.
doi: 10.1002/oca.957. |
[11] |
M. Gandhi and E. Theodorou, A comparison between trajectory optimization methods: Differential dynamic programming and pseudospectral optimal control, in 2016 AIAA Guidance, Navigation, and Control Conference, San Diego, California, USA, (2016), 1–16. Google Scholar |
[12] |
C. Goerzen, Z. Kong and B. Mettler,
A survey of motion planning algorithms from the perspective of autonomous UAV guidance, Journal of Intelligent and Robotic Systems, 57 (2010), 65-100.
doi: 10.1007/978-90-481-8764-5_5. |
[13] |
Y. F. Guo, D. Z. Feng and X. Wang, The earth-mars transfer trajectory optimization of solar sail based on hp-adaptive pseudospectral method, Discrete Dynamics in Nature and Society, 2018 (2018), Art. ID 6916848, 14 pp.
doi: 10.1155/2018/6916848. |
[14] |
R. P. Huang, S. J. Qu, X. G. Yang and Z. M. Liu,
Multi-stage distributionally robust optimization with risk aversion, Journal of Industrial and Management Optimization, 17 (2021), 233-259.
doi: 10.3934/jimo.2019109. |
[15] |
G. Q. Huang, Y. P. Lu and Y. Nan,
A survey of numerical algorithms for trajectory optimization of flight vehicles, Science China Technological Sciences, 55 (2012), 2538-2560.
doi: 10.1007/s11431-012-4946-y. |
[16] |
T. H. Kim, C. H. Lee, I. S. Jeon and M. J. Tahk, Augmented polynomial guidance with impact time and angle constraints, IEEE Transactions on Aerospace and Electronic Systems, 49 (2013), 2806-2817. Google Scholar |
[17] |
S. Kang, R. Tekin and F. Holzapfel,
Generalized impact time and angle control via look-angle shaping, Journal of Guidance, Control, and Dynamics, 42 (2019), 695-702.
doi: 10.2514/1.G003765. |
[18] |
A. Khatami, S. Mirghasemi and A. Khosravi,
A new PSO-based approach to fire flame detection using K-Medoids clustering, Expert Systems with Applications, 68 (2017), 69-80.
doi: 10.1016/j.eswa.2016.09.021. |
[19] |
M. Mertens, W. Koch and T. Kirubarajan,
Exploiting Doppler blind zone information for ground moving target tracking with bistatic airborne radar, IEEE Transactions on Aerospace and Electronic Systems, 50 (2014), 130-148.
doi: 10.1109/TAES.2013.120718. |
[20] |
F. W. Moore,
Radar cross-section reduction via route planning and intelligent control, IEEE Transactions on Control Systems Technology, 10 (2016), 696-700.
doi: 10.1109/TCST.2002.801879. |
[21] |
L. H. Nam, L. Huang, X. J. Li and J. F. Xu, An approach for coverage path planning for UAVs, in 2016 IEEE 14th International Workshop on Advanced Motion Control, Auckland, New Zealand, (2016), 411–416.
doi: 10.1109/AMC.2016.7496385. |
[22] |
N. Ozalo and O. K. Sahingoz, Optimal UAV path planning in a 3D threat environment by using parallel evolutionary algorithms, in 2013 International Conference on Unmanned Aircraft Systems, Grand Hyatt Atlanta, Atlanta, (2013), 308–317. Google Scholar |
[23] |
N. Ozaki, S. Campagnola, R. Funase and C. H. Yam,
Stochastic differential dynamic programming with unscented transform for low-thrust trajectory design, Journal of Guidance, Control, and Dynamics, 41 (2018), 377-381.
doi: 10.2514/1.G002367. |
[24] |
M. Patterson and A. Rao, Gpops-Ⅱ: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming, ACM Transactions on Mathematical Software, 41 (2014), Art. 1, 37 pp.
