# Automatic Optimal Robotic Base Placement for Collaborative Industrial Robotic Car Painting
## 1 Introduction
Given the complexity of simultaneous base placement and trajectory planning, it is not surprising that many generic solutions resort to computationally expensive meta-heuristic search algorithms (see Table 1). A  
Figure 1: Mutli-robot car-painting base placement problem. The base positions directly impact the quality of vehicle paint coverage and the possibility of robot collisions during painting. For instance, robots placed on golden diamonds are more prone to collisions. On the other hand, robots placed on red diamonds will not be able to ensure complete vehicle paint coverage. detailed discussion and comparison with three of the most recent approaches in Table 1 is provided in Section 7 (see **Discussion and Comparison with the State of the Art**). Considering the literature gaps, this paper exclusively focuses on the collaborative robotic car-painting application. This specific focus allows us to deviate from generic base placement methods, which try to perform base placement and trajectory planning simultaneously. Specifically, we leverage the unique geometric properties of this industrial automation process to develop a computationally efficient algorithm without the need for simultaneous path planning and base placement. Our hierarchical approach prioritizes determining optimal base positions before engaging existing robotic painting motion/trajectory planners. The core challenge lies in quantifying paint coverage maximization and collision avoidance minimization for multi-robot vehicle painting without relying on prior knowledge or real-time data from motion/trajectory planners. Furthermore, this quantification requires design of cost functions tailored to the collaborative robotic car-painting application, which can be efficiently computed in an iterative manner, hence making them well suited for being utilized within any standard multi-objective optimization algorithm. **Contributions of the paper. ** This paper presents a computationally efficient algorithm for multi-robot car-painting base placement problem. Our approach represents a departure from the generic methods in the literature (see Table 1 for a sample overview), which combine base placement and motion/trajectory planning. In particular, our proposed algorithm does not rely on information from motion/trajectory planners during any stage of the base placement computations. Instead, our solution provides a hierarchical framework where computed optimal base positions can be employed as input to existing robotic painting motion planners. By leveraging the unique geometric characteristics of car painting, we develop two types of cost functions specifically designed for multi-robot vehicle painting scenarios. These cost functions, which are tailored to the collaborative robotic car-painting application, can be efficiently computed in an iterative manner. Consequently, they are well suited for being utilized within any standard multi-objective optimization algorithm. A key advantage of our proposed approach is that it primarily involves planar computations, with the exception of a one-time three-dimensional (3D) point cloud rendering and ellipsoidal fitting in its pre-processing stage.