多UAV路徑跟蹤協(xié)同編隊(duì)機(jī)動(dòng)指令決策算法

楊宇龍, 王小平, 林秦穎, 狄方旭, 劉哲

(空軍工程大學(xué) 航空航天工程學(xué)院, 陜西 西安 710038)

多UAV路徑跟蹤協(xié)同編隊(duì)機(jī)動(dòng)指令決策算法

楊宇龍, 王小平, 林秦穎, 狄方旭, 劉哲

(空軍工程大學(xué) 航空航天工程學(xué)院, 陜西 西安 710038)

針對(duì)多UAV在空間路徑跟蹤下的協(xié)同編隊(duì)控制問(wèn)題,設(shè)計(jì)了一種機(jī)動(dòng)指令決策算法。對(duì)單架UAV的路徑跟蹤引入視距導(dǎo)航算法并進(jìn)行改進(jìn),得到航跡方位角和航跡傾斜角的參考指令;對(duì)于多UAV協(xié)同編隊(duì)控制,應(yīng)用圖論知識(shí)得到空速大小的參考指令;依據(jù)參考指令,通過(guò)函數(shù)解析與數(shù)值編程相結(jié)合的方法計(jì)算出機(jī)動(dòng)指令。仿真結(jié)果表明,該算法能夠有效控制多UAV從任意初始狀態(tài)進(jìn)行預(yù)期的路徑跟蹤協(xié)同編隊(duì)飛行。

多無(wú)人機(jī); 路徑跟蹤; 協(xié)同編隊(duì); 機(jī)動(dòng)指令

0 引言

多UAV的自主協(xié)同,以多UAV的路徑跟蹤協(xié)同編隊(duì)控制技術(shù)為基礎(chǔ),而相應(yīng)的機(jī)動(dòng)指令決策算法更是其中必不可少的關(guān)鍵環(huán)節(jié)和重要技術(shù)。無(wú)人機(jī)應(yīng)用廣泛,主要執(zhí)行復(fù)雜的、繁重/重復(fù)或具有一定危險(xiǎn)性的任務(wù)。如果采用多UAV協(xié)同編隊(duì)飛行,則能更好地提高無(wú)人機(jī)的執(zhí)行效率[1]和完成任務(wù)的成功率[2]。

國(guó)內(nèi)外對(duì)多無(wú)人機(jī)的協(xié)同編隊(duì)控制已經(jīng)開(kāi)展了大量的研究。基于領(lǐng)航跟隨法和行為分解法的思想,針對(duì)多無(wú)人機(jī)編隊(duì)飛行控制算法的研究有很多,并且取得了不錯(cuò)的仿真效果[3-4]。在國(guó)內(nèi),文獻(xiàn)[5]采用路徑函數(shù)的方法解決了二階多智能體沿多條正則曲線的編隊(duì)控制問(wèn)題。類似的思想被用于空間多飛行器的路徑跟蹤協(xié)同控制[6]。

視距導(dǎo)航算法由Fossen等[7]提出并廣泛應(yīng)用于欠驅(qū)動(dòng)水面船舶的控制領(lǐng)域。文獻(xiàn)[8]采用視距導(dǎo)航算法實(shí)現(xiàn)了多無(wú)人水下航行器的協(xié)同編隊(duì)控制。

本文改進(jìn)視距導(dǎo)航算法,引用圖論知識(shí)得到無(wú)人機(jī)空速大小、航跡方位角和航跡傾斜角的參考指令;再通過(guò)函數(shù)解析和數(shù)值編程相結(jié)合的方法,計(jì)算出機(jī)動(dòng)指令,據(jù)此設(shè)計(jì)路徑跟蹤協(xié)同編隊(duì)控制器,從而實(shí)現(xiàn)空間路徑跟蹤下的多UAV協(xié)同編隊(duì)控制。

1 無(wú)人機(jī)數(shù)學(xué)模型

多無(wú)人機(jī)編隊(duì)機(jī)動(dòng)的控制指令決策過(guò)程中,假設(shè)各無(wú)人機(jī)側(cè)力為0(無(wú)人機(jī)機(jī)動(dòng)過(guò)程中側(cè)力很小),并且無(wú)人機(jī)機(jī)動(dòng)過(guò)程中總是盡量使側(cè)滑角為0,則簡(jiǎn)化后的無(wú)人機(jī)三自由度動(dòng)態(tài)方程[9]為:

(1)

(2)

其中:

