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基于定制内点法的多无人机协同轨迹规划

王祝 徐广通 龙腾

王祝, 徐广通, 龙腾. 基于定制内点法的多无人机协同轨迹规划. 自动化学报, 2020, 41(x): 1−11 doi: 10.16383/j.aas.c200361
引用本文: 王祝, 徐广通, 龙腾. 基于定制内点法的多无人机协同轨迹规划. 自动化学报, 2020, 41(x): 1−11 doi: 10.16383/j.aas.c200361
Wang Zhu, Xu Guang-Tong, Long Teng. Customized interior-point method for cooperative trajectory planning of unmanned aerial vehicles. Acta Automatica Sinica, 2020, 41(x): 1−11 doi: 10.16383/j.aas.c200361
Citation: Wang Zhu, Xu Guang-Tong, Long Teng. Customized interior-point method for cooperative trajectory planning of unmanned aerial vehicles. Acta Automatica Sinica, 2020, 41(x): 1−11 doi: 10.16383/j.aas.c200361

基于定制内点法的多无人机协同轨迹规划

doi: 10.16383/j.aas.c200361
基金项目: 国家自然科学基金(61903033), 中央高校基本科研业务费专项资金(2020MS116), 中国博士后科学基金(2018M631361)资助
详细信息
    作者简介:

    王祝:华北电力大学自动化系讲师, 主要研究方向为机器人自主控制、轨迹规划、多机器人系统

    徐广通:北京理工大学宇航学院博士研究生, 主要研究方向为多无人机轨迹规划、凸优化

    龙腾:北京理工大学宇航学院教授, 主要研究方向为飞行器总体设计、多学科设计优化、协同任务规划

Customized Interior-Point Method for Cooperative Trajectory Planning of Unmanned Aerial Vehicles

Funds: Supported by National Natural Science Foundation of China (61903033), Fundamental Research Funds for the Central Universities (2020MS116), China Postdoctoral Science Foundation (2018M631361)
  • 摘要: 为了提高多无人机协同轨迹规划效率, 在解耦序列凸优化方法基础上, 提出一种高效求解凸优化子问题的定制内点法. 首先引入松弛变量, 构建子问题的等价描述形式, 并推导该形式下的子问题最优性条件. 然后在预测-校正原对偶内点法的框架下, 构建一套高效求解最优性条件方程组的计算流程以降低子问题计算复杂度, 并利用约束矩阵特征提出一种快速计算原对偶搜索方向的方法以提高规划效率. 仿真结果表明, 在解耦序列凸优化框架下, 定制内点法可将协同轨迹规划耗时降低一个数量级, 达到秒级.
  • 图  1  多无人机协同轨迹规划问题示意图

    Fig.  1  Illustration of multi-UAV cooperative trajectory planning problems

    图  2  解耦SCP方法架构

    Fig.  2  Frame of decoupled SCP method

    图  3  原对偶内点法计算框架

    Fig.  3  Frame of primal-dual interior-point method

    图  4  原对偶搜索方向计算复杂度变化图

    Fig.  4  Variations of computation complexity for primal-dual search direction

    图  5  编队集结协同轨迹二维结果图

    Fig.  5  Cooperative trajectories in 2D for formation rendezvous

    图  6  编队集结协同轨迹规划三维结果图

    Fig.  6  Cooperative trajectories in 3D for formation rendezvous

    图  7  编队重构协同轨迹规划二维结果图

    Fig.  7  Cooperative trajectories in 2D for formation reconfiguration

    图  8  编队重构协同轨迹规划三维结果图

    Fig.  8  Cooperative trajectories in 3D for formation reconfiguration

    图  9  编队集结任务无人机间最短距离变化曲线

    Fig.  9  History of minimum distance between UAVs for formation rendezvous

    图  10  编队重构任务无人机间最短距离变化曲线

    Fig.  10  History of minimum distance between UAVs for formation reconfiguration

    图  11  编队集结任务完成时间优化结果

    Fig.  11  Optimized completion time for formation rendezvous

    图  12  编队重构任务完成时间优化结果

    Fig.  12  Optimized completion time for formation reconfiguration

    图  13  基于SeDuMi的编队集结轨迹规划结果

    Fig.  13  Trajectory planning results using SeDuMi for formation rendezvous

    图  14  基于定制内点法的编队集结轨迹规划结果

    Fig.  14  Trajectory planning results using customized interior-point method for formation rendezvous

    图  15  基于SeDuMi的编队重构轨迹规划结果

    Fig.  15  Trajectory planning results using SeDuMi for formation reconfiguration

    图  16  基于定制内点法的编队重构轨迹规划结果

    Fig.  16  Trajectory planning results using customized interior-point method for formation reconfiguration

    图  17  编队集结轨迹规划耗时

    Fig.  17  Computation time for formation reconfiguration

    图  18  编队重构轨迹规划耗时

    Fig.  18  Computation time for formation reconfiguration

    表  1  原对偶搜索方向计算复杂度

    Table  1  Computation complexity for primal-dual search direction

    计算方法计算成本
    方法I 0.33$n_{{X}}^3$+3$n_A^3$+$n_{{X}}^2{n_A}$+${n_{{X}}}n_A^2$
    方法II2.67$n_{{X}}^3$+3$n_A^3$+$n_{{X}}^2{n_A}$+${n_{{X}}}n_A^2$
    方法III2.67(${n_{{X}}}$+2${n_A}$)3
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出版历程
  • 收稿日期:  2020-05-27
  • 修回日期:  2020-10-08
  • 网络出版日期:  2020-12-11

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