1752 T. SICE Vol.34 No.12 December 1998 Fig.2 Design of Secondary Mirror Fig.3 Design of Primary Mirror = (tantan tan ~~) -tan T llllfl) llll
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1 Omnidirectional Vision System Using Two Reflecting Mirrors Akito TAKEYAY, Takeshi KURODA*, Ken-ichi NISHIGUCHI* and Akira ICHIKAWA* Omnidirectional visual information is important to ensure the safety for the autonomous navigation of mobile robots. Usually such vision systems use a fish-eye lens or a reflecting mirror (spherical or hyperboloidal). The former system has a problem that unnecessary visual field occupies the most part of image. The latter one has also a problem that the camera image is blurred due to the physical property of the mirror curvature and thus the clear image cannot be obtained especially in a dark environment. In order to solve the above problems, we propose omnidirectional vision system using two reflecting mirrors with contrived curvature to obtain a panoramic image. Theoretical consideration is made to estimate the degree of aberration for the reflecting optical system that uses two mirrors with arbitrary curvatures, and a design method is developed to minimize the aberration of the image. The optical characteristics of a design example are evaluated and the results show the effectiveness of the proposed vision system. Key Words: panoramic image, catoptric system, mobile robot * Advanced Technology R & D Center, Mitsubishi Electric Co., Amagasaki (Received September 22, 1997) (Revised September 3, 1998) TR 0012/98/ (C) 1997 SICE
2 1752 T. SICE Vol.34 No.12 December 1998 Fig.2 Design of Secondary Mirror Fig.3 Design of Primary Mirror = (tantan tan ~~) -tan T llllfl) llll (1) T Il]:1X Fig.1 Omnidirectional Vision System (Cut Model)
3
4 E 1754 T. SICE Vol.34 No.12 December 1998 Fig.4 Position of Meridional Image 3 2 (x))2) r ntc - (1+(f 2 ~~ (21 f;(x) q me - (H+qn,, )cosyc 2(H+qn~,) +cos (22) me Ys r x z _~ (27) xvl+(f 1(x))2 rs, f (x) (23) - 2E -+1 (24) r, X28) Ỵ,.~ --xvl+(f2(x))2 x) (25) f( q s., (H+q,)) 2(H +q,) +1 (26) r.r.r x )2+(z '- =1
5 計 測 自動 制 御 学 会 論 文 集 第34巻 第12号 1998年12月 1755 Fig Depth of Field 評価 (1)画 質 の 評価 被 写 界 深 度 の 近 点Pn,遠 点Pfは 以 下 の 式 で 求 め る こ と が で きる12). D,D P - D D Dig+D こ こで,Dhは, pt 過 焦 点 距 離,Doは だ し,Dhは,レ 影 時 の絞 り値 をF,許 し て次 の 式 か ら計 算 す る. F c (30) (29)式,(30)式 Fig. 5 Plots of Mirrors and Image Planes (Initial Design) 焦 点 を 合 わせ た 距 離 で あ る.た ンズ の 焦 点 距 離 をf,撮 容 錯 乱 円 径 をcと D D,,-D<(29) か らわ か る よ う に,被 写 界深 度 は 焦 点 距 離fが 短 い 広 角 レ ン ズ ほ ど深 く,ま た,焦 点 を 合 わ せ た距 離Doが 長 い ほ ど深 くな る. 