基于DMPC-A*融合的多无人机路径规划算法

赵礼强; 刘雨欣; 王尔申; 徐宝升; 纪贵鹏

doi:10.3963/j.jssn.1674-4861.2025.05.017

基于DMPC-A*融合的多无人机路径规划算法

doi: 10.3963/j.jssn.1674-4861.2025.05.017

赵礼强^1,,
刘雨欣²,
王尔申^{2, 3, ,},
徐宝升²,
纪贵鹏⁴

1.
沈阳航空航天大学经济与管理学院沈阳 110136
2.
沈阳航空航天大学民用航空学院沈阳 110136
3.
沈阳航空航天大学电子信息工程学院沈阳 110136
4.
沈阳航空航天大学航空宇航学院沈阳 110136

基金项目:

国家自然科学基金项目 62173237

辽宁省应用基础研究计划项目 2025JH2/101300011

辽宁省教育厅科技计划项目 20250054

辽宁省教育厅科技计划项目 310125011

详细信息

作者简介:
赵礼强（1975—），博士，教授. 研究方向：交通运输规划与管理等. E-mail: zhao_liqiang@163.com

通讯作者:
王尔申（1980—），博士，教授. 研究方向：GNSS全球卫星导航定位等. E-mail: wanges_2016@126.com

中图分类号: U8
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- 被引次数: 0
出版历程
- 收稿日期: 2024-12-29
- 网络出版日期: 2026-03-05

A Multi-UAV Path Planning Algorithm Based on DMPC-A* Fusion

1.
College of Economics and Management, Shenyang Aerospace University, Shenyang 110136, China
2.
College of Civil Aviation, Shenyang Aerospace University, Shenyang 110136, China
3.
College of Electronic and Information Engineering, Shenyang Aerospace University, Shenyang 110136, China
4.
College of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China

摘要

摘要: 针对复杂三维空域环境中多无人机协同目标跟踪和动态避障的路径规划所面临的效率低、飞行稳定性差的问题，研究了基于分布式模型预测控制（distributed model predictive control，DMPC）与A*搜索算法融合的路径优化方法。利用A*算法生成多无人机的全局初始路径，为各无人机分配合理的目标航迹点，并为无人机提供基本可行的安全航迹。将贝塞尔曲线与DMPC预测模型融合，通过对曲线控制点参数优化实现路径平滑性和航迹连续性的提升，并综合考虑无人机动力学约束、航迹长度约束、安全距离约束及通信条件约束，构建多目标代价函数并采用滚动优化求解，实现航迹的实时动态调整。为平衡航程、威胁、能耗和控制输入等多个代价，重新标定代价权重系数，保证群体飞行的安全性和全局最优性。同时，针对传统集中式模型预测控制（model predictive control，MPC）计算量大、实时性差的问题，采用分布式求解策略，使得每架无人机独立优化控制输入，并通过信息交互实现协同目标跟踪，从而显著降低算法的计算复杂度。实验仿真环境采用5.2 m× 5.2 m×3.0m三维空间，部署10架无人机及不同形状的静态障碍物，通过多个Python程序仿真实验来验证方法的有效性。结果表明：与传统算法相比，本文提出的DMPC-A*融合方法可将路径长度缩短约4.2%，此外，航迹平滑度和稳定性也有所提升。本文算法具备良好的障碍规避能力和环境适应性，为多无人机协同路径规划的研究提供技术支撑。
- 多无人机 /
- 协同路径规划 /
- 分布式模型预测控制 /
- A*搜索算法 /
- 贝塞尔曲线
Abstract: Aiming at the problems of low efficiency and poor flight stability faced by path planning for multi-UAV cooperative target tracking and dynamic obstacle avoidance in complex three-dimensional airspace environments, A path optimization method based on the integration of distributed model predictive control (DMPC) and A* search algorithm was studied. The A* algorithm is utilized to generate the global initial paths of multiple unmanned aerial vehicles (UAVs), assign reasonable target trajectory points to each UAV, and provide basically feasible safe trajectories for the UAVs. The Bezier curve is integrated with the DMPC prediction model. By optimizing the parameters of the curve control points, the smoothness of the path and the continuity of the track are improved. Considering the dynamic constraints of the unmanned aerial vehicle, the track length constraints, the safety distance constraints and the communication condition constraints comprehensively, a multi-objective cost function is constructed and solved by rolling optimization to achieve real-time dynamic adjustment of the track. To balance multiple costs such as flight range, threat, energy consumption and control input, the cost weight coefficients are recalibrated to ensure the safety and global optimality of group flight. Meanwhile, in view of the problems of large computational load and poor real-time performance of the traditional centralized model predictive control (MPC), a distributed solution strategy is adopted, enabling each unmanned aerial vehicle to independently optimize the control input and achieve collaborative target tracking through information interaction, thereby significantly reducing the computational complexity of the algorithm. The experimental simulation environment adopts a three-dimensional space of 5.2 m×5.2 m×3.0 m, deploys 10 unmanned aerial vehicles and static obstacles with different shapes, and verifies the effectiveness of the method through multiple Python program simulation experiments. The results show that: Compared with the traditional algorithm, the DMPC-A* fusion method proposed in this paper can shorten the path length by approximately 4.2%. Besides, the track smoothness and stability are also improved. The algorithm proposed in this paper has good obstacle avoidance ability and environmental adaptability, providing technical support for the research on collaborative path planning for multiple unmanned aerial vehicles.
- multiple unmanned aerial vehicles /
- collaborative path planning /
- distributed model predictive control /
- A* search algorithm /
- Bezier curve

