# Workspace Analysis of a Mobile Manipulator with Obstacle Avoidance in 3D Printing Tasks
## 3 Results  
The CoopeliaSim simulation software was used to analyse the printing workspace of a mobile manipulator on a construction site [41]. The mobile manipulator used in the simulation consists of a UR5 robotic arm, an end-effector and a mobile platform. The motion constraints and rotation angles of the mobile manipulator were described in Section 2.3.1; these operating parameters were obtained using the Monte Carlo method [38]. Figures 6 and 7 show the desired trajectory of the end-effector, described by the solid magenta line, while the solid slate grey line corresponds to \(d_{1}\). The solid fossil grey line and the cloud grey line represent \(a_{2}\) and \(a_{3}\), respectively. The solid anchor grey line represents \(d_{4}\), while the solid pebble grey line represents \(d_{5}\) to the end-effector. Grey colours of different shades have represented the area of the printing workspace occupied by each manipulator link during the printing of the building elements. Furthermore, we have included the footprint left by the mobile platform as described in the yellow area, and a green dashed line describes the wheels of the mobile platform. The solid grey cubes represent obstacles in the environment. In order to analyse the printing workspace of the mobile manipulator during the 3D printing task and verify the effect of obstacle avoidance in printing building elements, we design a set of experiments. The first experiment is the avoidance of obstacles located in random positions of the construction site and analysis of the workspace of the mobile manipulator while performing a 3D printing task. The first column of Figure 6 shows the experiments with a circular building element at different heights (\(z_{1}=0\) m, \(z_{2}=0.85\) m and \(z_{3}=1.2\) m). Tests show that obstacle avoidance does not affect the shape of the workspace. The avoidance action produces a change in the movement of the mobile platform without affecting the movements of the manipulator. The second experiment consists of printing a square building element, as shown in the second column of Figure 6. The size of the profile is length = 2 m and width = 2 m and consists of three heights (\(z_{1}=0\) m, \(z_{2}=0.85\) m and \(z_{3}=1.2\) m). The obstacles were distributed as follows: two obstacles near the corner of the initial point, and the other two obstacles were placed two metres away from the corners. In these tests, obstacle avoidance produces a change in the displacement of the mobile platform and the manipulator's rotation angles. For this reason, it can be seen that the square envelope of the printing workspace varies in shape. However, for the test with \(z_{3}\), the movement changes were less significant because the mobile manipulator is closer to the printing profile than to the obstacles. The first column of Figure 7 shows the printing of a straight profile of 6 m in length. The obstacles have been arranged in a straight line and considering a distance between obstacles. The distance between the first obstacle and the second obstacle is 1.6 m; the second obstacle is 1.3 m away from the third obstacle, and finally, the third obstacle has a distance of 1.1 m from the fourth obstacle. In this third experiment, we considered three printing heights of the building element. The printing workspace shows a sinusoidal shape during 3D printing due to the obstacle avoidance action. The obtained results showed that obstacle avoidance changes the shape of the mobile manipulator's printing workspace and the displacement behaviour of the mobile manipulator. Based on these observations, we noticed that the mobile platform first evades the obstacle in this profile and then maintains its position while the manipulator moves forward in 3D printing.