# Automatic Optimal Robotic Base Placement for Collaborative Industrial Robotic Car Painting
## 7 Simulation Results
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Base Positions (\(p_{x}\),\(p_{y}\)) for** & **Overlap Areas (Units: [m])** & **Paint Coverage (\%)** & **Mean Normalized Manipulability (NM)** & **NM Standard Deviation** \\ \hline \((-4.5,1)(0,0)(4.5,1)\) & 0 & 56.1 & 0.2476 & 0.1902 \\ \hline \((-3.5,0)(0,0)(3.5,0)\) & 0 & 66.7 & 0.2669 & 0.2283 \\ \hline \((-3.0,0)(0,0)(3.0,0)\) & 0.4929 & 80.3 & 0.2831 & 0.2340 \\ \hline \((-2.5,1)(0,0)(2.5,1)\) & 2.05 & 98.5 & 0.6932 & 0.0974 \\ \hline \((-2,1.3)(0,0)(2,1.3)\) & **4.12** & **100** & **0.7717** & **0.0919** \\ \hline \((-1.5,0)(0,0)(1.5,0)\) & 9.13 & 90.9 & 0.4053 & 0.2428 \\ \hline \((-1.0,1)(0,0)(1.0,1)\) & 10.88 & 92.4 & 0.7211 & 0.1317 \\ \hline \((-1.0,0)(0,0)(1.0,0)\) & 12.96 & 83.3 & 0.4886 & 0.2719 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Impact of robotic base positions on paint coverage and manipulability with the homogeneous robotic team consisting of ABB IRB 4600 robots. The gray entries demonstrate the results obtained from our proposed optimal base placement algorithm. Figure 10 depicts the snapshots of the homogeneous team of six ABB IRB 4600 robots painting a Ford Motor Company F-150 truck where the robot base positions were obtained from our proposed optimal base placement algorithm. Furthermore, Figure 11 depicts the snapshots of the same team placed at non-optimal positions. The figures demonstrate that in the non-optimal case, the robots failed to paint the top of the vehicle completely, despite the fact that both painting scenarios were utilizing the same motion planning algorithm. Furthermore, suboptimal base positions forced the robots to traverse configurations close to elbow and shoulder singularities during painting, which can be clearly seen when the arms have to overstretch to perform their painting task. Finally, the histograms in Figure 12 depict the normalized manipulability values of the robots during painting. The percentage values on each bar in the histograms provide the painting duration during which  
**Simulations with a heterogeneous robotic team:** In all simulation scenarios, suboptimal base positions led to degraded algorithm performance, even when using the same path planning algorithm. This resulted in reduced coverage and frequent encounters with singular configurations. Specifically, elbow and shoulder singularities occurred during the painting process when the robot bases were poorly positioned. Elbow singularities arise when the robotic arm is fully extended, while shoulder singularities occur when the shoulder joint aligns in a way that restricts the arm's ability to rotate freely in certain directions (see Figure 13). The collection of simulation results considered six robotic arms of different types, namely, four ABB IRB 4600 and two Fanuc R2000 iC robots. Figure 14 depicts the snapshots of the heterogeneous team of robots painting the Ford Motor Company F-150 truck where the robot base positions were obtained from our proposed optimal base placement algorithm. Furthermore, Figure 15 depicts the snapshots of the same team placed at non-optimal positions. The figures demonstrate that in the non-optimal case, the robots failed to paint the top of the vehicle completely, despite the fact that both painting scenarios were utilizing the same motion planning algorithm. Furthermore, suboptimal base positions forced the robots to traverse configurations close to elbow and shoulder singularities during painting, which can be clearly seen when the arms have to overstretch to perform their painting task. Figure 12: The normalized manipulability of the robotic arms during collaborative vehicle painting: (left) optimal and (right) non-optimal base positions. The percentage values on each bar in the histograms provide the painting duration during which the robot manipulability belonged to a certain interval.