A Vision Based Method for Aircraft Approach Angle Estimation

Transcript

1 ISSN -9825, CODEN RUXUEW Journal of Software, Vol7, No5, May 6, pp ttp://wwwjosorgcn DOI: 36/jos7959 Tel/Fax: by Journal of Software All rigts reserved, +, ( )8) A Vision Based Metod for Aircraft Approac Angle Estimation ZHU Hai-Jiang, WU Fu-Cao +, HU Zan-Yi (National Laboratory of Pattern Recognition (Institute of Automation, Te Cinese Academy of Sciences), Beijing 8, Cina) + Corresponding autor: Pn: , Fax: , fcwu@nlpriaaccn, ttp://wwwiaaccn Zu HJ, Wu FC, Hu ZY A vision based metod for aircraft approac angle estimation Journal of Software, 6,7(5): ttp://wwwjosorgcn/-9825/7/959tm Abstract: An algoritm for estimating aircraft approac angle using computer vision is proposed in tis paper During te landing of an aircraft, te descent of te aircraft may be approximately considered as a pure translation motion In tis case te epipole as te same coordinates in all images and is called te Focus-of-Expansion (FOE), and te vanising line of te ground plane is termed te Horizon Furtermore, ow te Focus-of-Expansion and te Horizon are extracted from a few calibrated sequential images is first introduced, ten te aircraft approac angle is derived from tese parameters Simulated and real experiments validate tis algoritm Key words: : aircraft approac angle; FOE (focus-of-expansion); orizon,,, FOE(focus-of-expansion) Horizon FOE Horizon, : ;FOE(focus-of-expansion);orizon : TP39 : A (unmanned aerial veicle UAV) [,2] [3] GPS(global positioning system) INS(inertial navigation system), [5] GPS Supported by te National Natural Science Foundation of Cina under Grant Nos6754, ( ); te National Hig-Tec Researc and Development Plan of Cina under Grant No2AA42223 ( (863)) Received 4-7-2; Accepted 5--

2 96 Journal of Software Vol7, No5, May 6,,, [6], 3 : (principal point),,,,,,, (epipole) ( ) FOE(focus-of-expansion), (principal axis, ), FOVC(field of view center) Horizon P P n, FOE W ; P n V, VP V, VP ( ); P,P,,P n t,t,,t n ; FOVC α Camera centre Time t t P t n P P n FOE FOVC VP Image plane W α Ground plane V Fig Geometry of te aircraft approac angle

3 : ,P n ;Horizon ;FOE ;VP α β β [],, β FOE VP Horizon P n (Camera centre) FOE β VP Ground plane W α Fig2 Measurement of te approac angle α 2 α V Image plane K, w=k T K, FOE VP e v β T T T e ( K K ) v e w v cos( β ) = = () T T T T T T e ( K K ) e v ( K K ) v e w e v w v β α 2 FOE VP [2] 2, FOE, VP FOE VP, () [3,4] FOE FOE VP X x 2 x, :sx =Hx,H, 3 3 ;s H = u s v = u u v u 2 + v 2 + v x = u, v, x=[u,v,] T [ ] T uu uv 3 3 vu vv i u v 33 33, H H 2 n, x x (i=,2,,n) : i i = = A = (2) [ ] T = ;

4 962 Journal of Software Vol7, No5, May 6 u v uu vu u u v uv vv v A = M M M M M M M M M u n vn unun vnun un u n vn unvn vnvn vn A, H,, 4 H 4, 4 3, H [5] 3 u l ;l u [] u u 3 l u 2 Fig3 Geometry of Homograpy H H H U=U V U = u, 3 H : [ u ] 2 u3 λ V = λ2 λ 3 (u i U i );V 3 3,λ I (i=,2,3) H λ 2 =λ 3, λ u FOE; λ 2,λ 3 u 2 u 3 l Horizon [5],, w l p v p, l p =w v p (3) Horizon (3) VP :, 4 3 4, 4 P4P [6] FOE VP 4, π Z=, 4 H π, H π =K[r,r 2,t] :K ;r,r 2 R ;t H π R t R,R 2 t,t 2 2

5 : 963 : T e = K ( R2R ) ( t2 R2R t), e = K ( t R R ) t R R 2, e =e 2 =K(t 2 t ), FOE VP 3 (), [2] ; (2) (2) H; (3) FOE Horizon;, (3) VP; (4) 2 () 4 4 f u =, f v =,s=,u =3,v =24 (), 4 A,B,C,D 4 Z=, 4 X A =[,,] T,X B =[4,,] T,X C =[5,,] T,X D =[,3,] T r=(8568, 3549,374) T θ =5325π ( r θ R) α [5,75 ], α =,r=z/tan(α),z= C =(77r,77r,z) T t = R C ; 2 C 2 =(47r,47r,667z) T t 2 = R C σ( ), FOE VP, P4P 4(a) 4(b), RMS(root mean square), 5(a) 5(b) P4P RMS ; RMS, RMS P4P (2), 6 2,3,,6, 5 6, 6(a) 6(b) 5,3,45 RMS,, RMS

