Master Thesis - Hochschule Bonn-Rhein-Sieg

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5. Algorithms Master Thesis Björn Ostermann page 90 of 126 In Figure 63e the rotational part of the matrix is determined. The camera’s coordinate system matrix is converted by using the unity matrix into the coordinate system of the robot. In parallel, all used conversions are applied to a unity matrix, which results in the rotation matrix (see Equation 11). �C � � C �� C 1x 1y 1z C C C �1 � � 0 �� 0 2x 2 y 2z 0 1 0 C C C 3x 3 y 3z � � � � �� 0� 0 � � � 1�� 1 � � 0 �� 0 �a� � � d� �� g� 0 1 0 b� e� h� 0� 0 � � � 1�� c� � f � � � � i� �� R � � R �� R �a � � d �� g 1x 1y Equation 11: Determining a rotation matrix [61] The translation vector is determined, by rotating the position vector of the first point 0P 1 from the camera’s coordinate frame to the robot’s coordinate frame and by calculating the translation between this rotated first point with the original first point of the robot’s coordinate frame (see Equation 12). �k � �P � � � � � l � � P �� m�� P R1x R1y R1z � �a � � � � � d �� g c � �P f � � � � � P i �� P C1x C1y C1z Equation 12: Determining the translation vector [61] Graphically this can be described as rotating the camera’s point of origin – 0 – around the first measurement point – P 1 – and then calculating the shift between the rotated camera origin and the original robot origin – 0� – (see Figure 63f). b e h � � � �� 1z b e h R R R 2x 2 y 2z c � f � � i �� R R R 3x 3 y 3z � � � ��
5. Algorithms Master Thesis Björn Ostermann page 91 of 126 5.5.3 Determining the reachable space This algorithm is designed to divide the workspace into reachable and unreachable space (as defined in chapter 4.3.4). Thereby, as defined in chapter 2.3.1, generally all space above and behind a dynamic object, must not be accessible to the robot and thereby builds the unreachable space. Figure 64 shows the result of the algorithm, as it is depicted on the computer screen, showing the green robot, a red intruding object and the blue border of the reachable space. Figure 64: Image depicting the reachable space to the user The algorithm, used to create this result, is depicted in Figure 65.
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Master Thesis ”Industrial jointed
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Statutory Declaration Master Thesis
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Contents Master Thesis Björn Oster
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1. Introduction Master Thesis Björ
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2. Overview on human-robot Master T
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3. Hard- and software Master Thesis
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Master Thesis - Hochschule Bonn-Rhein-Sieg

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