PhD Thesis Poppinga: RRT - Jacobs University

LIST OF FIGURES
3.6 The data returned by the SwissRanger (left) and the stereo camera (right) for the
scenes from the Outdoor 1 dataset. Photos in figure 3.5. . . . . . . . . . . . . . . . . 55
3.7 Photos of the robotics lab with a locomotion test arena in form of a high bay rack. . . 56
3.8 ALRF range image from the lab dataset . . . . . . . . . . . . . . . . . . . . . . . . 57
3.9 The Crashed Car Park in Disaster City in Texas where one of the datasets used in the
experiments was recorded. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.10 Perspective view of two point clouds from the Dwelling dataset from Disaster City . 58
3.11 The Hannover ’09 Hall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.12 Two views of a point cloud containing 78528 points from the Hannover ’09 Arena
dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.13 An overview of the Lesumsperrwerk as seen from the river’s surface. . . . . . . . . . 61
3.14 Two views of a sonar point cloud from the Lesumsperrwerk dataset . . . . . . . . . . 61
4.1 The definition for the angles ρ x and ρ y . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 An example scene where the stereo camera delivers few data points; especially ground
information is missing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3 Two-dimensional depictions of the three dimensional parameter (Hough-)space for
several example snapshots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4 Mean processing time and cardinality of point clouds . . . . . . . . . . . . . . . . . 73
5.1 Applying a 3D transform to a 2D polygon . . . . . . . . . . . . . . . . . . . . . . . 80
5.2 Different methods of projecting the point of a sub point cloud to the optimal plane
fitted to them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3 Problems with the two types of projection . . . . . . . . . . . . . . . . . . . . . . . 85
5.4 Differences between orthogonal projection and projection along the beam . . . . . . 86
5.5 Late projection can cause intersections when applied to ALRF data . . . . . . . . . . 87
5.6 An α-shape (grey) of a 2D point cloud (orange) . . . . . . . . . . . . . . . . . . . . 88
5.7 Some examples for convex polygons on a grid . . . . . . . . . . . . . . . . . . . . . 89
5.8 An example iteration of the algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.9 Triangulation of convex grid polygons . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.10 Comparison of triangulation with/without the restriction to the area covered by the
naive triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.11 Triangles with annotated spikyness . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.12 Time taken, number of polygons and spikyness for the different triangulation algorithms
on the German Open ’09 Arena dataset. . . . . . . . . . . . . . . . . . . . . 93
5.13 Time taken, number of polygons and spikyness for the different triangulation algorithms
on the German Open ’09 Hall dataset. . . . . . . . . . . . . . . . . . . . . . 94
5.14 Time taken, number of polygons and spikyness for the different triangulation algorithms
on the Planar/Round/Holes dataset. . . . . . . . . . . . . . . . . . . . . . . . 96
5.15 An example of outlining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.16 Class structure of the different variants of the patch map framework . . . . . . . . . 98
5.17 One dimensional case of bounding box based broad phase intersection test . . . . . . 102
5.18 A run of the kD-tree based collision detection algorithm detecting no collision. . . . 104
5.19 Map used in preliminary experiments . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.1 Real-world example for an explored volume . . . . . . . . . . . . . . . . . . . . . . 116
6.2 Using explored volume to compare different map types . . . . . . . . . . . . . . . . 117
12