6 964 Journal of Software Vol7, No5, May 6 Mean of te approac angle Mean of te approac angle Fig4 Noise (pixel) (a) Our metod (a) Noise (pixel) (b) Based on P4P metod (b) P4P Te averages of te estimated approac angle under different noise levels 4 25 RMS error 5 RMS error Fig5 Noise (pixel) (a) Our metod (a) Noise (pixel) (b) Based on P4P metod (b) P4P Te RMS errors of te estimated approac angle under different noise levels 5 RMS

7 : 965 Mean of te approac angle (degree) Fig Te number of images (a) Te averages of te estimated approac angle (a) RMS errors (pixeeels) Te number of images (b) Te RMS errors of te estimated approac angle (b) RMS Te averages and te RMS errors of te estimated approac angle under different number of images 42 6 RMS,, ; 8 2 6, 35 [2] Canny, 4 ( ); FOE Horizon, , Fig7 Te st image sequence of te lab scene 7

8 966 Journal of Software Vol7, No5, May 6 Fig8 Te 2nd image sequence of te lab scene 8 2,, 726, 3 9 ( ),FOE Horizon; 7249 Fig9 Te 3rd image sequence of te lab scene 9 3 5,,,, References: [] Suter D, Hamel T, Maony R Visual servoing based on omograpy estimation for te stabilization of an x4-flyer In: Proc of te 4st IEEE Conf on Decision and Control, Vol ttp://wwwdsengmonaseduau/suter_publications/cdcps

9 : 967 [2] Beard RW, Mclain TW, Goodric MA, Anderson EP Coordinated target assignment and intercept for unmanned air veicles IEEE Trans on Robotics and Automation, 2,8(6):9 922 [3] Sim DG, Park RH, Kim RC, Lee SU, Kim IC Integrated position estimation using aerial image sequences IEEE Trans on Pattern Analysis and Macine Intelligence, 2,24():8 [4] Werner S, Fürst S, Dickmanns D, Dickmanns ED A vision based navigation system for autonomous aircraft 998 ttp://wwwunibw-muencende/ campus/lrt/lrt3/deutsc/artikel/fued_ias98pdf [5] Beets E, Boukir S, Suter D Aircraft pose estimation from Homograpy 4 ttp://wwwdsengmonaseduau/tecrep/reports/ 4/MECSE--4pdf [6] Tung D, Suter D, Bab-Hadiasar A Aircraft approac angle estimation: Vision based landing 3 ttp://wwwdsengmonaseduau/tecrep/reports/3/mecse-28-3pdf [7] Sakerniat O, Ma Y, Koo TJ, Hespana J, Sastry SS Vision guided landing of an unmanned air veicle In: Proc of te 38t Conf on Decision and Control, Vol999 6 ttp://citeseeristpsuedu/23549tml [8] Sakernia O, Sarp CS, Vidal R, Sim DH, Ma Y, Sastry S Multiple view motion estimation and control for landing an unmanned aerial In: Proc of te Int l Conf on Robotics and Automation, Vol ttp://roboticseecsberkeleyedu/~omids/ papers/icra2pdf [9] Sarp CS, Sakernia O, Sastry SS A vision system for landing an unmanned aerial veicle In: Proc of te Int l Conf on Robotics and Automation, Vol 7727 ttp://citeseeristpsuedu/653634tml [] Saripalli S, Montgomery JF, Sukatme GS Vision-Based autonomous landing of an unmanned aerial veicle In: Proc of te IEEE Int l Conf on Robotics and Automation, Vol ttp://cresuscedu/pubdb_tml/files_upload/334pdf [] Fisler MA, Bolles RC Random sample consensus: A paradigm for model fitting wit applications to image analysis and automated cartograpy Communications of te ACM, 98,24(6): [2] Zang ZY A flexible new tecnique for camera calibration IEEE Trans on Pattern Analysis and Macine Intelligence,,22():33334 [3] Negadaripour S, Horn BKP A direct metod for locating te focus of expansion Computer Vision, Grapics and Image Processing, 989,46(3): [4] Cen ZZ, Pears N, McDermid J, Heseltine T Epipole estimation under pure camera translation In: Sun C, Talbot H, Ourselin S, Adriaansen T, eds Proc of te 7t Digital Image Computing: Tecniques and Applications Collingwood: CSIRO Publising, [5] Hartley RI, Zisserman A Multiple View Geometry in Computer Vision Cambridge: Cambridge University Press, 7 76 [6] Hu ZY, Lei C, Wu FC A sort note on P4P problem ACTA AUTOMATICA SINICA,,27(6): (in Cinese wit Englis abstract) : [6] P4P,,27(6): (97 ),,, (96 ),,,Houg, (957 ),,,,