高原山区无人机运动轨迹规划及能耗评估模型

伍景琼; 田娜; 陈子伟; 奠然; 李云起

doi:10.3963/j.jssn.1674-4861.2025.04.010

高原山区无人机运动轨迹规划及能耗评估模型

doi: 10.3963/j.jssn.1674-4861.2025.04.010

伍景琼^1, ,,
田娜^{1, 2},
陈子伟¹,
奠然¹,
李云起¹

1.
昆明理工大学交通工程学院昆明 650500
2.
云南交通运输职业学院交通安全与应急管理学院昆明 650300

基金项目:

国家自然科学基金项目 71904068

云南省“兴滇英才支持计划”青年人才项目 XDYC-QNRC-2023-0122

云南省大学生创新训练项目 S202410674149

详细信息

通讯作者:
伍景琼（1984—），博士，副教授. 研究方向：物流系统优化、冷链物流等. E-mail：mote_1984@163.com

中图分类号: U8
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出版历程
- 收稿日期: 2024-12-17

Trajectory Planning and Energy Consumption Evaluation Model of UAVs in Plateau and Mountainous Areas

WU Jingqiong^{1
, ,},
TIAN Na^{1, 2},
CHEN Ziwei¹,
DIAN Ran¹,
LI Yunqi¹

1.
Faculty of Transportation Engineering, Kunming University of Science and Technology, Kunming 650500, China
2.
Faculty of Traffic Safety and Emergency Management, Yunnan Vocational College of Transportation, Kunming 650300, China

摘要

摘要: 为解决无人机在高原山区复杂地形环境下的路径规划与能耗评估不精准的问题，研究了基于高分辨率数字高程模型的三维运动轨迹规划与电池容量评估方法。以无人机飞行的地形适应性为核心，利用高分辨率数字高程数据构建三维数字地形图，综合考虑飞行范围、飞行高度和路径精度约束，建立以路径长度最小化、高度变化最小化和偏转角最小化为目标的加权优化函数，构建高原山区无人机三维运动轨迹规划模型，从而能够准确反映地形起伏对飞行轨迹的影响。进一步修正空间直线路径与实际飞行航迹的偏差，量化横向距离飞行与纵向高度爬升对单位能耗的影响，构建无人机电池容量评估模型，并开展能耗分析。以云南省迪庆州香格里拉市建塘镇吉迪村为案例，规划松茸交易市场与15个采集点间的无人机飞行轨迹，并对耗电进行精准评估。结果表明：修正后飞行路径比直线距离增加264~724 m，修正率为2.85%~18.94%，平均修正值438 m，平均修正率7.64%；单点单向运输任务总能耗集中在28%~58%，显示出一定的任务扩展潜力。在所有航线中，识别出38条能耗超过正常分布范围的潜在风险路线，以及4条能耗明显偏高的高风险路线。通过采用低能耗替代路段、选择高效机型和设置中途补给站等策略，可有效降低能耗风险，提升无人机在高原山区的运输可行性。
- 高原山区 /
- 无人机 /
- 轨迹规划 /
- 能耗评估 /
- 数字高程模型
Abstract: To address the challenges of trajectory planning and energy evaluation for unmanned aerial vehicles (UAVs) in plateau mountainous terrains, a three-dimensional path planning and battery capacity evaluation method is proposed. High-resolution digital elevation data are applied to construct a 3D terrain model, incorporating constraints such as flight range, altitude, and path accuracy. A weighted optimization function with objectives of minimizing path length, altitude variation, and deflection angle is designed to build a UAV trajectory planning model that reflects terrain undulation. Deviations between spatial straight-line paths and actual flight trajectories are corrected, and the effects of lateral distance flight and vertical altitude ascent on unit energy consumption are quantified. Based on this, a UAV battery capacity evaluation model is constructed to support energy analysis. An application is carried out in Jidi Village, Jiantang Town, Shangri-La City, Diqing Tibetan Autonomous Prefecture, Yunnan Province, where flight paths between a matsutake trading market and fifteen collection sites are evaluated. Results indicate that the corrected flight paths are 264—724 m longer than straight line paths, with an average correction of 438 m and an average correction rate of 7.64%. Energy consumption for single-point one-way tasks ranges from 28% and 58%, revealing task expansion potential. Among all flight routes, 38 potentially high-energy-risk routes and 4 significant high-risk routes are identified. Strategies including low-energy alternative routes, efficient UAV selection, and mid-route supply stations are found effective to reduce energy risks and enhance the feasibility of UAV transportation in plateau mountainous environments.
- plateau and mountainous areas /
- unmanned aerial vehicle /
- trajectory planning /
- energy consumption evaluation /
- digital elevation model