HTML全文

图 1 DMPC的工作原理图

Figure 1. The working principle diagram of DMPC

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图 2 DMPC-A*融合算法流程图

Figure 2. DMPC-A* fusion algorithm flowchart

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图 3 6架无人机初始位置

Figure 3. Initial positions of 6 UAVs

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图 4 6架无人机飞行过程中路径探索

Figure 4. Path exploration of 6 UAVs in flight process

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图 5 6架无人机到达各自目标点

Figure 5. 6 UAVs reached the target location

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图 6 8架无人机初始位置

Figure 6. Initial positions of 8 UAVs

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图 7 8架无人机目标位置

Figure 7. The target locations for 8 UAVs

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图 8 20架无人机初始位置

Figure 8. Initial positions of 20 UAVs

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图 9 20架无人机飞行中路径探索

Figure 9. Path exploration for 20 UAVs in flight

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图 10 20架无人机目标位置

Figure 10. The target locations for the 20 UAVs

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图 11 有障碍物时A*搜索算法的路径图初始状态

Figure 11. Initial state of the path map for the A* search algorithm when obstacles are present

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图 12 有障碍物时A*搜索算法的路径图最终位置

Figure 12. Final position on the path map of the A* search algorithm when obstacles are present

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图 13 有障碍物时DMPC的路径图初始状态

Figure 13. Initial state of the DMPC path map when obstacles are present

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图 14 有障碍物时DMPC的路径图最终位置

Figure 14. Final positions of the DMPC path map when obstacles are present

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图 15 有障碍物时DMPC-A*融合算法的初始状态

Figure 15. Initial state of the DMPC-A* fusion algorithm in the presence of obstacles

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图 16 有障碍物时DMPC-A*融合算法的最终位置

Figure 16. Final position of the DMPC-A* fusion algorithm in the presence of obstacles

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表 1 系统初始化数值

Table 1. System initialization values

参数	数值
航迹长度约束/m	5
飞行高度/m	1.2
安全距离/m	1.2
最大速度/（m/s）	1.5
四旋翼重量/kg	5
半径/cm	2.4
无人机速度/（m/s）	1.5
最大偏航角/（°）	60

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表 2 6架无人机初始位置和目标位置

Table 2. Initial and target positions of 6 UAVs

无人机编号	初始位置（x，y，z）	目标位置（x，y，z）
无人机1	1.83, 1.22, 0.5	-2.44, -3.05, 0.5
无人机2	0.61, 2.44, 0.5	0, -0.61, 0.5
无人机3	-2.44, 0.61, 0.5	0.61, -3.05, 0.5
无人机4	-1.83, -0.61, 0.5	2.44, -1.83, 0.5
无人机5	0.61, -3.05, 0.5	-2.44, 0.61, 0.5
无人机6	2.44, -1.83, 0.5	-1.83, -0.61, 0.5

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表 3 8架无人机初始位置和目标位置

Table 3. Initial and target positions of 8 UAVs

无人机编号	初始位置（x, y, z）	目标位置（x, y, z）
无人机1	1.83, 1.22, 0.5	-2.44, -3.05, 0.5
无人机2	0.61, 2.44, 0.5	0, -0.61, 0.5
无人机3	-2.44, 0.61, 0.5	0.61, -3.05, 0.5
无人机4	-1.83, -0.61, 0.5	2.44, -1.83, 0.5
无人机5	-2.44, -3.05, 0.5	1.83, 1.22, 0.5
无人机6	0, -0.61, 0.5	0.61, 2.44, 0.5
无人机7	0.61, -3.05, 0.5	-2.44, 0.61, 0.5
无人机8	2.44, -1.83, 0.5	-1.83, -0.61, 0.5

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表 4 障碍物位置

Table 4. Obstacle Location

障碍物编号	初始位置(x，y，z，r)
圆锥障碍物1	1.90，0.61，1.5，0.3
圆锥障碍物2	0.61，1.22，2.0，0.4
圆锥障碍物3	-1.83，1.22，1.8，0.25
圆柱障碍物1	-1.22，0，1.2，0.35
圆柱障碍物2	-1.22，-1.22，1.5，0.4
圆柱障碍物3	-0.61，-1.90，1.0，0.3

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表 5 长方体障碍物位置

Table 5. Rectangular obstacle location

障碍物编号	初始位置（x，y，z）
障碍物1	1.83，-1.90，1.2
障碍物2	1.90，-1.22，0.9

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表 6 无人机初始位置和目标位置

Table 6. Initial and target positions of UAVs

无人机编号	初始位置（x，y，z）	目标位置（x，y，z）
无人机1	1.83，1.22，0.5	-2.44，-1.95，0.5
无人机2	0.61，2.44，0.5	0，-0.61，0.5
无人机3	-2.44，0.61，0.5	0.61，-1.95，0.5
无人机4	-1.83，-0.61，0.5	2.44，-1.83，0.5
无人机5	-2.44，-1.95，0.5	1.83，1.22，0.5
无人机6	0，-0.61，0.5	0.61，2.44，0.5
无人机7	0.61，-1.95，0.5	-2.44，0.61，0.5
无人机8	2.44，-1.83，0.5	-1.83，-0.61，0.5

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表 7 算法性能对比

Table 7. Algorithm Performance Comparison

算法	平均路径长度/m	计算时间/s	避障成功率/%	能量消耗/J
A*算法	8.76	0.42	92.5	156.3
DMPC算法	8.43	1.23	96.2	142.8
DMPC-A*算法	8.19	0.58	98.5	138.5

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