Tham khảo tài liệu 'robot localization and map building part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 64 Robot Localization and Map Building Camera model Generally a camera has 6 degrees of freedom in three-dimensional space translations in directions of axes x y and z which can be described with translation matrix T x y z and rotations around them with angles a fi and Y which can be described with rotation matrices Rx a Ry fi and Rz y . Camera motion in the world coordinate system can be described as the composition of translation and rotation matrices C T x y z Rz y Ry fi Rx a 12 where Rx a Ry b Rz g 1 0 0 0 0 cosa -sina 0 0 sina cosa 0 00 0 1 cosfi 0 sinfi 0 0 1 0 0 -sinfi 0 cosfi 0 0 0 0 1 cosy - siny 0 0 siny cosy 0 0 0 0 1 0 0 0 0 1 T x y z 1 0 0 x 0 1 0 y 0 0 1 z 0 0 0 1 Inverse transformation C 1 is equal to extrinsic parameters matrix that is C 1 a fi Y x y z Rx -a Ry -fi Rz -y T -x -y -z . 13 Perspective projection matrix then equals to P SC-1 where S is intrinsic parameters matrix determined by off-line camera calibration procedure described in Tsai 1987 . The camera is approximated with full perspective pinhole model neglecting image distortion x y T axXc ayYc 7 x0 ị. y0 Zc Zc 14 where ax f sx and ay f Sy sx and Sy are pixel height and width respectively f is camera focal length Xc Yc Zc is a point in space expressed in the camera coordinate system and x0 y0 T are the coordinates of the principal optical point in the retinal coordinate system. The matrix notation of 14 is given with WX ax 0 x0 0 WY 0 ay y0 0 W 0 0 1 0 S -1 r Xc 1 Yc Zc 1 15 Model based Kalman Filter Mobile Robot Self-Localization 65 In our implementation the mobile robot moves in a plane and camera is fixed to it at the height h which leaves the camera only 3 degrees of freedom. Therefore the camera pose is equal to the robot pose p. Having in mind particular camera definition in Blender the following transformation of the camera coordinate system is necessary C-1 - n 2 0 n ty Px Py h in order to achieve the alignment of its optical axes with z and its x and y axes with the retinal
