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采用上述系统装置完成激光对空中移动MUAV的实时充电,需分两步实现。第1步是激光束对MUAV的扫描与捕获;第2步则是激光束对MUAV的跟踪瞄准。
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首先,在选定单片机芯片作为控制扫描振镜的主处理器后,为使系统整体工作模式简洁高效,采用2维图形扫描作为主要扫描方式。
位于地面控制端的DAC模块可通过SPI接口读取16位二进制数字电压信号,为此,首先将MUAV飞行空域的2维平面离散为65535×65535个像素点,其次将扫描算法所用的2维扫描图形进行离散化处理,计算得出图形中各离散点的2维坐标,再将其转化为数组存入到单片机的数据存储器中。在单片机运行扫描算法时,就可直接按照扫描顺序调用数组中的坐标值,通过算法处理后,直接由单片机芯片的输入/输出(in/out, I/O)端口输出相应的数字电压信号,DAC模块再将其转换为模拟电压信号,驱动振镜转动相应角度,从而控制激光束发射方向,完成激光束对MUAV工作空域的扫描工作。图 5为系统扫描程序原理框图。本文中选用螺线扫描方式对MUAV飞行空域进行扫描,示意图如图 6所示。
扫描起始坐标为(32767,32767),扫描参数方程为:
$ \left\{ {\begin{array}{*{20}{c}} {\mathit{x}{\rm{ = }}\mathit{vt}{\rm{cos[(}}\mathit{\omega }{\rm{ - }}\mathit{at}{\rm{)}}\mathit{t}{\rm{] + 32767}}}\\ {\mathit{y}{\rm{ = }}\mathit{vt}{\rm{sin[}}\left( {\mathit{\omega }{\rm{ - }}\mathit{at}} \right)\mathit{t}{\rm{] + 32767}}} \end{array}} \right. $
(1) 式中, v为扫描线速度, ω为扫描角速度, a为常数,t为时间。在中心点附近区域扫描角速度较大,这样可降低扫描密度,有效提高扫描速度;而在扫描区域边缘附近时扫描角速度较小,但分辨率和精度较高。该扫描方式有利于提高系统的扫描效率,可使激光束在较短的时间内捕获到硅光电池阵列。
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在激光束对硅光电池阵列的跟瞄过程中,采用和差算法通过对阵列中各硅光电池输出的电信号进行处理实现跟瞄。系统照射到硅光电池阵列上的激光束近似为圆形光斑,且能量分布均匀。首先对阵列内的子电池进行编号,如图 7所示,然后以位于中心的5号子电池为坐标原点,建立2维坐标系,在坐标系中对其余子电池进行坐标定位。
和差算法根据激光斑发生位置偏移后各子电池负载电压信号的不同进行定位,在MUAV飞行过程中,激光斑中心相对硅光电池阵列中心有偏离时,各子电池会由于光斑信号的变化产生不同光电流I1,I2,…, I9,进而产生不同电压信号U1,U2,…, U9,且每个电压信号的大小与照射到各子电池光敏面上的激光斑面积大小成正比。采用和差算法对该系列电压信号进行处理,即可得到光斑与光电池阵列的相对位置信息。通过定量计算可得,激光斑中心在硅光电池阵列坐标系中的位置为:
$ \begin{array}{c} \mathit{x}{\rm{ = }}\mathit{\lambda }\frac{{\left( {{\mathit{I}_{\rm{1}}}{\rm{ + }}{\mathit{I}_{\rm{4}}}{\rm{ + }}{\mathit{I}_{\rm{7}}}} \right) - \left( {{\mathit{I}_{\rm{3}}}{\rm{ + }}{\mathit{I}_{\rm{6}}}{\rm{ + }}{\mathit{I}_{\rm{9}}}} \right)}}{{{\mathit{I}_{\rm{1}}}{\rm{ + }}{\mathit{I}_{\rm{2}}}{\rm{ + }}{\mathit{I}_{\rm{3}}}{\rm{ + \ldots + }}{\mathit{I}_{\rm{9}}}}}{\rm{ = }}\\ \mathit{\lambda }\frac{{\left( {{\mathit{U}_{\rm{1}}}{\rm{ + }}{\mathit{U}_{\rm{4}}}{\rm{ + }}{\mathit{U}_{\rm{7}}}} \right) - \left( {{\mathit{U}_{\rm{3}}}{\rm{ + }}{\mathit{U}_{\rm{6}}}{\rm{ + }}{\mathit{U}_{\rm{9}}}} \right)}}{{{\mathit{U}_{\rm{1}}}{\rm{ + }}{\mathit{U}_{\rm{2}}}{\rm{ + }}{\mathit{U}_{\rm{3}}}{\rm{ + \ldots + }}{\mathit{U}_{\rm{9}}}}} \end{array} $
