基于罚函数序列凸规划的多无人机轨迹规划

doi:10.7527/S1000-6893.2016.0064

Abstract

Abstract:

Trajectory planning of multiple unmanned aerial vehicles (UAVs) is an optimal control problem which subjects to nonlinear motion and nonconvex path constraints. Based on the sequential convex programming approach, such nonconvex optimal control is approximated to be a series of convex optimization subproblems, which can be solved by the state-of-the-art convex optimization algorithm. A good balance between solution quality and computational tractability can then be achieved. Nonconvex optimal control model for multi-UAV trajectory planning is formulated first, and is then approximated to be a convex optimization by discretization and convexification methods. To convexify the nonconvex model, equations of motion of UAVs are linearized, and constraints of threat avoidance and inter-UAVs collision avoidance are convexified. Meanwhile, an inter-sample threat avoidance method is provided to guarantee UAVs' safety at intervals between discrete trajectory points. Based on convex optimization formulation, the detailed procedure of using sequential convex programming based on penalty function to solve multi-UAV trajectory planning is provided. Numerical simulations are conducted to show the effectiveness of the proposed method. The results show that the method can acquire the solution with better optimality and efficiency than the pseudospectral method, especially for larger scale UAV formation.

Key words: unmanned aerial vehicle, trajectory planning, collision avoidance, optimal control, convex programming

CLC Number:

V279

WANG Zhu, LIU Li, LONG Teng, WEN Yonglu. Trajectory planning for multi-UAVs using penalty sequential convex pro-gramming[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(10): 3149-3158.

References

[1] 沈林成, 牛轶峰, 朱华勇, 等. 多无人机自主协同控制理论与方法[M]. 北京:国防工业出版社, 2013:1-9. SHEN L C, NIU Y F, ZHU H Y, et al. Theories and methods of autonomous cooperative control for multiple UAVs[M]. Beijing:National Defense Industry Press, 2013:1-9(in Chinese).
[2] 丁明跃, 郑昌文, 周成平, 等. 无人飞行器航迹规划[M]. 北京:电子工业出版社, 2009:6-15. DING M Y, ZHENG C W, ZHOU C P, et al. Route planning for unmanned aerial vehicles[M]. Beijing:Publishing House of Electronics industry, 2009:6-15(in Chinese).
[3] 张煜, 张万鹏, 陈璟, 等. 基于Gauss伪谱法的UCAV对地攻击武器投放轨迹规划[J]. 航空学报, 2011, 32(7):1240-1251. ZHANG Y, ZHANG W P, CHEN J, et al. Air-to-ground weapon delivery trajectory planning for UCAVs using Gauss pseudospectral method[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(7):1240-1251(in Chinese).
[4] 白瑞光, 孙鑫, 陈秋双, 等. 基于Gauss伪谱法的多UAV协同航迹规划[J]. 宇航学报, 2014, 35(9):1022-1029. BAI R G, SUN X, CHEN Q S, et al. Multiple UAV cooperative trajectory planning based on Gauss pseudospectral method[J]. Journal of Astronautics, 2014, 35(9):1022-1029(in Chinese).
[5] RICHARDS A, HOW J P. Aircraft trajectory planning with collision avoidance using mixed integer linear programming[C]//Proceedings of the American Control Conference. Reston:AIAA, 2002:1936-1941.
[6] KUWATA Y, HOW J P. Cooperative distributed robust trajectory optimization using receding horizon MILP[J]. IEEE Transactions on System Technology, 2011, 19(2):423-431.
[7] 熊伟, 陈宗基, 周锐. 运用混合遗传算法的多机编队重构优化方法[J]. 航空学报, 2008, 29(S1):209-214. XIONG W, CHEN Z J, ZHOU R. Optimization of multiple flight vehicle formation reconfiguration using hybrid genetic algorithm[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29(S1):209-214(in Chinese).
[8] DUAN H B, LIU S Q, WU J. Novel intelligent water drops optimization approach to single UCAV smooth trajectory planning[J]. Aerospace Science and Technology, 2009, 13(8):442-449.
[9] BOYD S, VANDENBERGHE L. Convex optimization[M]. New York:Cambridge University Press, 2004:1-15.
[10] BYRD R H, GILBERT J C, NOCEDAL J. A trust region method based on interior point techniques for nonlinear programming[J]. Mathematical Programming, 2000, 89(1):149-185.
[11] LIU X F, LU P. Solving nonconvex optimal control problems by convex optimization[J]. Journal of Guidance, Control, and Dynamics, 2014, 37(3):750-765.
[12] LU P, LIU X F. Autonomous trajectory planning for rendezvous and proximity operations by conic optimization[J]. Journal of Guidance, Control, and Dynamics, 2013, 36(2):375-389.
[13] LIU X F, SHEN Z J, LU P. Entry trajectory optimization by second-order cone programming[J]. Journal of Guidance, Control, and Dynamics, 2016, 39(2):227-241.
[14] LIU X F, SHEN Z J, LU P. Solving the maximum-crossrange problem via successive second-order cone programming with a line search[J]. Aerospace Science and Technology, 2015, 47:10-20.
[15] MORGAN D, CHUNG S. Model predictive control of swarm of spacecraft using sequential convex programming[J]. Journal of Guidance, Control, and Dynamics, 2014, 37(6):1725-1740.
[16] AUGUGLIARO F, SCHOELLIG A P, D'ANDREA R. Generation of collision-free for a quadrocopter fleet:a sequential convex programming approach[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, NJ:IEEE Press, 2012:1917-1922.
[17] CHEN Y F, CUTLER M, HOW J P. Decoupled multiagent path planning via incremental sequential convex programming[C]//IEEE International Conference on Robotics and Automation. Piscataway, NJ:IEEE Press, 2015:5954-5961.
[18] KABAMBA P T, MEERKOV S M, ZEITZ F H. Optimal path planning for unmanned combat aerial vehicles to defeat radar tracking[J]. Journal of Guidance, Control, and Dynamics, 2006, 29(2):279-288.
[19] MAIA M H, GALVAO R K H. On the use of mixed-integer linear programming for predictive control with avoidance constraints[J]. International Journal of Robust and Nonlinear Control, 2009, 19(7):822-828.
[20] RICHARDS A, TURNBULL O. Inter-sample avoidance in trajectory optimizers using mixed-integer linear programming[J]. International Journal of Robust and Nonlinear Control, 2015, 25(4):521-526.
[21] CVX Research Inc. CVX:Matlab software for disciplined convex programming, version 2.0[EB/OL]. (2011-06-17)[2015-10-09]. http://cvxr.com/cvx.
[22] GRANT M AND BOYD S. Graph implementations for nonsmooth convex programs[M]//Blondel V, Boyd S, and Kimura H. Recent Advances in Learning and Control. Berlin:Springer, 2008:95-110.
[23] TUTUNCU R H, TOH K C, TODD M J. Solving semidefinite-quadratic-linear programs using SDPT3[J]. Mathematical Programming, Series B, 2003, 95(2):189-217.
[24] PATTERSON M A, RAO A V. GPOPS-Ⅱ:A matlab software for solving multiple-phase optimal control problems using hp-adaptive gaussian quadrature collocation methods and sparse nonlinear programming[J]. ACM Transactions on Mathematical Software, 2014, 41(1):1-37.