上 記 設 計 例 で1/2inchCCDを 鏡 の 見 込 み角 が18.6度 焦 点 距 離f=12mmの F= に に 示 す.こ 直 画 角20度 が 得 ら れ る の レ ン ズ の 絞 り値 点 を合 わせ た距 離 を 容 錯 乱 円 径 を1/2inchCCDの して(29)式,(30)式 の 図 か ら は,絞 mmに の で,得 と な る の で,垂 レ ンズ が 必 要 と な る.こ お け る 被 写 界 深 度 を,焦 D o= mm,許 c=8μmと 使 う と す る と,原 点 か ら見 た 副 か ら求 め た.そ 画 素 サ イズ の結 果 をFig. 7 り値 が1.5以 上 の と き,z= 存在 す る像 面 はすべ て被 写 界深度 内 に含 まれ る られ る 全 方 位 画像 は焦 点 の あ っ た 鮮 鋭 な画 像 と な る こ とが わ か る. (2)双 曲 面 鏡 を 用 い た視 覚 セ ンサ と の 比較 本 視 覚 シ ス テ ム と比 較 す る 従 来 の 視 覚 セ ンサ と して,双 面 鏡 を用 い た視 覚 セ ンサ を選 ん だ,こ 曲 の 視 覚 セ ンサ に は,実 時 間 で 全 方 位 像 が得 ら れ る こ とや,全 方 位 画像 の 解 像 力 が 優 れ て い る な ど,本 視 覚 シ ス テ ム と の類 似 点 が 多 い.今 象 とす る 双 曲面 鏡 は,上 回,比 較 の 対 記 設 計 例 の 主 鏡 と ほ ぼ 同 じ径 を持 ち, か つ,副 鏡 と ほ ぼ 同 じ地 点 に位 置 す る,次 の 式 で 表 され る 双 曲 線 の 断 面 を持 つ も の と した. 1 (31) ( )Z( )' こ の 視 覚 セ ン サ の 双 曲 面 鏡 の 断 面 形 状 と2つ Fig. 6 Plots of Mirrors and Image Planes (Final Design) Fig. 8に 示 す.こ の 図 か ら,像 の 像面 位 置 を 面 はz= mmに
6 1756 T. SICE Vol.34 No.12 December 1998 Photo. 1 Prototype of Omnidirectional Vision System Fig. 8 Former Visual Sensor (Hyperboloidal Mirror Type) Photo. 2 Input Omnidirectional Image Fig. 9 Depth of Field (Hyperboloidal Mirror Type)
7 Fig. A.1 Image Distance aq,, ak aq.z aq.x (Fx Q.x)k (A.10) a F a-q.z-k- ak Q, (All) a F,-Q,=a k (A.12) aq X k(k-a) y = IF-QI Ik-aIV' 1+k2 dk IaQ,I (A.13) cosy -sing -a -(acosy-siny) siny cosy 1 = -(asinycos y) j (A.14) n= 1 (-1) (A.5 1 +a2 ) k= asinycos y sing±c~osy (A.4 1+a2 ) k-a=-(1+a2) cosy smy+c~osy (A.1.5) (A.16) 3 (A.6) (1+a2 ) 2 l+k 2 = 1+ a2 1 (A.17) smy+c osy r=_= K 1 (1+a2)2 (A.7) a -a =f,~(q)=$ ~(A.18) aq~ lsiny=(l,v)= 1 1+ a2 (L+aL) a.,,a.20
8 1758 T. SICE Vol.34 No.12 December 1998 Icosr-(L,n)= I (-al,+l,.) (A.21) 1+ a'- 2aL, -( I_ a2 )L, k (I- a2 )L,.+2 al,, Q'; _-I al,, aq,. (A.22) (A.23) dq = a =-a (A.24) 3 dk 2)7 21d+cosy dq - l+a l(siny+acosy~ (A.25) q /cosy 2xf+ cosy /cosy -+cosy 2/ (A.26) r 1) K.B. Saraclik: gcharacterizing an indoor environment with a mobile robot and uncalibrated stereo, h Proc. IEEE Int. Conf. Robotics and Automation, 984/989 (1989) 2) Z.L. Cao, et al.: gdynamic omnidirectional vision for mobile robots, h J. Robotic Systems, Vol.3, No.1, 5/17 (1986) 3) Y. Yagi, et al.: gpanorama scene analysis with conic projection, h Proc. IEEE Int. Workshop Intelligent Robots & Systems, 181/187 (1990) 4) J. Hong, et al.: gimage-based homing, h Proc. IEEE Int. Conf. Robotics and Automation, 910/915 (1991) 5) K. Yamazawa, et al.: gomnidirectional imaging with hyperboloidal projection, h Proc. Int. Conf. on Intelligent Robots and Systems, Yokohama, Japan, 1029/1034 (1993)
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