# Workspace Analysis of a Mobile Manipulator with Obstacle Avoidance in 3D Printing Tasks
## 5 Conclusions  
We presented an analysis of the printing workspace of a mobile manipulator in 3D printing applications on a construction site with obstacles. The study uses two widely known concepts in robotic technology: the Monte Carlo method and trajectory tracking control. The Monte Carlo method allowed defining the rotation constraint of each joint of the mobile manipulator and established a priori knowledge of its limitations. As a case study, we present four printing profiles (circular, square, straight and sinusoidal), representing the geometry of building elements in the construction industry performed by robots. To guarantee 3D printing, we controlled the position of the end-effector through a linear algebra controller. In addition, we analysed the workspace based on potential fields and distance function; these methods allowed solving constraints associated with possible collisions between mobile manipulator and obstacles, mobile platform and manipulator, and mobile manipulator and the printed building element.  
The results show the relevance of the mobile manipulator in construction, especially for large building elements and low heights, even if they are in variable environments and with obstacles (which is very common in building and infrastructure). Furthermore, these results demonstrate the adaptability of the mobile manipulator to different displacements while maintaining the regularity of the printing task within a suitable tolerance range. However, the printing workspace shape varies with the presence of obstacles affecting the displacement of the mobile platform without affecting the 3D printing of the profile. In addition, the printing error is affected as the height of the printing profile increases. Therefore, it has been determined that the parameters necessary to perform the analysis of the printing workspace are: the type of printing profile, the distance between the mobile platform and the obstacles, the minimum distance between the mobile platform with the desired printing profile and the maximum distance between the desired trajectory and the obstacles. The future research aims to implement printing workspace analysis in an in situ construction considering the terrain, dynamic obstacles, and complex building elements.  
Conceptualization: All authors; The research was performed under the supervision of F.A.C. Literature Review: R.G.R., F.A.C., R.G.A. and A.M.-R. Research Method: R.G.R. and F.A.C.; Software: R.G.R. Drafting the article based on the results: R.G.R. and F.A.C. Reviewed the paper R.G.A. and A.M.-R. All authors have read and agreed to the published version of the manuscript.  
This research was funded by ANID (ex CONICYT) FONDECYT 1181015, the Advanced Center of Electrical and Electronic Engineering AC3E ANID FB008, DGIIP-UTFSM Chile, and the 6 th Own Research and Knowledge Transfer Plan of the University of Seville (VI PPTI-US).  
Not applicable.  
The authors would like to acknowledge FONDECYT 1181015 and the Advanced Center of Electrical and Electronic Engineering AC3E ANID FB0008, DGIIP-UTFSM Chile.  
The authors declare no conflict of interest.