# Efficient Reachable Workspace Division under Concurrent Task for Human-Robot Collaboration Systems
## 3 Results  
### Workspace Division  
Figure 5a shows the mean \(\pm\) SD of the angle of each area with different heights under the gaze. When chair height is 62 cm, 55 cm, and 48 cm, the angle of the type (1) is 44.143 \(\pm\) 2.037\({}^{\circ}\), 45.363 \(\pm\) 2.763\({}^{\circ}\), and 44.779 \(\pm\) 2.394\({}^{\circ}\). The angle of type (2) is 66.904 \(\pm\) 4.005\({}^{\circ}\), 68.466 \(\pm\) 2.381\({}^{\circ}\), and 67.364 \(\pm\) 3.835\({}^{\circ}\). The angle of type (3) is 78.453 \(\pm\) 3.052\({}^{\circ}\), 82.317 \(\pm\) 4.936\({}^{\circ}\), and 82.554 \(\pm\) 4.372\({}^{\circ}\). No significant difference was found between the angle and height of each area. (All \(p>0.05\), \(p\) = 0.3997, \(p\) = 0.5269, \(p\) = 0.4177). Figure 5b shows the mean \(\pm\) SD of each area angle when the initial angle of the head differs under nongaze. When the initial angle of the head was upward 60\({}^{\circ}\), upward 30\({}^{\circ}\), flat, downward 30\({}^{\circ}\), or downward 60\({}^{\circ}\), the angle of the type (1) is 45.421 \(\pm\) 3.019\({}^{\circ}\), 45.143 \(\pm\) 2.898\({}^{\circ}\), 46.587 \(\pm\) 3.571\({}^{\circ}\), 46.955 \(\pm\) 3.798\({}^{\circ}\), and 44.049 \(\pm\) 2.664\({}^{\circ}\). The angle of type (2) is 154.214 \(\pm\) 4.381\({}^{\circ}\), 153.293 \(\pm\) 4.451\({}^{\circ}\), 154.903 \(\pm\) 4.317\({}^{\circ}\), 151.926 \(\pm\) 3.712\({}^{\circ}\), and 152.159 \(\pm\) 4.114\({}^{\circ}\). The angle of type (3) is 180\({}^{\circ}\). No significant difference was found between the angle and height of each area. (All \(p>0.05\), \(p\) = 0.4031, \(p\) = 0.6047).  
Figure 5c shows the mean \(\pm\) SD of each area angle when the task type differs under the gaze and the non-gaze states. The workspace could be divided into three areas in either case. In the gaze state, the angle of type (1) is 44.761 \(\pm\) 2.398\({}^{\circ}\), the angle of type (2) is 67.578 \(\pm\) 3.407\({}^{\circ}\), and the angle of type (3) is 81.108 \(\pm\) 4.120\({}^{\circ}\). The results show that the effect of task type on the angle is significant (task type 1 and 2: \(p<0.01\), task type 1 and 2: \(p<0.01\), and task type 1 and 3: \(p<0.001\)). In the non-gaze state, the angle of type (1) is 45.631 \(\pm\) 3.190\({}^{\circ}\), the angle of type (2) is 153.173 \(\pm\) 4.195\({}^{\circ}\), and the angle of type (3) is 180\({}^{\circ}\). The results show that the effect of task type on the angle is significant (task type 1 and 2: \(p<0.001\), task type 2 and 3: \(p<0.01\)). There was no significant difference between the angles corresponding to type (1) in the gaze and non-gaze states (\(p>0.5\)), which divide into area I. There was a significant difference between the angles corresponding to types (2) and (3) (\(p<0.001\)), and the reachable workspace in the non-gaze state is substantially higher than the gaze state, so we defined the extent of task type 2 in the gaze state as area II, and task type 3 as area III. The extent of task types 2 and 3 in the non-gaze state includes areas I-III and the coverage is larger, defined as areas IV and V. The results of the visualization for each area's extent and body pattern are shown in Figure 5d.