﻿ 自适应引导长度的无人机航迹跟踪方法<sup>*</sup>
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1. 国防科学技术大学 航天科学与工程学院, 长沙 410073;
2. 海军航空工程学院 飞行器工程系, 烟台 264001

Path following method with adaptive guidance length for unmanned aerial vehicles
LI Yue1,2, CHEN Qingyang1, HOU Zhongxi1
1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China;
2. Department of Airborne Vehicle Engineering, Naval Aeronautical and Astronautical University, Yantai 264001, China
Received: 2016-06-15; Accepted: 2016-09-21; Published online: 2016-11-14 09:09
Foundation item: China Postdoctoral Science Foundation (2014M562652)
Corresponding author. CHEN Qingyang, E-mail: chy1982_008@nudt.edu.cn
Abstract: To guarantee the flight stability and high accuracy of path following for unmanned aerial vehicles (UAVs), a nonlinear path following method with adaptive guidance length is proposed. First, the kinematic model of UAVs was built. Second, the relation between guidance length and velocity of UAVs was found according to the theoretical analysis and flight experiments of nonlinear guidance law. Then the theory and detailed realization process of the adaptive guidance length method was discussed. Finally, simulation in various situations was carried out to verify the effectiveness of the proposed method. The simulation results show that the proposed method is able to track complex trajectory accurately, even with large initial cross track error or during waypoint switching process. It can satisfy the requirement of actual flight missions.
Key words: path following     UAV     nonlinear guidance method     adaptive guidance length     high accuracy

1 非线性制导方法 1.1 无人机运动方程

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1.2 基于航迹引导点的非线性制导方法

 图 1 非线性制导方法几何示意图 Fig. 1 Geometric drawing of nonlinear guidance method

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 图 2 无人机滚转时重力与升力的平衡关系 Fig. 2 Equilibrium relationship between weight and lift on rolling of UAV

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1.3 引导长度对跟踪效果的影响

 图 3 飞行试验用无人机 Fig. 3 UAV for flight experiment

 图 4 不同引导长度下的航迹 Fig. 4 Flight track with different guidance lengths

 图 5 稳定跟踪过程的侧偏距 Fig. 5 Cross track error of stable tracking process

 L/m 侧偏距的均方根/m 50 1.148 2 70 3.740 0 90 4.674 5 110 5.361 7 130 8.245 1 150 9.243 7

 图 6 不同引导长度下的滚转角变化 Fig. 6 Variation of roll angle under different guidance lengths

1) 在飞行速度范围内，相同的引导长度下，随着飞机地速的增加，紧密跟踪航迹的能力变差，直接体现在飞机稳定跟踪上期望轨迹的时间较长，同时拐弯段震荡超调明显。

2) 在曲率变化较小的稳定跟踪段，飞行速度恒定时，引导长度越短，跟踪精度越高。

3) 引导长度越短，滚转角变化越剧烈，由于无人机在实际飞行中存在滚转角幅值和速率限幅，引导长度过短很可能会导致飞机失稳。

2 引导长度自适应的原理 2.1 引导长度范围的确定

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=AX+BU为横侧向线性状态方程的标准式，其中矩阵AB由量纲导数及其一导数组成，具体如式(9)~式(11)。

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 图 7 辨识结果与原始数据对比 Fig. 7 Comparison between identification results and initial data

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 图 8 滚转通道闭环传递函数的框图 Fig. 8 Block diagram of roll channel closed-loop transfer function

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H(s)的伯德图如图 9所示。从图 9得出控制带宽ωUAV大约是0.9，从而根据式(8) 可以求出速度v下的引导长度下限。

 图 9 滚转通道闭环传递函数的伯德图 Fig. 9 Bode diagram of roll channel closed-loop transfer function

2.2 引导长度的评价准则

 图 10 自适应引导长度的航迹跟踪方法原理图 Fig. 10 Illustrative diagram of path following method with adaptive guidance length

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w1的值随着侧偏距的变化而变化，可通过式(18) 进行计算：

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1) 当引导长度为L时，对预测航迹和期望航迹分别进行等间距离散采样，得到L个采样点。分别为(x01, y01)，(x02, y02)，…，(x0n, y0n)和(x01, y01)，(x02, y02)，…，(x0n, y0n)，其中1≤nL

2) 分别计算期望航迹与预测航迹上采样点的坐标：对于期望航迹上的采样点坐标计算，首先计算出飞机当前位置在期望轨迹上的投影点(x00, y00)。计算过程如式(19)：

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3) 计算期望航迹与预测航迹的距离偏差。根据对应采样点的坐标，通过迭代搜索，计算出预测航迹与期望航迹的最大距离偏差dmax，过程如下：

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4) 计算期望航迹与预测航迹在引导点处的角度偏差：其中期望航迹的航向θ1可通过式(23) 求得

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5) 通过对不同的引导长度进行评价得到最优的引导长度Lbest，过程如下：

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3 仿真验证 3.1 复杂航迹跟踪效果验证

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 图 11 跟踪曲线y1时航迹示意图 Fig. 11 Schematic of flight track when tracking curve y1
 图 12 跟踪曲线y1时滚转角示意图 Fig. 12 Schematic of roll angle when tracking curve y1
 图 13 跟踪曲线y1时侧偏距示意图 Fig. 13 Schematic of cross track error when tracking curve y1
 图 14 跟踪曲线y2时航迹示意图 Fig. 14 Schematic of flight track when tracking curve y2
 图 15 跟踪曲线y2时滚转角示意图 Fig. 15 Schematic of roll angle when tracking curve y2
 图 16 跟踪曲线y2时侧偏距示意图 Fig. 16 Schematic of cross track error when tracking curve y2

3.2 方法改进前后对比

 图 17 定引导长度与自适应引导长度航迹对比 Fig. 17 Comparison of flight track between fixed guidance length and adaptive guidance length
 图 18 侧偏距对比 Fig. 18 Comparison of cross track error
 图 19 滚转角对比 Fig. 19 Comparison of roll angle
 图 20 引导长度变化对比 Fig. 20 Comparison of guidance length variation

4 结论

1) 在大的尺度下，飞行速度越高，引导长度越长，两者之间必须保证满足飞行器的动态特性；在小的尺度下，引导长度影响航迹跟踪的精度与飞机的稳定性。

2) 引导长度的搜索范围受无人机飞行控制系统带宽的影响，后者可近似用无人机横向滚转通道的闭环控制带宽计算。

3) 引导长度自适应的航迹跟踪方法能较好地跟踪各种复杂航迹，除受无人机自身转弯半径限制的飞行段以外，跟踪精度能达到2 m以内。

4) 引导长度自适应的航迹跟踪方法可以较好地解决较大的初始偏差情况下及航路点切换过程中易出现的超调严重、滚转角过大、无人机飞行不稳定等问题。

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#### 文章信息

LI Yue, CHEN Qingyang, HOU Zhongxi

Path following method with adaptive guidance length for unmanned aerial vehicles

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(7): 1481-1490
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0522