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List of Figures
1.1 Three state-of-the-art robots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Components which allow to do collision avoidance. . . . . . . . . . . . . . . . . . . 2
1.3 Abstract robot model consisting of links and joints. . . . . . . . . . . . . . . . . . . 3
1.4 General tf tree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1 Relationship between frames and joints. . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Translation of a square in R 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 Rotation of a square in R 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4 Quaternion Operations on Vectors. [17, p. 117] . . . . . . . . . . . . . . . . . . . . 14
3.5 Relationship between clocks when they tick at different rates. . . . . . . . . . . . . . 15
3.6 Way to get the current time from a time server. . . . . . . . . . . . . . . . . . . . . . 16
3.7 Clock synchronization in PTP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1 Components needed for collision avoidance. . . . . . . . . . . . . . . . . . . . . . . 20
4.2 Hardware setup and tf tree of a statically mounted laser scanner. . . . . . . . . . . . 20
4.3 Hardware setup and tf tree of a tilting laser scanner. . . . . . . . . . . . . . . . . . . 21
4.4 Tilting laser scanner moves the laser scan from the xy-plane to a oblique plane. . . . 21
4.5 Hardware setup and tf tree of a sensor mounted on an robot arm. . . . . . . . . . . . 22
4.6 Components needed to capture a 3D point cloud. . . . . . . . . . . . . . . . . . . . 22
4.7 The elements to represent different systems. . . . . . . . . . . . . . . . . . . . . . . 26
4.8 How the different elements can be combined to form a system. . . . . . . . . . . . . 27
4.9 TF Data labeled with names that link the data to the frame in the tf tree. . . . . . . . 28
4.10 Mapping of polar to Cartesian coordinates. . . . . . . . . . . . . . . . . . . . . . . . 30
4.11 Uncertainty in polar and Cartesian coordinates. . . . . . . . . . . . . . . . . . . . . 31
4.12 Tf tree with three frames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.13 Single uncertainties for the frames. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.14 Complete tf chain with the single uncertainties and the total uncertainty. . . . . . . . 34
4.15 Different types of matching time stamps. . . . . . . . . . . . . . . . . . . . . . . . . 36
4.16 Gaps and overlaps in range of valid data. . . . . . . . . . . . . . . . . . . . . . . . . 36
4.17 Valid TF Data with overlaps but without gaps. . . . . . . . . . . . . . . . . . . . . . 37
4.18 Switch from fixed state to moving state. . . . . . . . . . . . . . . . . . . . . . . . . 37
4.19 Simple tf tree with two frames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.20 TF tree for the example setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.21 Modelling of the ROS tf system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.22 Modelling of the current tf support in SMARTSOFT. . . . . . . . . . . . . . . . . . . 40
4.23 Model where a central component manages all actuators. . . . . . . . . . . . . . . . 41
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