| 引用本文: | 李杰,彭双春,安宏雷,等.基于微分几何与李群的无人机编队会合方法.[J].国防科技大学学报,2013,35(6):157-164.[点击复制] |
| LI Jie,PENG Shuangchun,AN Honglei,et al.UAVs formation rendezvous method based on differential geometry and Lie group[J].Journal of National University of Defense Technology,2013,35(6):157-164[点击复制] |
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| 基于微分几何与李群的无人机编队会合方法 |
| 李杰1, 彭双春2, 安宏雷1, 相晓嘉1, 沈林成1 |
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(1.国防科技大学 机电工程与自动化学院， 湖南 长沙 410073;2.国防科技大学 航天科学与工程学院，湖南 长沙 410073)
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| 摘要: |
| 在领航-跟随编队模式下，设计了一种基于追缉策略的无人机编队会合方法。基于微分几何曲线论和弗雷涅-塞雷标架建立了无人机非解耦三维运动模型，其中将曲率和挠率作为控制量；结合该模型给出了无人机三维编队会合问题的数学描述，它将导弹制导问题中的终端落角约束映射为编队会合问题中僚机的航迹倾角约束，同时引入额外的航迹方位角约束；使用特殊正交群的元素来度量长僚机方向偏差，并通过局部坐标映射将其映射为对应李代数空间中的旋量；基于该旋量设计了编队会合几何导引律，并给出相应的曲率和挠率控制指令；分别在长机稳定平飞和转弯机动条件下进行了多机编队会合数字仿真实验，仿真结果显示僚机能够有效地跟踪长机航向并收敛至指定位形，说明了方法的有效性。 |
| 关键词: 无人机 编队会合 微分几何 李群 几何控制 |
| DOI： |
| 投稿日期：2013-03-14 |
| 基金项目:湖南省研究生科研创新资助项目(CX2010B011) |
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| UAVs formation rendezvous method based on differential geometry and Lie group |
| LI Jie1, PENG Shuangchun2, AN Honglei1, XIANG Xiaojia1, SHEN Lincheng1 |
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(1.College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha 410073, China;2.College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China)
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| Abstract: |
| With the leader-follower formation pattern, a method for UAV formation rendezvous was developed based on the pursuit strategy. Firstly, the UAV non-decoupling 3D kinematics models were established by using the curve theory of differential geometry and the Frenet-Serret frames, where the curvature and the torsion were considered as the control effort. Secondly, the mathematical descriptions of the three-dimensional formation rendezvous were provided with the models, where the impact angular constraint in missile guidance was mapped to a flight path angle of the follower in formation rendezvous, and an additional azimuth angular constraint was introduced. Thirdly, the orientation deviation between the leader and the follower was measured by using an element of the special orthogonal group, and the element was mapped to a twist in an Lie algebra space corresponding to the Lie group by local coordinate mapping. Then, a geometric guidance law for formation rendezvous was developed by using the twist, and the corresponding curvature command and torsion command were presented. Finally, the numerical simulation for multi-UAVs formation rendezvous was carried out, under the leader flying straightly and making a turn, respectively. The simulation results show that the follower can track the orientation of the leader successfully and can converge to a specified configuration, which indicates that the proposed method is available. |
| Keywords: unmanned aerial vehicle formation rendezvous differential geometry Lie group geometric control |
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