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图 1 高原山区数字地形图

Figure 1. Digital topographic map in plateau mountainous area

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图 2 高原山区无人机实际飞行情况

Figure 2. The actual flight situation of UAV in plateau mountainous area

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图 3 采集点整体分布图

Figure 3. The overall distribution map of the collection points

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图 4 各算法收敛曲线对比

Figure 4. Comparison of convergence curves of various algorithms

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图 5 无人机飞行距离修正值热图

Figure 5. UAV flight distance correction value heat map

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图 6 无人机飞行距离修正率热图

Figure 6. UAV flight distance correction rate heat map

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图 7 5↔6无人机运动轨迹规划

Figure 7. 5↔6 UAV trajectory planning

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图 8 2↔3无人机运动轨迹规划

Figure 8. 2↔3 UAV trajectory planning

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图 9 2↔4无人机运动轨迹规划

Figure 9. 2↔4 UAV trajectory planning

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图 10 2↔14无人机运动轨迹规划

Figure 10. 2↔14 UAV trajectory planning

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图 11 高原山区无人机能耗百分比热图

Figure 11. Percentage heat map of UAV energy consumption in plateau mountainous area

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表 1 DBO算法主要运行参数设置

Table 1. Input volume of external road

参数符号	参数含义	参数取值
nPop	种群数规模	30
MaxIt	最大迭代次数	50
n Var	变量的数量	3N
Var Min	解空间的下界	0
Var Max	解空间的上界	1
CostFunction	成本函数	minJ_cost

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表 2 模型参变量设置

Table 2. Model parameter setting

类别	符号	参变量含义	参变量取值
目标函数参数	ω₁	飞行距离成本函数权重	0.5
	ω₂	飞行高度成本函数权重	0.3
	ω3	飞行偏转角成本函数权重	0.2
约束条件参数	h_safe	无人机安全飞行高度	100
约束条件参数	n	路径精度系数	1
变量	Q₁(x₁, y₁, z₁)	无人机起点坐标	根据求解需要设置
变量	Q_N(x_N, y_N, z_N)	无人机终点坐标	根据求解需要设置

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表 3 采集点地理坐标信息

Table 3. Collect the geographic coordinate information of the point

序号	经度/(°)	纬度/(°)	高度/m
0	99.655 7	28.040 4	3 348
1	99.639 6	28.094 0	3 518
2	99.676 3	28.093 8	3 708
3	99.663 2	28.074 0	3 441
4	99.669 0	28.105 1	3 751
5	99.712 6	28.043 2	3 458
6	99.609 0	28.108 2	3 554
7	99.622 6	28.095 1	3 661
8	99.618 2	28.011 3	3 517
9	99.622 6	28.069 6	3 542
10	99.680 1	28.008 7	3 500
11	99.684 0	28.046 5	3 437
12	99.694 3	28.069 3	3 514
13	99.624 3	28.044 9	3 380
14	99.606 3	28.027 1	3 591
15	99.639 6	28.002 1	3 509

