Abstract:Quad-rotor UAV formation trajectory optimization is the basis of high precision tracking control. To study quad-rotor UAV formation trajectory optimization, firstly a nonlinear quad-rotor UAV model is built and simplified, meanwhile the model parameters are obtained. Then the collision avoidance problem, state variable constraints and control variable constraints are considered. Finally, an hpadaptive pseudospectral method that selects the discrete points adaptively is used to convert the optimal control problem to a nonlinear programming problem. Simulation result shows that the method has good effect on the optimal trajectory of a research object composed of six quad-rotor UAVs, while satisfying the engineering requirements.
[1] 朱战霞, 袁建平. 无人机编队飞行问题初探[J]. 飞行力学, 2003, 21(2): 5-7. Zhu Zhanxia, Yuan Jianping. Discuss on formation flight of UAV[J]. Flight Dynamic, 2003, 21(2): 5-7.
[2] 程晓明, 曹东, 李春涛. 多无人机协同航迹规划技术研究[J]. 航空计算技术, 2014(4): 71-75. Cheng Xiaoming, Cao Dong, Li Chuntao. cooperative path planning for multiple UAVs[J]. Aeronautical Computing Technique, 2014(4): 71-75.
[3] 杨洁, 王新民, 谢蓉. 基于改进APF的无人机编队航迹规划[J]. 西北工业大学学报, 2013, 31(2): 200-205. Yang Jie, Wang Xinmin, Xie Rong. Route planning of UAV formation based on improved APF[J]. Journal of Northwestern Polytechnical University, 2013, 31(2): 200-205.
[4] 宋绍梅, 张克, 关世义. 基于层次分解策略的无人机多机协同航线规划方法研究[J]. 战术导弹技术, 2004(1): 44-48. Song Shaomei, Zhang Ke, Guan Shiyi. A trajectory planning method based on hierarchy decomposition strategy for coordination of multiple unmanned air vehicles[J]. Tactical Missile Technology, 2004(1): 44-48.
[5] Prasanna H M, Ghose D, Bhat M S, et al. Ascent phase trajectory optimization for a hypersonic vehicle using nonlinear programming[C]//International Conference on Computational Science and ITS Applications. Berlin: Springer-Verlag, 2005: 548-557.
[6] Nah R S, Braden E, Vadali S R, et al. Fuel-optimal, low-thrust, three-dimensional earth-mars trajectories[J]. Journal of Guidance Control & Dynamics, 2001, 24(6): 1100-1107.
[7] Barron R L, Chick C M. Trim-reference functions for indirect method of trajectory optimization[J]. Journal of Guidance Control & Dynamics, 1971, 30(4): 1189-1193.
[8] Fahroo F, Ross I M. Costate estimation by a legendre pseudospectral method[J]. Journal of Guidance, Control, and Dynamics Guidance, 2001, 24(2): 270-277.
[9] David B. A Gauss pseudospectral transcription for optimal control[D]. Cambridge: Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2005.
[10] Ross I M, Sekhavat P, Fleming A, et al. Optimal feedback control: foundations, examples, and experimental results for a new approach[J]. Journal of Guidance Control & Dynamics, 2015, 31(2): 307-321.
[11] Wang D, Zhang W, Shan J. Optimal trajectory planning for a quadrotor via a Gauss Pseudo-spectrum Method[C]//International Conference on Natural Computation. Shenyang, 2013. 1666-1670.
[12] Darby C L, Hager W W, Rao A V. An hp-adaptive pseudospectral method for solving optimal control problems[J]. Optimal Control Applications & Methods, 2011, 32(4): 476-502.
[13] 王丹. 基于DMOC的四旋翼飞行器轨迹优化与控制算法研究[D]. 北京: 北京理工大学, 2015. Wang Dan. Trajectory optimization and control algorithm of four rotor aircraft based on DMOC[J]. Beijing: Beijing Institute of Technology, 2015.
[14] Zhang W, Zhang Y, Li W, et al. Path planning for rapid large-angle maneuver of satellites based on the gauss pseudospectral method[J]. Mathematical Problems in Engineering, 2016, 2016(1): 1-7.