(2) $ \begin{array}{l} {\rm{y = }}\mathit{\lambda }\frac{{\left( {{\mathit{I}_{\rm{7}}}{\rm{ + }}{\mathit{I}_{\rm{8}}}{\rm{ + }}{\mathit{I}_{\rm{9}}}} \right) - \left( {{\mathit{I}_{\rm{1}}}{\rm{ + }}{\mathit{I}_{\rm{2}}}{\rm{ + }}{\mathit{I}_{\rm{3}}}} \right)}}{{{\mathit{I}_{\rm{1}}}{\rm{ + }}{\mathit{I}_{\rm{2}}}{\rm{ + }}{\mathit{I}_{\rm{3}}}{\rm{ + \ldots + }}{\mathit{I}_{\rm{9}}}}}{\rm{ = }}\\ \mathit{\lambda }\frac{{\left( {{\mathit{U}_{\rm{7}}}{\rm{ + }}{\mathit{U}_{\rm{8}}}{\rm{ + }}{\mathit{U}_{\rm{9}}}} \right) - \left( {{\mathit{U}_{\rm{1}}}{\rm{ + }}{\mathit{U}_{\rm{2}}}{\rm{ + }}{\mathit{U}_{\rm{3}}}} \right)}}{{{\mathit{U}_{\rm{1}}}{\rm{ + }}{\mathit{U}_{\rm{2}}}{\rm{ + }}{\mathit{U}_{\rm{3}}}{\rm{ + \ldots + }}{\mathit{U}_{\rm{9}}}}} \end{array} $
(3) 式中, λ为常数,由此和差算法对激光束的位置信息判断简单迅速。需要说明的是,在单片机芯片对硅光电池阵列上输出电压的两次采样之间,若光斑偏移距离较大,则该算法得出的激光斑位置信息误差较大,因此该算法对单片机芯片的采样频率要求较高。
同时,还采用卡尔曼滤波算法对激光斑中心下一时刻的位置进行预测与修正,以减小跟踪延迟,提高跟踪速度及精度。设常态情况下MUAV匀速运动,但由于空气中气流干扰或飞行控制系统误差,也会出现非匀速飞行的状态。卡尔曼滤波算法可将激光光斑中心在硅光电池阵列上的相对位置作为观测数据,对其进行滤波处理,将干扰项随机加速度u2×1(k-1)(k表示采样次数)作为输入向量,硅光电池输出电压信号的误差作为观测噪声v2×1(k), 下标2×1表示2行1列的矩阵。将x、y轴方向的坐标和速率作为状态向量:
$ \mathit{\boldsymbol{X}}\left( \mathit{k} \right){\rm{ = [}}\mathit{x}\left( \mathit{k}\right)\qquad \mathit{\dot x}\left( \mathit{k}\right)\qquad \mathit{y}\left( \mathit{k}\right)\qquad \mathit{\dot y}\left( \mathit{k} \right){{\rm{]}}^{\rm{T}}} $
(4) 式中,x, y表示位置坐标,ẋ,ẏ表示该方向上的速率。跟瞄系统的状态方程和观测方程分别为:
$ \begin{array}{c} \mathit{\boldsymbol{X}}\left( \mathit{k} \right) = \left[ {\begin{array}{*{20}{c}} {\mathit{x}\left( \mathit{k} \right)}\\ {\mathit{\dot x}\left( \mathit{k} \right)}\\ {\mathit{y}\left( \mathit{k} \right)}\\ {\mathit{\dot y}\left( \mathit{k} \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&\mathit{T}&0&0\\ 0&1&0&0\\ 0&0&1&\mathit{T}\\ 0&0&0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\mathit{x}\left( {\mathit{k - 1}} \right)}\\ {\mathit{\dot x}\left( {\mathit{k - 1}} \right)}\\ {\mathit{y}\left( {\mathit{k - 1}} \right)}\\ {\mathit{\dot y}\left( {\mathit{k - 1}} \right)} \end{array}} \right] + \\ \left[ {\begin{array}{*{20}{c}} {{\rm{0}}{\rm{.5}}{\mathit{T}^{\rm{2}}}}\\ \mathit{T}\\ 0\\ 0 \end{array}} \right.\left. {\begin{array}{*{20}{c}} 0\\ 0\\ {{\rm{5}}{\mathit{T}^{\rm{2}}}}\\ \mathit{T} \end{array}} \right]{\mathit{\boldsymbol{u}}_{{\rm{2 \times 1}}}}\left( {\mathit{k - }{\rm{1}}} \right) \end{array} $