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表 4 三维欧氏距离矩阵

Table 4. Three-dimensional Euclidean distance matrix 单位: km

d_j	d_i
d_j	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
0	0	6.152 9	6.268 5	3.799 0	7.303 5	5.607 3	8.812 1	6.890 8	4.904 4	4.595 8	4.259 3	2.866 4	4.971 1	3.129 2	5.084 8	4.535 4
1	6.152 9	0	3.613 9	3.210 9	3.150 6	9.125 8	3.396 0	1.682 2	9.408 4	3.180 5	10.263 0	6.842 2	6.036 4	5.650 1	8.109 3	10.190 0
2	6.268 5	3.613 9	0	2.559 5	1.444 7	6.655 0	6.809 0	5.282 6	10.788 2	5.926 0	9.445 8	5.306 1	3.248 3	7.460 8	10.105 6	10.791 8
3	3.799 0	3.210 9	2.559 5	0	3.509 0	5.939 2	6.542 0	4.632 8	8.242 4	4.024 0	7.429 2	3.672 0	3.103 6	5.005 5	7.641 7	8.303 8
4	7.303 5	3.150 6	1.444 7	3.509 0	0	8.098 4	5.912 6	4.696 1	11.541 4	6.029 8	10.747 7	6.670 5	4.690 9	8.001 4	10.623 7	11.784 0
5	5.607 3	9.125 8	6.655 0	5.939 2	8.098 4	0	12.480 6	10.560 0	9.939 0	9.324 6	4.986 1	2.837 3	3.408 6	8.688 9	10.610 3	8.506 7
6	8.812 1	3.396 0	6.809 0	6.542 0	5.912 6	12.480 6	0	1.977 3	10.782 6	4.484 2	13.062 7	10.060 9	9.432 1	7.180 4	8.996 6	12.143 6
7	6.890 8	1.682 2	5.282 6	4.632 8	4.696 1	10.560 0	1.977 3	0	9.303 2	2.830 0	11.126 6	8.096 8	7.610 8	5.575 9	7.709 0	10.447 9
8	4.904 4	9.408 4	10.788 2	8.242 4	11.541 4	9.939 0	10.782 6	9.303 2	0	6.478 9	6.098 2	7.559 9	9.869 6	3.776 1	2.108 5	2.340 0
9	4.595 8	3.180 5	5.926 0	4.024 0	6.029 8	9.324 6	4.484 2	2.830 0	6.478 9	0	8.809 1	6.561 0	7.052 0	2.748 6	4.978 1	7.669 2
10	4.259 3	10.263 0	9.445 8	7.429 2	10.747 7	4.986 1	13.062 7	11.126 6	6.098 2	8.809 1	0	4.209 3	6.863 1	6.802 0	7.543 6	4.052 3
11	2.866 4	6.842 2	5.306 1	3.672 0	6.670 5	2.837 3	10.060 9	8.096 8	7.559 9	6.561 0	4.209 3	0	2.724 6	5.875 8	7.942 7	6.582 3
12	4.971 1	6.036 4	3.248 3	3.103 6	4.690 9	3.408 6	9.432 1	7.610 8	9.869 6	7.052 0	6.863 1	2.724 6	0	7.399 1	9.840 8	9.191 4
13	3.129 2	5.650 1	7.460 8	5.005 5	8.001 4	8.688 9	7.180 4	5.575 9	3.776 1	2.748 6	6.802 0	5.875 8	7.399 1	0	2.660 1	4.980 4
14	5.084 8	8.109 3	10.105 6	7.641 7	10.623 7	10.610 3	8.996 6	7.709 0	2.108 5	4.978 1	7.543 6	7.942 7	9.840 8	2.660 1	0	4.292 8
15	4.535 4	10.190 0	10.791 8	8.303 8	11.784 0	8.506 7	12.143 6	10.447 9	2.340 0	7.669 2	4.052 3	6.582 3	9.191 4	4.980 4	4.292 8	0

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表 5 各算法对比结果

Table 5. Comparison results of various algorithms

算法	平均最优值	平均运行时间/s
DBO	589.18	30.55
ABC	627.82	65.43
GA	685.66	29.74
DE	631.87	29.63

