Master Thesis - Hochschule Bonn-Rhein-Sieg

9. List of Figures Master Thesis Björn Ostermann page 125 of 126
Figure 63: Gaining the transposition matrix from one coordinate frame to another P1 to P3 mark the
reference points measured by the camera 0 marks the origin of the camera’s
coordinate system P1’ to P3’ and 0’ mark the respective points in the robot’s
coordinate system ........................................................................................................ 88
Figure 64: Image depicting the reachable space to the user.................................................................. 91
Figure 65: Determining the reachable space ......................................................................................... 92
Figure 66: Robot working below intruding object ................................................................................ 94
Figure 67: Resetting the height of intruding objects to match the robot’s tool centre point ................. 94
Figure 68: Selection of the significant part ........................................................................................... 95
Figure 69: a) Red safety border line and b) its significant part ............................................................. 96
Figure 70: Sample intrusion map .......................................................................................................... 97
Figure 71: Graphical explanation of the calculation of the shortest evasion path................................. 98
Figure 72: Flowchart for the “shortest Line” algorithm........................................................................ 99
Figure 73: Risk graph of the EN 13849-1 [72].................................................................................... 105
Figure 74: Relationship between categories, DCavg, MTTFd of each channel and PL of the EN 13849-1
[72] ............................................................................................................................ 106
Figure 75: Risk graph of the EN 13849-1 [72], reduced robot speed ................................................. 106
Figure 76: Relationship between categories, DCavg, MTTFd of each channel and PL of the EN 13849-1
[72] ............................................................................................................................ 107
Figure 77: Reachable space computation, no intrusion present .......................................................... 109
Figure 78: Distance calculation, intrusion at different distances to the robot, offset at 12cm ............ 110
Figure 79: Overall reaction time of the program when executing the evasion path............................ 111
Figure 80: Overall reaction time of the program when executing the speed control .......................... 111
Figure 81: Overall system stopping performance when executing the evasion path .......................... 112
Figure 82: Overall system stopping performance when executing the speed control ......................... 112