# Workspace Analysis of a Mobile Manipulator with Obstacle Avoidance in 3D Printing Tasks
## 3 Results
The fourth experiment shows the workspace of the sinusoidal profile printing, as shown in the second column of Figure 7. The size of the profile is 7 m. We distributed the obstacles in a sinusoidal line with the following distances between obstacles: the first obstacle is 1.6 m away from the second obstacle, the second obstacle is 1.4 m away from the third obstacle, and finally, the third obstacle has a distance of 1.3 m from the fourth obstacle. Figure 6: The solid magenta line describes the circular and square printing profiles. (**a–f**) show the tests carried out for three heights, \(z_{1}\), \(z_{2}\) and \(z_{3}\) for a circular profile of 2 m radius and a square profile of 2 m width and 2 m length. For the sinusoidal building element, the shape of the printing workspace is also sinusoidal. For printing profile heights \(z_{1}\) and \(z_{2}\), the mobile platform first avoids the obstacle and then maintains its position as the manipulator advances in 3D printing. For height \(z_{3}\), obstacle avoidance produces changes in the displacement of the mobile platform without affecting the sinusoidal shape of the printing workspace. The first column of Figure 8 shows the simulation environment with obstacles of the mobile manipulator in the CoopeliaSim software. The second column shows the four proposed printing profiles. The grey dashed line represents the displacement of the wheels of the mobile platform, and the solid cyan line describes the displacement of the centre. The black circle represents the obstacles. The magenta dashed line represents the current trajectory, and the solid black line is the reference trajectory. Figure 7: The solid magenta line describes the sinusoidal and straight printing profiles. (**a–f**) show the tests carried out for three heights, \(z_{1}\), \(z_{2}\) and \(z_{3}\) for a sinusoidal profile of 7 m radius and a straight profile of 6 m.  
Figure 8: The trajectory reproduced in CoppeliaSim is shown in the first column (**a**,**d**,**g**,**j**). The second column (**b**,**e**,**h**,**k**) shows the four proposed printing profiles. The third column (**c**,**f**,**i**,**l**) shows the cumulative printing errors for three different heights. The results of the cumulative errors can be seen in Figure 8. Height \(z_{3}\) registered the highest cumulative error, then \(z_{2}\) and finally \(z_{1}\), as shown in Figure 8c. The error increases as the height of the printing profile increases. In addition, when the height increases, the robotic platform performs a sharp displacement that affects the printing error, which decreases due to the control action described in Section 2.4.2. The combination of height increase and obstacle avoidance action generates an increase in cumulative error. For example, Figure 8f shows that \(z_{3}\) had the highest cumulative error compared to \(z_{1}\) and \(z_{2}\). Furthermore, this test recorded the highest cumulative error of all tests. The action of the potential fields causes a change in the behaviour of the mobile platform when it has an object nearby, resulting in changes in the displacement of the mobile platform. Figure 8i shows the cumulative error for the straight building element. The height \(z_{3}\) has the highest cumulative error compared to the heights \(z_{1}\) and \(z_{2}\). The sinusoidal displacement of the mobile manipulator due to the obstacle avoidance action produced by the potential field method and the height variation of the printed building element generates an increase in the cumulative error due to the action implemented by the distance function described in Section 2.4.2. Figure 8l shows that the highest cumulative error occurs at \(z_{3}\) compared to \(z_{1}\) and \(z_{2}\). The cumulative error increases due to the action of the potential fields, which causes variations in the displacement of the mobile platform when an object is detected.