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表 6 无人机飞行近似距离矩阵

Table 6. UAV flight approximate distance matrix 单位: km

d'_j	d'_i
d'_j	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
0	0	6.669 8	6.753 3	4.280 9	7.972 0	6.068 7	9.446 8	7.394 1	5.272 0	4.893 7	4.736 4	3.192 2	5.468 1	3.483 2	5.437 2	4.911 5
1	6.669 8	0	3.964 9	3.533 1	3.424 3	9.710 4	3.760 1	1.982 7	9.909 9	3.589 2	10.971 7	7.330 7	6.515 7	6.161 5	8.555 1	10.623 3
2	6.753 3	3.964 9	0	2.823 6	1.718 3	7.083 4	7.238 1	5.647 8	11.131 2	6.250 2	9.946 3	5.706 4	3.519 2	7.799 3	10.393 7	11.158 7
3	4.280 9	3.533 1	2.823 6	0	3.930 0	6.416 9	7.029 0	5.026 0	8.698 6	4.455 6	8.106 3	4.107 6	3.488 5	5.465 4	8.047 8	8.833 7
4	7.972 0	3.424 3	1.718 3	3.930 0	0	8.621 4	6.295 5	5.005 4	11.878 7	6.380 2	11.387 4	7.116 9	5.065 7	8.343 5	10.938 7	12.170 6
5	6.068 7	9.710 4	7.083 4	6.416 9	8.621 4	0	13.204 7	11.156 2	10.416 3	9.825 4	5.441 1	3.155 1	3.810 2	9.290 1	11.087 6	8.958 9
6	9.446 8	3.760 1	7.238 1	7.029 0	6.295 5	13.204 7	0	2.269 1	11.437 3	4.936 6	13.745 9	10.770 4	10.052 4	7.743 1	9.506 5	12.792 0
7	7.394 1	1.982 7	5.647 8	5.026 0	5.005 4	11.156 2	2.269 1	0	9.827 6	3.218 9	11.701 0	8.659 7	8.131 8	6.091 6	8.095 3	10.899 3
8	5.272 0	9.909 9	11.131 2	8.698 6	11.878 7	10.416 3	11.437 3	9.827 6	0	6.825 3	6.394 5	7.968 5	10.400 0	4.118 5	2.440 0	2.642 9
9	4.893 7	3.589 2	6.250 2	4.455 6	6.380 2	9.825 4	4.936 6	3.218 9	6.825 3	0	9.182 9	6.915 6	7.622 0	3.063 8	5.257 5	8.102 7
10	4.736 4	10.971 7	9.946 3	8.106 3	11.387 4	5.441 1	13.745 9	11.701 0	6.394 5	9.182 9	0	4.555 8	7.308 5	7.218 1	7.869 5	4.345 5
11	3.192 2	7.330 7	5.706 4	4.107 6	7.116 9	3.155 1	10.770 4	8.659 7	7.968 5	6.915 6	4.555 8	0	3.065 1	6.284 4	8.342 6	7.046 0
12	5.468 1	6.515 7	3.519 2	3.488 5	5.065 7	3.810 2	10.052 4	8.131 8	10.400 0	7.622 0	7.308 5	3.065 1	0	7.944 3	10.278 4	9.710 4
13	3.483 2	6.161 5	7.799 3	5.465 4	8.343 5	9.290 1	7.743 1	6.091 6	4.118 5	3.063 8	7.218 1	6.284 4	7.944 3	0	2.950 2	5.363 9
14	5.437 2	8.555 1	10.393 7	8.047 8	10.938 7	11.087 6	9.506 5	8.095 3	2.440 0	5.257 5	7.869 5	8.342 6	10.278 4	2.950 2	0	4.702 3
15	4.911 5	10.623 3	11.158 7	8.833 7	12.170 6	8.958 9	12.792 0	10.899 3	2.642 9	8.102 7	4.345 5	7.046 0	9.710 4	5.363 9	4.702 3	0

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表 7 关键飞行路线信息

Table 7. Key flight route information collation

飞行路线(采集点)	空间直线距离/km	目标函数值	飞行近似距离/km	距离修正值/m	距离修正率/%
5↔6	12.480 6	1 687.089	13.204 7	724	5.80
2↔3	2.559 5	438.234 5	2.823 6	264	10.32
2↔4	1.444 7	319.847 5	1.718 3	274	18.94
2↔14	10.105 6	439.687 6	10.393 7	288	2.85

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表 8 能耗情况统计

Table 8. Energy consumption statistics 单位: %

统计指标	Max	Min	Avg	SD	Med
距离能耗	68.73	8.59	35.31	14.22	35.19
爬升能耗	16.89	2.97	7.62	3.11	7.28
总能耗平均值	80.10	13.93	42.92	14.95	42.15

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