# Automatic Optimal Robotic Base Placement for Collaborative Industrial Robotic Car Painting
## 1 Introduction  
In this paper, we investigate the problem of optimal robotic base placement for industrial multi-robot car painting (see Figure 1). Robotic spray painting, which aims at covering object surfaces with varnish, paint, or ink, utilizes compressed-air driven spray guns. These spray guns atomize fluid particles, directing them onto industrial target surfaces [1, 2, 3]. Conventional industrial painting automation systems using robots, however, suffer from time-consuming trajectory generation for the robotic arms [4, 5]. To avoid the time-consuming process of manually guiding the robot arm through a complete spraying cycle, CAD-based methods have emerged as a viable and faster alternative for generating robot trajectories [2, 6]. These methods employ various techniques for path planning, such as RRT-based algorithms [7], iterative schemes with adaptive spray-gun stroke diameters [8], and path-constrained trajectory planning [4]. In all these algorithms, poor robot baseplacement can detrimentally affect motion/trajectory planning in terms of convergence time and quality of generated paths/motion trajectories (see, e.g., [9]). Base placement plays a critical role in optimizing performance across various robotic application domains, including industrial manufacturing [10; 11], surgical robotics [12], and human-robot interaction [13; 14]. In particular, the placement of a robot's base affects the robot's reachability, manipulability, and workspace coverage during task execution [15]. These factors can, in turn, minimize redundant movements in flexible production lines with limited workspace and further optimize the robot energy consumption profiles [16; 17]. In an increasing number of flexible manufacturing settings such as vehicle painting, teams of collaborative robots need to execute a delicate and complex task such as coating/painting/welding, where a single robot is not capable of accomplishing the objectives individually (see, e.g., [18; 19; 20; 21]). It should come as no surprise that base placement is of crucial importance to the field of collaborative industrial robotics, where repositioning of the robots is costly and time-consuming. As opposed to traditional, highly repetitive industrial processes, a primary goal in collaborative robotics is to enable flexible manufacturing systems for agile product customization. For example, in flexible manufacturing-based car painting, if one or more robotic arms malfunction and uninterrupted production is essential, the manufacturer may need to replace the inoperative arms with different robotic manipulators from their inventory. Alternatively, the manufacturer might need to rapidly change the vehicle model in the production line. In both cases, a new set of base positions and motion trajectories must be planned swiftly to meet agile manufacturing demands. Indeed, one of the keys to successful trajectory/motion planning for industrial collaborative robots is that of properly choosing the fixed base positions on the factory floor/ceiling. **Gaps in the literature:** Table 1 provides an overview of various industrial robotic base placement algorithms that have been proposed in the literature. Many of these algorithms have been designed to be general and applicable to a wide range of applications including robotic welding, coating, and painting. Consequently, their generality prevents them from leveraging the inherent geometrical and task specific features in particular industrial applications such as robotic-based vehicle painting. Furthermore, a majority of these algorithms take a holistic and centralized approach to the problem by combining base placement and motion/trajectory planning together. However, centralized approaches to multi-robot path planning are plagued by NP-hardness, where the computational complexity grows exponentially with increasing robot numbers [22; 23].