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Tham khảo tài liệu 'feedback.control.for.a.path.following.robotic.car part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Patricia Mellodge Chapter 4. Curvature Estimation 20 The third equation in 3.10 is VitanÁ v1c s cosỡp 1 - 1 - dCs 4.2 This equation can be rearranged as X n VidtanÁ VitanÁ . c s vicosỡp 1 r - ỡpd l - ỡp 4.3 which is linearly parameterizable in c s . This can be rewritten in the following form where y wa 4.4 vitanÁ 4.5 y 1 p n vidtanÁ w vicospp - 1 vpd 4.6 a c s 4.7 Knowing w and y a can be obtained using a least squares estimator. We want to find the à that minimizes J where J y wà 2dr J0 4.8 Making @J 0 gives t JO Differentiating gives an update equation for aà t Jo aà 4.9 aà -Pwe 4.10 where P e 1 Jq w2dr waà - y and w is defined in 4.6 . We can make the equation for P iterative by using the following update equation. P P2w2 4.11 where P is initialized to some large value. Patricia Mellodge Chapter 4. Curvature Estimation 21 can z image plane road surface Figure 4.3 Side view of the car s camera configuration. 4.1.3 Estimation Using Image Processing In addition to the constraints on the path s curvature the track itself consists of a black surface with a white line. The white line is the path that the car is to follow. This scheme allows for fairly easy processing to be performed on images of roadway. This section describes the image processing methods used to estimate the curvature On the FLASH car a camera is mounted in such a way as to capture an image of the road directly in front of the car. The configuration of the camera is shown in Fig. 4.3. The car s frame is given by x y z and the camera s frame by xc yc zc . One sample image is shown in Fig. 4.4. It is assumed that in the camera s field of view the track is a plane and perpendicular to the car s y-axis. The problem is to determine the radius of the curve in the car s frame of reference. Then the curvature is found by taking the reciprocal of the radius. Based on this value the actual curvature can selected to be used in the control algorithm as the curvature of the path at that point. Edge Detection The