doi: 10.1145/2558904. |
[25] |
Y. H. Qu, Y. T. Zhang and Y. M. Zhang, Optimal flight path planning for UAVs in a 3-D threat environment, in 2014 International Conference on Unmanned Aircraft systems, Orlando, FL, USA, (2014), 149–155.
doi: 10.1109/ICUAS.2014.6842250. |
[26] |
A. V. Rao, D. A. Benson and C. Darby, Algorithm 902: GPOPS A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method, ACM Transactions on Mathematical Software, 37 (2010), Article 22.
doi: 10.1145/1731022.1731032. |
[27] |
J. R. Riehl, G. E. Collins and J. P. Hespanha,
Cooperative search by UAV teams: A model predictive approach using dynamic graphs, IEEE Transactions on Aerospace and Electronic systems, 47 (2011), 2637-2656.
doi: 10.1109/TAES.2011.6034656. |
[28] |
V. Roberge, M. Tarbouchi and G. Labonte,
Comparison of parallel genetic algorithm and particle swarm optimization for real-time UAV path planning, IEEE Transactions on Industrial Information, 9 (2013), 132-141.
doi: 10.1109/TII.2012.2198665. |
[29] |
B. M. Sathyaraj, L. C. Jain, A. Finn and S. Drake,
Multiple UAVs path planning algorithms: A comparative study, Fuzzy Optimization and Decision Making, 7 (2008), 257-267.
doi: 10.1007/s10700-008-9035-0. |
[30] |
P. Y. Volkan, A new vibrational genetic algorithm enhanced with a Voronoi diagram for path planning of autonomous UAV, Aerospace Science and Technology, 16 (2012), 47-55. Google Scholar |
[31] |
B. Z. Xu, Y. J. Wang and L. Liu, Multi-stage boost aircraft trajectory optimization strategy based on hp adaptive Gauss pseudo spectral method, in 10th International Conference on Modelling, Identification and Control, Guiyang, China, 2018, 1–7.
doi: 10.1109/ICMIC.2018.8529869. |
[32] |
P. Yao, Z. X. Xie and P. Ren,
Optimal UAV route planning for coverage search of stationary target in river, IEEE Transactions on Control Systems Technology, 27 (2019), 822-829.
doi: 10.1109/TCST.2017.2781655. |
[33] |
M. Zhang, Z. Zhu, Z. Zhao and X. Li, Trajectory optimization for missile-borne SAR imaging phase via Gauss Pseudospectral Method, in 2011 IEEE CIE International Conference on Radar, Chengdu, China, (2011), 867–870.
doi: 10.1109/CIE-Radar.2011.6159678. |
show all references
References:
[1] |
D. Benson, Gauss Pseudospectral Transcription for Optimal Control, Massachusetts Institute of Technology, 2005. Google Scholar |
[2] |
J. T. Betts and W. P. Huffman,
Application of sparse nonlinear programming to trajectory optimization, Journal of Guidance, Control, and Dynamics, 15 (1992), 198-206.
doi: 10.2514/3.20819. |
[3] |
K. Bousson, Single gridpoint dynamic programming for trajectory optimization, in 2005 AIAA Atmospheric Flight Mechanics Conference and Exhibit, San Francisco, USA, (2005), 1–8.
doi: 10.2514/6.2005-5902. |
[4] |
X. T. Chen and J. Z. Wang,
Sliding-mode guidance for simultaneous control of impact time and angle, Journal of Guidance, Control, and Dynamics, 42 (2019), 394-401.
doi: 10.2514/1.G003893. |
[5] |
X. M. Cheng, H. F. Li and R. Zhang,
Efficient ascent trajectory optimization using convex models based on the Newton-Kantorovich/Pseudospectral approach, Aerospace Science and Technology, 66 (2017), 140-151.
doi: 10.1016/j.ast.2017.02.023. |
[6] |
Y. Cherfaoui and M. Moulai,
Biobjective optimization over the efficient set of multiobjective integer programming problem, Journal of Industrial and Management Optimization, 17 (2021), 117-131.