表1 無(wú)人機(jī)約束條件Table 1 The constraint of the UAV

2 多UAV路徑跟蹤協(xié)同編隊(duì)控制器設(shè)計(jì)

2.1 路徑跟蹤控制器設(shè)計(jì)

如圖1所示,將無(wú)人機(jī)對(duì)給定路徑L的跟蹤問(wèn)題轉(zhuǎn)變成無(wú)人機(jī)對(duì)給定路徑上目標(biāo)點(diǎn)D(xd,yd,zd)的跟蹤問(wèn)題。

圖1 無(wú)人機(jī)路徑跟蹤示意圖Fig.1 Diagram of UAV path tracking

定義

(3)

則:

(4)

χp=

(5)

(6)

(7)

(8)

式中:χp和μp為無(wú)人機(jī)指向目標(biāo)點(diǎn)的機(jī)動(dòng)方向,使無(wú)人機(jī)機(jī)動(dòng)到目標(biāo)點(diǎn)上;χv和μv為目標(biāo)點(diǎn)在給定路徑上沿運(yùn)動(dòng)方向的切線方向,使無(wú)人機(jī)沿給定路徑飛行。為實(shí)現(xiàn)良好的路徑跟蹤效果,采用式 (9)～式(12)綜合考慮上述兩個(gè)方向:

(9)

(10)

(11)

(12)

2.2 協(xié)同編隊(duì)控制器設(shè)計(jì)

本文通過(guò)調(diào)節(jié)無(wú)人機(jī)的空速大小,使多無(wú)人機(jī)在給定路徑上形成并保持給定的相對(duì)位置來(lái)完成協(xié)同編隊(duì)。

假設(shè)V(t)∈(Vmin,Vmax),?t≥t0,確定常數(shù)h>0滿足:

Vdi(t)∈[Vmin+h,Vmax-h]

(i=1,2,…,n; ?t≥t0)

(13)

取協(xié)同編隊(duì)控制器的空速大小參考指令為:

Vci(t)=Vdi(t)-f(·) (i=1,2,…,n)

(14)

則:

(15)

圖2 編隊(duì)隊(duì)形示意圖Fig.2 Schematic diagram of UAVs formation

2.3 無(wú)人機(jī)機(jī)動(dòng)指令決策

(1)無(wú)人機(jī)空速大小V

(16)

將式(16)移項(xiàng)后結(jié)合式(2),可得:

(17)

整理式(17),可得:

(18)

(2)無(wú)人機(jī)航跡方位角χ

無(wú)人機(jī)航跡方位角χ的算法與空速大小V類似,可得:

(19)

整理式(19),可得:

Lsinφ+Tsinφsinα=

(20)

(3)無(wú)人機(jī)航跡傾斜角μ

無(wú)人機(jī)算航跡傾斜角μ的算法與空速大小V類似,可得:

(21)

整理式(21),可得:

Lcosφ+Tcosφsinα=

(22)

(4)解算無(wú)人機(jī)機(jī)動(dòng)指令

①滾轉(zhuǎn)角φ。將式(20)除以式(22),可得:

(23)

因此,無(wú)人機(jī)機(jī)動(dòng)指令滾轉(zhuǎn)角

(24)

②推力T和迎角α。將式(24)的值代入式(22)并移項(xiàng),可得:

L+Tsinα=

(25)

將式(25)移項(xiàng)整理為:

g(T,α)=

(26)

將式(18)移項(xiàng)整理為:

h(T,α)=Tcosα-D-mgsinμ-

(27)

定義目標(biāo)函數(shù)J(T,α)為:

J(T,α)=[g(T,α)]2+[h(T,α)]2

(28)

采用窮舉法將推力T和迎角α分別在約束區(qū)間[400,2 000]和[-5,15]等分為400份,取401個(gè)樣本點(diǎn);每個(gè)周期內(nèi),將4012=160 801組(T,α)分別代入目標(biāo)函數(shù)J(T,α),將最小目標(biāo)函數(shù)值所對(duì)應(yīng)的(T,α)min作為下一個(gè)周期的無(wú)人機(jī)機(jī)動(dòng)指令。

3 仿真驗(yàn)證

Li(t)=

(k=0,1,…,N;i=1,2,3)

(29)