(5) $ \mathit{\boldsymbol{Z}}\left( \mathit{k} \right){\rm{ = }}\left[ {\begin{array}{*{20}{c}} {\rm{1}}\\ 0 \end{array}} \right.\begin{array}{*{20}{c}} \mathit{T}\\ 0 \end{array}\begin{array}{*{20}{c}} 0\\ 1 \end{array}\left. {\begin{array}{*{20}{c}} 0\\ \mathit{T} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\mathit{x}\left( \mathit{k} \right)}\\ {\mathit{\dot x}\left( \mathit{k} \right)}\\ {\mathit{y}\left( \mathit{k} \right)}\\ {\mathit{\dot y}\left( \mathit{k} \right)} \end{array}} \right]{\rm{ + }}{\mathit{\boldsymbol{v}}_{{\rm{2 \times 1}}}} $
(6) 式中, T为信号采集周期,k为采样次数, Z (k)为第k次采样对应的相对位置观测量。将(5)式和(6)式代入到卡尔曼滤波的预测和校正方程后, 即可实现对下一时刻激光斑中心位置的预测,减小跟瞄的时间延迟。卡尔曼滤波算法是一个递归的过程,只需知道初始时刻MUAV坐标测量值和速度计算值,即可得到下一时刻的最优估计,该算法不需要保存其它原始数据,占用内存极小且速度很快,非常适用于本系统中连续实时跟瞄的工作模式。
激光对微型无人机跟瞄充电系统的设计与实现
Design and implementation of a laser tracking, aiming and charging system for micro-unmanned aerial vehicle
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摘要: 为了提高微型无人机(MUAV)的续航时间, 基于二轴扫描振镜的工作原理, 设计了一套激光对MUAV的远程实时跟瞄充电系统。系统采用硅光电池阵列作为光斑位置传感器, 其信号经扫描跟踪算法处理后, 在地面与MUAV间建立起无线数传反馈链路, 控制二轴扫描振镜改变激光发射方向, 实现激光束对MUAV的扫描与实时跟踪; 同时硅光电池阵列也作为充电器件, 实现对MUAV的实时充电。结果表明, 当MUAV在高度为80m、直径50m圆形区域内以低于2m/s速率飞行时, 可实现激光对MUAV的准确跟踪, 跟瞄精度小于0.63mrad。该系统具有跟踪速度快、瞄准精度高的特点, 为激光对移动目标的远程实时能量传输提供了一种有效的解决方案。Abstract: In order to improve the endurance of the micro-unmanned aerial vehicle (MUAV), based on the working principle of the two-axis scanning galvanometer, a remote real-time laser tracking and pointing charging system for the MUAV was designed. In the system, a silicon photocell array was used as the spot position sensor. Firstly, the signal was processed through a scanning tracking algorithm, then a wireless data transmission feedback link was established between the ground and the MUAV, and the emission direction of a laser beam could be changed by controlling the two-axis scanning galvanometer. At the same time, the silicon photocell array was also used as a charging device to realize real-time charging of MUAV. The experimental test results show that when the MUAV flies at a speed of less than 2m/s in a circular area with a height of 80m and a diameter of 50m, the system can accurately track the MUAV with a tracking accuracy of less than 0.63mrad. It has the characteristics of fast tracking speed and high aiming accuracy. This research provides an effective solution for laser remote real-time energy transmission to moving targets.
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