doi: 10.3934/jimo.2019102. |
[7] |
J. M. C. Clark, P. A. Kountouriotis and R. B. Vinter, A methodology for incorporating the Doppler blind zone in target tracking algorithms, in 2008 11th International Conference on Information Fusion, Cologne, Germany, (2008), 1–8. Google Scholar |
[8] |
H. B. Dan, X. X. Wei and Z. M. Dong,
Multiple UCAVs cooperative air combat simulation platform based on PSO, ACO, and game theory, IEEE Transactions on Aerospace and Electronic System Magazine, 28 (2013), 12-19.
doi: 10.1109/MAES.2013.6678487. |
[9] |
C. L. Darby, W. W. Hager and A. V. Rao, An improved adaptive hp algorithm using pseudospectral methods for optimal control, in 2010 AIAA Guidance, Navigation, and Control Conference, Reston, USA, 2012.
doi: 10.2514/6.2010-8272. |
[10] |
C. L. Darby, W. W. Hager and A. V. Rao,
An hp-adaptive pseudospectral method for solving optimal control problems, Optimal Control Applications and Methods, 32 (2011), 476-502.
doi: 10.1002/oca.957. |
[11] |
M. Gandhi and E. Theodorou, A comparison between trajectory optimization methods: Differential dynamic programming and pseudospectral optimal control, in 2016 AIAA Guidance, Navigation, and Control Conference, San Diego, California, USA, (2016), 1–16. Google Scholar |
[12] |
C. Goerzen, Z. Kong and B. Mettler,
A survey of motion planning algorithms from the perspective of autonomous UAV guidance, Journal of Intelligent and Robotic Systems, 57 (2010), 65-100.
doi: 10.1007/978-90-481-8764-5_5. |
[13] |
Y. F. Guo, D. Z. Feng and X. Wang, The earth-mars transfer trajectory optimization of solar sail based on hp-adaptive pseudospectral method, Discrete Dynamics in Nature and Society, 2018 (2018), Art. ID 6916848, 14 pp.
doi: 10.1155/2018/6916848. |
[14] |
R. P. Huang, S. J. Qu, X. G. Yang and Z. M. Liu,
Multi-stage distributionally robust optimization with risk aversion, Journal of Industrial and Management Optimization, 17 (2021), 233-259.
doi: 10.3934/jimo.2019109. |
[15] |
G. Q. Huang, Y. P. Lu and Y. Nan,
A survey of numerical algorithms for trajectory optimization of flight vehicles, Science China Technological Sciences, 55 (2012), 2538-2560.
doi: 10.1007/s11431-012-4946-y. |
[16] |
T. H. Kim, C. H. Lee, I. S. Jeon and M. J. Tahk, Augmented polynomial guidance with impact time and angle constraints, IEEE Transactions on Aerospace and Electronic Systems, 49 (2013), 2806-2817. Google Scholar |
[17] |
S. Kang, R. Tekin and F. Holzapfel,
Generalized impact time and angle control via look-angle shaping, Journal of Guidance, Control, and Dynamics, 42 (2019), 695-702.
doi: 10.2514/1.G003765. |
[18] |
A. Khatami, S. Mirghasemi and A. Khosravi,
A new PSO-based approach to fire flame detection using K-Medoids clustering, Expert Systems with Applications, 68 (2017), 69-80.
doi: 10.1016/j.eswa.2016.09.021. |
[19] |
M. Mertens, W. Koch and T. Kirubarajan,
Exploiting Doppler blind zone information for ground moving target tracking with bistatic airborne radar, IEEE Transactions on Aerospace and Electronic Systems, 50 (2014), 130-148.
doi: 10.1109/TAES.2013.120718. |
[20] |
F. W. Moore,
Radar cross-section reduction via route planning and intelligent control, IEEE Transactions on Control Systems Technology, 10 (2016), 696-700.
