﻿ 高空太阳能无人机三维航迹优化<sup>*</sup>
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Three-dimensional optimal path planning for high-altitude solar-powered UAV
WANG Shaoqi, MA Dongli, YANG Muqing, ZHANG Liang
School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, China
Received: 2018-08-31; Accepted: 2018-10-15; Published online: 2018-10-29 14:59
Corresponding author. YANG Muqing. E-mail: buaa_yangli@163.com
Abstract: In order to enhance the flight performance and load capacity of high-altitude solar-powered UAV, a three-dimensional optimal path planning model that examines the interaction between flight status, energy acquisition, storage, and consumption was established. The Gauss pseudo-spectral method was employed to transform the optimal control problem into a nonlinear programming problem through approximating the state variables and control variables on discrete points and satisfying the constraints of dynamic equations on a set of collocation points. Then optimization and simulation were carried out for a typical point-to-point mission and the optimum path was compared with current constant-altitude constant-velocity path. The results indicate that appropriate changes of flight attitude angle increase the net energy of solar-powered UAV by 9.2%. By comprehensive utilization of changing flight attitude angle and flight altitude, the proposed optimum path brings more energy profits, which improves the battery pack final state of charge by 18.8%.
Keywords: solar-powered UAV     optimal path planning     solar cell     battery pack     Gauss pseudo-spectral method

1 航迹优化建模 1.1 动力学模型

 (1)
 图 1 地面坐标系和机体坐标系示意图 Fig. 1 Schematic diagram of earth-fixed coordinate system and aircraft body-fixed coordinate system

 (2)

CLCD受翼型、迎角α和雷诺数Re的影响，通过式(3)计算，式中系数AijBij通过计算流体力学(Computational Fluid Dynamics，CFD)方法得到，数值见表 1表 2

 (3)

 i j=0 j=1 j=2 0 7.983×10-1 9.208×10-3 -9.792×10-5 1 5.898×100 1.392×10-2 2.255×10-3 2 -7.246×100 4.610×10-2 -1.894×10-2

 i j=0 j=1 j=2 0 2.284×10-2 -6.603×10-4 1.493×10-5 1 1.403×10-1 2.108×10-4 -8.493×10-5 2 1.362×100 -6.438×10-2 2.983×10-3

 (4)

1.2 能源系统模型

1.2.1 太阳能电池模型

 (5)

 (6)

 (7)

 (8)

 (9)

1.2.2 储能电池模型

 (10)

 (11)

1.2.3 功率消耗模型

 (12)

 (13)

 (14)
 (15)

 i j=0 j=1 j=2 0 -2.481×100 2.783×100 -1.818×10-1 1 6.882×100 -4.081×100 -1.432×100 2 -3.640×100 8.042×10-1 2.200×100

 (16)
1.3 优化问题描述

αϕPBT为控制变量，以任务结束时刻储能电池的电量状态SOCf为目标函数，高空太阳能无人机三维飞行航迹优化问题可以描述为最优控制问题，即

 (17)

2 离散方法

 (18)

N阶Legendre-Gauss多项式GN(τ)的零点τ={τ1, τ2, …, τN}作为配点，τ分布在区间(-1, 1)上，添加τ0=-1，以τ*={τ0, τ1, …, τN}作为离散点。

 (19)

N+1阶Lagrange插值多项式Li(τ)作为基函数，将状态变量近似为

 (20)

 (21)

 (22)

 (23)

 (24)

 (25)

 (26)

 (27)

3 优化结果分析 3.1 仿真参数

 参数 数值 m/kg 134 S/m2 25.5 Ssc/m2 20.4 Dp/m 1.5 c0.75R/m 0.10 QB/(kW·h) 21.5 VOC/V 120 RI/Ω 0.12

 % 参数 数值 ηsc 21 ηMPPT 95 ηm 90

3.2 结果分析

1) 当Psc=0且SOC > 0.25时，令PB=Pm

2) 当Psc > 0且0.25≤SOC < 0.9时，令PB= Pm-Psc

3) 当Psc > 0且SOC=0.9时，令PB=0。

 参数 常规航迹 优化航迹 净吸收能量/(kW·h) 31.60 34.51 SOC最小值 0.261 0.272 SOCf 0.560 0.665 最小飞行高度/km 15.0 15.0 最大飞行高度/km 15.0 22.6

 图 2 常规航迹及优化航迹功率 Fig. 2 Power of common flight path and optimized flight path

 图 3 航迹在x-y平面内的投影对比 Fig. 3 Comparison of flight path projection on x-y plane

 图 4 常规航迹与优化航迹的飞行高度及飞行速度对比 Fig. 4 Comparison of flight altitude and velocity between common and optimized flight path
 图 5 常规航迹与优化航迹的迎角、滚转角、航迹倾角和航迹偏角对比 Fig. 5 Comparison of angle of attack, roll angle, flight path angle and heading angle between common and optimized flight path

 图 6 常规航迹与优化航迹的储能电池电量状态对比 Fig. 6 Comparison of battery pack state of charge between common and optimized flight path

4 结论

1) 高斯伪谱法适用于高空太阳能无人机航迹优化问题。

2) 通过调整飞行姿态，可以使高空太阳能无人机的净吸收能量提高9.2%。

3) 结合调整飞行姿态和改变飞行高度两种措施能够获得更大的能量优势，使储能电池剩余电量提高18.8%。

4) 为了使储能电池剩余电量最大化，应在储能电池充满电之后再爬升。

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文章信息

WANG Shaoqi, MA Dongli, YANG Muqing, ZHANG Liang

Three-dimensional optimal path planning for high-altitude solar-powered UAV

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(5): 936-943
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0511