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Longitudinal Slip Ratio from Digital Image Correlation
The slip ratio is determined by post processing a sequence of images obtained from a single calibrated and undistorted camera. Features on both the tyre and the road, close to the contact patch, are tracked using the DIC method described in 4.1.2. The SIFT feature tracker is used due to the poor result obtained using the Lucas-Kanade (section 4.1.1) optical ow algorithm. This could be due to larger motions being experienced or one of the other assumptions of the algorithm being invalid. A small window is selected in image It which encapsulates both the tyre and road close to the contact interface. The key points in this image is tracked across the whole of image It+1 (see Figure 6.1).
The DIC method used can at times produce mismatched key points. In order to reduce the mismatched key points, an initial outlier rejection is performed. Since the speed of the regions under consideration should be mostly horizontal, matches that result in large deviation in the y-direction are rejected, i.e. key points which move too much in the vertical direction. Once the key points have been matched they have to be separated into three categories, points lying on the tyre, points lying on the road and any additional outliers. At rst a simplistic method was proposed whereby a horizontal line is drawn at the contact point. Any points above this line is considered to be on the tyre and any points below are on the road. This method, while being very ecient and successful at the start of the test, causes some points to be categorized incorrectly due to the contact point moving vertically during the test. The method also fails to remove any additional outliers which are present. The vertical movement of the contact patch is due to the roll radius changing as a result of load being transferred during braking as well as the test rig bouncing. A more robust method for categorizing the points is therefore required. In this study a clustering technique is implemented to characterize the key points into the three categories. Two clustering methods generally used are the K-means and agglomerative clustering technique [Gupta et al., 2011]. In the K-means approach, K cluster centroids are chosen and all points are joined to these centroids. The centroids are updated after all points have been joined to the clusters. The process then restarts by joining all the points to the new updated centroids. This process continues until the centroid’s position change very little. The disadvantage of this method is that the process continues until steady state of the centroids are reached. In the agglomerative clustering technique each point is considered as a cluster. Iteratively the two clusters which are the closest are joined and the cluster centroid is recalculated. The process is repeated until the desired numbers of clusters are obtained. The disadvantage of this method is that prior knowledge of the number of clusters is required. In this application while we require three groups (tyre, road and outliers), the situation could arise when there is no outlier cluster, resulting in two clusters containing either tyre or road points. An alternate case is where there may be more than one outlier cluster, with one outlier cluster closer in distance to either the tyre cluster or the road cluster rather than another outlier cluster. This would result in outliers being clustered together with either the tyre or road clusters.
The clustering algorithm implemented in this study includes aspects from both clustering techniques.
Two main clusters are initially created, a tyre and a road cluster, containing initial points in each cluster. The remaining key points are considered to be an individual cluster themselves. The distance from each cluster to one of the two main clusters is calculated. The cluster with the smallest distance to one of the main clusters is then included into the corresponding main cluster. The cluster centroid is recalculated along with the distance to each of the remaining individual clusters. This process is repeated until the smallest distance between clusters exceeds some threshold. The remaining clusters, not included into one of the main clusters, are considered outliers. This process is graphically illustrated in Figure 6.2. The initialisation creates the initial tyre (cluster 1) and road (cluster 2) clusters. Iteratively the point closest to any of these two clusters is joined into that cluster. In the rst iteration a point is joined into cluster 2. The centre of this cluster is recalculated and the distance to each point is recalculated. This process is continued for N iterations until the distance of a point to a cluster is larger than a threshold. The nal clusters are then obtained with the remaining points classied as outliers.
Experimental Setup And Results
The method is validated by comparing it to the traditional method of estimating the slip-ratio from equation 6.1. The method is tested on a tyre test rig as shown in Figure 6.7. The tyre test rig is equipped with a wheel force transducer, developed by the University of Pretoria, which can measure all six force/moment components as well as the rotational angle of the wheel. A road proling laser is used to measure the eective tyre rolling radius and a dierential GPS is used to measure the test rig speed.
The tyre test rig is pulled using a large truck with the vehicle speed kept as constant as possible. The test rig is equipped with an electronically controlled pneumatic braking system which is programmed to provide a gradual increase in braking, thus generating a gradually increasing slip-ratio. A Point Grey Flea3 (USB 3.0) (see Appendix A for specications) camera is mounted facing the contact patch of the tyre, as shown encircled in Figure 6.7. A 4mm wide angle lens is used (see Appendix A for specications). The camera is sampled and synchronized with the data by using a 100Hz trigger. During the braking test a fairly low resolution grey-scale video of 640 480 pixels is captured of the contact patch region. The slip-ratio is then determined in post processing from the recorded video.
1 Introduction
1.1 Problem Statement
1.2 Layout of the Study
2 Camera Basics
2.1 Digital Cameras
2.2 Lenses and Camera Settings
2.3 Conclusion
3 Mathematical Camera Models and Calibration
3.1 Pinhole Camera Model
3.2 Homogeneous Coordinates
3.3 Lens Distortion
3.4 Single View Calibration
3.5 Multiple View Calibration
3.6 Conclusion
4 Digital Image Correlation Techniques
4.1 Sparse Image Correlation
4.2 Full Image Correlation
4.3 Conclusion
5 Side-slip Angle Measurement on Rough Terrain
5.1 Introduction
5.2 Slip Angle Measurement Using Ecient 2D Planar Method
5.3 Slip Angle Measurement Using Pose Estimation from Image Correspondence
5.4 Slip Angle Measurement Using Stereograhical System
5.5 Experimental Test
5.6 Maximum Operating Speed
5.7 Future Work
5.8 Conclusion
6 Tyre Longitudinal Slip-Ratio Measurement
6.1 Introduction
6.2 Longitudinal Slip Ratio from Digital Image Correlation
6.3 Experimental Setup And Results
6.4 Future Work
6.5 Conclusion
7 Rough Terrain Proling Using Digital Image Correlation
7.1 Introduction
7.2 Stereography
7.3 Compilation of Surfaces
7.4 Experimental Results
7.5 Drift Removal
7.6 Future Work
7.7 Conclusion
Conclusions and Recommendations
Conclusions
Recommendations
Appendices
Appendix A
Bibliography