doi: 10.1109/TCST.2002.801879. |
[21] |
L. H. Nam, L. Huang, X. J. Li and J. F. Xu, An approach for coverage path planning for UAVs, in 2016 IEEE 14th International Workshop on Advanced Motion Control, Auckland, New Zealand, (2016), 411–416.
doi: 10.1109/AMC.2016.7496385. |
[22] |
N. Ozalo and O. K. Sahingoz, Optimal UAV path planning in a 3D threat environment by using parallel evolutionary algorithms, in 2013 International Conference on Unmanned Aircraft Systems, Grand Hyatt Atlanta, Atlanta, (2013), 308–317. Google Scholar |
[23] |
N. Ozaki, S. Campagnola, R. Funase and C. H. Yam,
Stochastic differential dynamic programming with unscented transform for low-thrust trajectory design, Journal of Guidance, Control, and Dynamics, 41 (2018), 377-381.
doi: 10.2514/1.G002367. |
[24] |
M. Patterson and A. Rao, Gpops-Ⅱ: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming, ACM Transactions on Mathematical Software, 41 (2014), Art. 1, 37 pp.
doi: 10.1145/2558904. |
[25] |
Y. H. Qu, Y. T. Zhang and Y. M. Zhang, Optimal flight path planning for UAVs in a 3-D threat environment, in 2014 International Conference on Unmanned Aircraft systems, Orlando, FL, USA, (2014), 149–155.
doi: 10.1109/ICUAS.2014.6842250. |
[26] |
A. V. Rao, D. A. Benson and C. Darby, Algorithm 902: GPOPS A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method, ACM Transactions on Mathematical Software, 37 (2010), Article 22.
doi: 10.1145/1731022.1731032. |
[27] |
J. R. Riehl, G. E. Collins and J. P. Hespanha,
Cooperative search by UAV teams: A model predictive approach using dynamic graphs, IEEE Transactions on Aerospace and Electronic systems, 47 (2011), 2637-2656.
doi: 10.1109/TAES.2011.6034656. |
[28] |
V. Roberge, M. Tarbouchi and G. Labonte,
Comparison of parallel genetic algorithm and particle swarm optimization for real-time UAV path planning, IEEE Transactions on Industrial Information, 9 (2013), 132-141.
doi: 10.1109/TII.2012.2198665. |
[29] |
B. M. Sathyaraj, L. C. Jain, A. Finn and S. Drake,
Multiple UAVs path planning algorithms: A comparative study, Fuzzy Optimization and Decision Making, 7 (2008), 257-267.
doi: 10.1007/s10700-008-9035-0. |
[30] |
P. Y. Volkan, A new vibrational genetic algorithm enhanced with a Voronoi diagram for path planning of autonomous UAV, Aerospace Science and Technology, 16 (2012), 47-55. Google Scholar |
[31] |
B. Z. Xu, Y. J. Wang and L. Liu, Multi-stage boost aircraft trajectory optimization strategy based on hp adaptive Gauss pseudo spectral method, in 10th International Conference on Modelling, Identification and Control, Guiyang, China, 2018, 1–7.
doi: 10.1109/ICMIC.2018.8529869. |
[32] |
P. Yao, Z. X. Xie and P. Ren,
Optimal UAV route planning for coverage search of stationary target in river, IEEE Transactions on Control Systems Technology, 27 (2019), 822-829.
doi: 10.1109/TCST.2017.2781655. |
[33] |
M. Zhang, Z. Zhu, Z. Zhao and X. Li, Trajectory optimization for missile-borne SAR imaging phase via Gauss Pseudospectral Method, in 2011 IEEE CIE International Conference on Radar, Chengdu, China, (2011), 867–870.
