# Workspace Analysis of a Mobile Manipulator with Obstacle Avoidance in 3D Printing Tasks
## 1 Introduction  
Three-dimensional printing (3 DP) consists of building a component layer by layer [1]; this technique employs a computer-aided design (CAD) model [2]. Currently, this technology is evolving towards large scale 3D printing, where the main novelty is the use of concrete. In this context, a new technique known as 3D extrusion-based concrete printing (3 DCP) emerged [3]. The advantages of 3 DCP include reducing the use of labour, improving flexibility in architectural design, and saving costs during the construction process [4]. The construction industry has involved robotic platforms and additive manufacturing techniques to reduce the time required to produce complex geometries. These robotic platforms perform repetitive motions and deposit material uniformly. Furthermore, the robot has structural conditions, dexterity, ability, and flexibility to improve the efficiency of 3D printing [5]. Despite the advantages of robots, positioning these robotic platforms is a great challenge that requires analysis of their workspace, degrees of freedom (DOFs), and perception of the construction environment. There are several methods to evaluate the workspace of a manipulator, through simulation software, manual trials, and error fields tests, which provide information about the constraints of a robot. However, the techniques for workspace evaluation are geometric, iterative, and use analytical methods that can be mathematically complex and computationally expensive [6]. The workspace of an industrial robot is a region of points that the end-effector can reach. The strategy to obtain the optimal workspace considers the kinematic design of the robotic platform and the size and shape of the space, parameters that depend on the DOFs and the geometry of the robot arm. In some cases, the workspace is flat, cylindrical, spherical, and more complex depending on the industrial robot [7]. Several papers report strategies used for workspace analysis of industrial manipulators. The strategy for analysing the workspace of the DELTA robot used CAD software, which studies the impact of the design parameters of the manipulator [8]. The CAD-Virtual Basic (VB) method determines the accessible workspace of the SRMs manipulator from 2 to 9 DOF (degrees of freedom) [9]. The Maximum Surrounding Workspace (MSW) proposes an analysis based on the kinematics of the Delta robot, which discusses the geometrical representation of the desired workspace. The study presents the analysis of the accessible workspace of the manipulator considering the geometrical parameters of the robot based on a right circular cylinder inscribed in the MSW [10] and other methods based on geometric algorithms studied the optimal workspace of an industrial robot in an environment with obstacles [11]. Other strategies for determining the optimal workspace are the gradient ascent method [12] and the direct and inverse positional kinematics model [13]. The study of robot workspace in 3D printing tasks on construction sites involves the analysis of the environment, which constrains the operation capabilities of robots. These constraints can be mobile and fixed obstacles, humans and possible interactions between robots. In manipulability applications, the implementation of a genetic algorithm allows maximising the minimum manipulability by obtaining a collision-free trajectory [14]. In addition, in trajectory tracking tasks, the limited error-controlled iterative learning (BEILC) algorithm has shown promising results in obstacle avoidance without affecting the trajectory tracking of the robotic platform [15]. Obstacle detection allows robotic platforms to circulate and avoid an object present in the environment. In processes involving humans, control barrier functions (CBF) prevent the robot from colliding with humans. This study analyses the action considering human joint velocities and accelerations [16]. Furthermore, some studies reported on different objects detection devices such as ultrasonic sensors, 3D LIDAR, and vision sensors [17; 18; 19].