# Workspace Analysis of a Mobile Manipulator with Obstacle Avoidance in 3D Printing Tasks
## 1 Introduction
The workspace analysis strategies focus on the robot model, DOFs, kinematic model, and inverse model as shown in Table 1. The importance of the workspace in applications such as welding, medical robots, 3D mine mapping, 5-axis moving gantry with diversified machine system (DMS) and DMS 3-axis CNC routing has enabled optimization of robot characteristics. Currently, the use of robots in the construction industry is emerging. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Industrial** & & **Optimal Workspace Analysis** & **References** \\
**Prototypes** & & \\ \hline RV-M1 Mitsubishi & The model of the optimal workspace of an industrial manipulator is based on the & [20] \\  & Denavit–Hartenberg parameters. & \\ \hline FANUC cr & The workspace is estimated with a window algorithm with singularity visualization for & [21] \\  & manipulator configuration. & \\ \hline ABB IRB-140 & The study of the workspace uses the kinematic model and shape analyses. & [22] \\ \hline Robotic arm & ABB IRB-1660 ID & A visual method is compared with the Monte Carlo method to obtain the optimal workspace of the manipulator robot. The results show that the visual model presents better modeling and digitalization features. & [23] \\ \hline Kuka LWR 4+ & The study analyses the workspace of two redundant robots by discretising some joints & \\ Staubli TX90 & and then reconstructs the 3D by revolution the plane area computed. The advantage of & \\  & this method is that it calculates the value of the workspace volume, allowing better & \\  & tracking of the differences between the workspaces. & \\ \hline PUMA 560 & The technique of mapping the workspace with deficient-DOF solves the problems of & \\  & maneuverability and stability of the robotic arm. & [25] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Methods to obtain the optimal workspace for industrial robots. The importance of this study and analysis of the workspace on construction sites is that it allows us to propose management strategies that guarantee the progress of the work and provide safety in the execution of construction tasks [30; 31]. However, analysing the workspace of robots is a challenging task since the construction continuously evolves and changes over time [32], as shown in Figure 1. In this case, we can observe the common elements in construction sites, such as piles of sand, metal, scaffolding, mouldings, support bars, and wooden supports, which represent a challenge for the robot design and the efficiency of the construction process. The approach of the following work is the analysis of the printing workspace of a mobile manipulator on a construction site. Therefore, to evaluate the printing workspace, we have considered a construction site with obstacles, which allows us to obtain the geometrical constraints, visualise the workspace and detect possible collisions during the 3D printing of building elements. For testing purposes, the profiles considered for printing are square, straight, circular, and sinusoidal. Finally, we present a simulation environment for the visualisation of the printing workspace, demonstrating that the proposed avoidance strategy allows us to avoid obstacles during 3D printing. A suitable strategy for analysing the printing workspace of the mobile manipulator in printed tasks is crucial for the success of a 3D printed construction process. In this