doi: 10.1109/CIE-Radar.2011.6159678. |












Method | Aboved 2v1 scenario | 50 scenarios | |
run time | blind zone time | solution probability | |
PSO | 195s | 58s | 80% |
GPM | 176s | 51s | 92% |
HPAGPM | 109s | 40s | 96% |
Method | Aboved 2v1 scenario | 50 scenarios | |
run time | blind zone time | solution probability | |
PSO | 195s | 58s | 80% |
GPM | 176s | 51s | 92% |
HPAGPM | 109s | 40s | 96% |
[1] |
Yi Gao, Rui Li, Yingjing Shi, Li Xiao. Design of path planning and tracking control of quadrotor. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021063 |
[2] |
Sheng-I Chen, Yen-Che Tseng. A partitioning column approach for solving LED sorter manipulator path planning problems. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021055 |
[3] |
Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327 |
[4] |
Zheng Chang, Haoxun Chen, Farouk Yalaoui, Bo Dai. Adaptive large neighborhood search Algorithm for route planning of freight buses with pickup and delivery. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1771-1793. doi: 10.3934/jimo.2020045 |
[5] |
Mohsen Abdolhosseinzadeh, Mir Mohammad Alipour. Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 321-332. doi: 10.3934/naco.2020028 |
[6] |
İsmail Özcan, Sirma Zeynep Alparslan Gök. On cooperative fuzzy bubbly games. Journal of Dynamics & Games, 2021 doi: 10.3934/jdg.2021010 |
[7] |
Haiyan Wang. Existence and nonexistence of positive radial solutions for quasilinear systems. Conference Publications, 2009, 2009 (Special) : 810-817. doi: 10.3934/proc.2009.2009.810 |
[8] |
M. R. S. Kulenović, J. Marcotte, O. Merino. Properties of basins of attraction for planar discrete cooperative maps. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2721-2737. doi: 10.3934/dcdsb.2020202 |
[9] |
Tian Hou, Yi Wang, Xizhuang Xie. Instability and bifurcation of a cooperative system with periodic coefficients. Electronic Research Archive, , () : -. doi: 10.3934/era.2021026 |
[10] |
Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209 |
[11] |
Raimund Bürger, Christophe Chalons, Rafael Ordoñez, Luis Miguel Villada. A multiclass Lighthill-Whitham-Richards traffic model with a discontinuous velocity function. Networks & Heterogeneous Media, 2021, 16 (2) : 187-219. doi: 10.3934/nhm.2021004 |
[12] |
Zhihua Zhang, Naoki Saito. PHLST with adaptive tiling and its application to antarctic remote sensing image approximation. Inverse Problems & Imaging, 2014, 8 (1) : 321-337. doi: 10.3934/ipi.2014.8.321 |
[13] |
Murat Uzunca, Ayşe Sarıaydın-Filibelioǧlu. Adaptive discontinuous galerkin finite elements for advective Allen-Cahn equation. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 269-281. doi: 10.3934/naco.2020025 |
[14] |
Alfonso Castro, Jorge Cossio, Sigifredo Herrón, Carlos Vélez. Infinitely many radial solutions for a $ p $-Laplacian problem with indefinite weight. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021058 |
[15] |
Lipeng Duan, Jun Yang. On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021056 |
[16] |
Norman Noguera, Ademir Pastor. Scattering of radial solutions for quadratic-type Schrödinger systems in dimension five. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3817-3836. doi: 10.3934/dcds.2021018 |
[17] |
Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521 |
[18] |
Rabiaa Ouahabi, Nasr-Eddine Hamri. Design of new scheme adaptive generalized hybrid projective synchronization for two different chaotic systems with uncertain parameters. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2361-2370. doi: 10.3934/dcdsb.2020182 |
[19] |
Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 |
[20] |
Mikhail Dokuchaev, Guanglu Zhou, Song Wang. A modification of Galerkin's method for option pricing. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021077 |
2019 Impact Factor: 1.366
Tools
Article outline
Figures and Tables
[Back to Top]