式中:R1=900 m,R2=950 m,R3=1 000 m;ω=Vd2/R2;采樣時(shí)間ts=0.02 s。

設(shè)置UAV的初始條件為：位置為p1=(300,-100,120) m,p2=(980,0,190) m,p3=(1 400,200,240) m;空速大小為V1(0)=28 m/s,V2(0)=40 m/s,V3(0)=70 m/s;航跡方位角為χi(0)=0°,航跡傾斜角為μi(0)=0°,推力Ti=629 N,迎角αi=3.2°,滾轉(zhuǎn)角φi=0°,i=1,2,3。控制器增益kV=56.4,kχ=49.4,kμ=31.1,kv1=4.9,kp1=65.7,kv2=1.7,kp2=79.6;函數(shù)f(·)=40[arctan(·)]/π∈(-20,20)。仿真結(jié)果見(jiàn)圖3～圖6。

圖3 et變化曲線Fig.3 Curves of the errors of UAVs tracking space-paths

圖4 無(wú)人機(jī)相互之間的夾角和空速變化曲線Fig.4 Curves of the angle between each 2 UAVs and the change of airspeed

圖5 多無(wú)人機(jī)路徑跟蹤協(xié)同編隊(duì)的三維效果圖Fig.5 3D effect diagram of UAVs path tracking and coordinated formation

圖6 UAV路徑跟蹤協(xié)同編隊(duì)的機(jī)動(dòng)指令Fig.6 Maneuvering commands for UAVs path tracking and coordinated formation

可以看出:3架UAV的路徑跟蹤誤差最終收斂穩(wěn)定在可接受的范圍內(nèi); 3架UAV相互之間的夾角及2號(hào)UAV的空速大小最終收斂到給定值,形成并保持給定編隊(duì)隊(duì)形;本文算法能使3架UAV從任意初始位置跟蹤上各自的期望路徑,同時(shí)形成并保持期望編隊(duì)隊(duì)形;3架UAV路徑跟蹤協(xié)同編隊(duì)的機(jī)動(dòng)指令決策軌跡經(jīng)過(guò)短暫振蕩后迅速趨于穩(wěn)定,說(shuō)明該算法能夠控制UAV快速穩(wěn)定地達(dá)到期望效果。

4 結(jié)束語(yǔ)

本文基于行為分解法的思想,將多UAV的編隊(duì)飛行控制問(wèn)題解耦為路徑跟蹤和協(xié)同編隊(duì)兩個(gè)子問(wèn)題。對(duì)于路徑跟蹤問(wèn)題,構(gòu)造了一組自適應(yīng)路徑跟蹤距離誤差的系數(shù)來(lái)改進(jìn)視距導(dǎo)航算法,通過(guò)改進(jìn)后的視距導(dǎo)航算法得到航跡方位角和航跡傾斜角參考指令。對(duì)于協(xié)同編隊(duì)問(wèn)題,在前者的基礎(chǔ)上,通過(guò)調(diào)節(jié)無(wú)人機(jī)的空速大小實(shí)現(xiàn)多UAV間的協(xié)同編隊(duì),得到空速大小的參考指令。然后,依據(jù)參考指令,采用函數(shù)解析和數(shù)值編程相結(jié)合的方法,計(jì)算出機(jī)動(dòng)指令決策軌跡。最后,通過(guò)MATLAB程序仿真驗(yàn)證了該算法的有效性。

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(編輯：李怡)

Maneuvering command control algorithm for multi-UAV path tracking and coordinated formation

YANG Yu-long, WANG Xiao-ping, LIN Qin-ying, DI Fang-xu, LIU Zhe

(Aeronautics and Astronautics Engineering College, AFEU, Xi’an 710038, China)

For the problems of multi-UAV both path tracking and coordinated formation, a coordinated control algorithm for maneuvering command was designed. For the single UAV path tracking, the reference commands for flight-path azimuth angle and bank angle were got by improving line of sight guidance algorithm. For the multi-UAV coordinated formation control, the reference commands for airspeed were got by applying graph theory. According to the reference commands, the coordinated control commands were calculated by analyzing and programming. Simulation results show that the algorithm can effectively control multi-UAV to perform the expected path tracking and coordinated formation from the any initial states.

multi-UAV; path tracking; coordinated formation; maneuvering command

2015-01-08;

2015-04-25;

時(shí)間:2015-06-24 15:03

航空科學(xué)基金資助(20145196023)

楊宇龍(1988-)，男，湖北當(dāng)陽(yáng)人，碩士，主要從事多無(wú)人機(jī)協(xié)同編隊(duì)飛行的自主控制技術(shù)研究。

V279; TP273.1

A

1002-0853(2015)05-0471-05