Trajectory planning for multi-UAVs using penalty sequential convex pro-gramming

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Yuanliang XUE, Guodong JIN, Lining TAN, Jiankun XU. Adaptive UAV target tracking algorithm based on multi-scale fusion [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 326107-326107.
[2]	Qilei GUO, Weimin SANG, Junjie NIU, Ye YUAN. UAV flight strategy considering icing risk under complex meteorological conditions [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 627518-627518.
[3]	HU Yangxiu, ZHAO Changchun, JIA Chenglong, QIAN Zhouyuan, HU Tao. Synchronous path formation control of UAV swarm based on robot operating system (ROS) [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S1): 726914-726914.
[4]	HU Wei, WAN Wenzhang, CHEN Mou. Neural network and disturbance observer based control for automatic carrier landing of UAV [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S1): 726963-726963.
[5]	LI Hui, LONG Teng, SUN Jingliang, XU Guangtong. Adaptive line-of-sight method for 3D path following of UAVs [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 326105-326105.
[6]	SUN Yang, CHANG Min, BAI Junqiang. Trajectory planning and control for micro-quadrotor perching on vertical surface [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 325756-325756.
[7]	RAN Qingbo, XIAO Hong, YANG Fuhong, DUAN Yugang. Trajectory planning algorithm for automatic wire laying on perforated surface [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 425602-425602.
[8]	ZHANG Zhouyu, CAO Yunfeng, FAN Yanming. Research progress of vision based aerospace conflict sensing technologies for small unmanned aerial vehicle in low altitude [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 25645-025645.
[9]	XIE Hua, LI Zihong, YANG Lei, ZHU Yongwen, LIU Fangzi. Optimization of four-dimensional trajectory of city pair with limited capacity [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 325581-325581.
[10]	XING Ling, JIA Xiaofan, ZHAO Pengcheng, WU Honghai. Location privacy protection scheme for unmanned aerial vehicle group based on matrix encryption [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 325386-325386.
[11]	LI Chunpeng, ZHANG Tiejun, QIAN Zhansen, LIU Tiezhong. Aerodynamic design of modular configuration for multi-mission unmanned aerial vehicle [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(7): 125411-125411.
[12]	LIU Fang, SUN Yanan. UAV target tracking algorithm based on adaptive fusion network [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(7): 325522-325522.
[13]	SUN Qin, LI Hongxu, WANG Yuzhi, ZHOU Liping, ZHANG Yingchao. Resilient UAV swarm modeling and solving based on multi-domain collaborative method [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 325340-325340.
[14]	LIU Fang, HAN Xiao. Adaptive aerial object detection based on multi-scale deep learning [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 325270-325270.
[15]	XU Guangtong, WANG Zhu, CAO Yan, SUN Jingliang, LONG Teng. Dynamic-priority-decoupled UAV swarm trajectory planning using distributed sequential convex programming [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(2): 325059-325059.