# Efficient Reachable Workspace Division under Concurrent Task for Human-Robot Collaboration Systems
## 3 Results
### Completion Time of HRC Tasks  
Figure 6a shows the results of the quantitative analysis for the efficiency of the human operator or human and robotic arm collaboration to complete the task. The left \(Y\)-axis corresponds to the mean \(\pm\) SD of task completion time to the human operator or human and robotic arm collaborating when the target ball is located at the first to eighteenth grasping points, respectively. There was a significant difference between the task completion times for each group between human operators and HRC. When the target ball position is located in area I and area II, the difference is small between the task completion time for humans and robots (\(p<0.5\)), and in area III, the difference grows gradually (\(p<0.01\)). In area IV and area V, there is an evident difference in task completion time between the human and robot (\(p<0.001\)). From area I to area V, human operators have significantly increased task completion times, while the robot is essentially constant.  
Figure 5: Task type 1 is keeping the head still, task type 2 is keeping the head and trunk still, and task type 3 is unlimited. (**a**) Mean \(\pm\) SD of each area angle when height differs under the gaze state. There was no significant (\(p>0.05\)). (**b**) Mean \(\pm\) SD of each area angle when the initial angle of the head differs under the non-gaze state. There was no significant (\(p>0.05\)). (**c**) Mean \(\pm\) SD of each area angle when task type differs under the gaze and non-gaze state. **\(p<0.01\), and **** denotes \(p<0.0001\). The results of the visualization for each area’s extent and body pattern are shown in Figure 6 (**d**).  
and in area V, the time required for the human operator has a small increase compared to the robot (\(p<0.5\)). There was no significant difference for phase 1, from area I to area II, between human operators and HRC (\(p>0.5\)), and in area III, the difference in task completion time grows gradually (\(p<0.01\)). In area IV and area V, there is a distinct increase in task completion time for human operators, with a significant difference between humans and robots. (**9-12:**\(p<0.001\), **12-18:**\(p<0.0001\)).  
The right \(Y\)-axis corresponds to the mean \(\pm\) SD of warning frequency to the human operator or human and robotic arm collaborating when the target ball is located at the first to the eighteenth grasping point, respectively. In area I and area II, there was no significant difference between human operators and HRC, and in area III, the difference grows gradually (**8**: \(p<0.5\)). In area IV and area V, there is an evident difference in warning frequency between the human and robot (**9-10:**\(p<0.001\), **11-18:**\(p<0.0001\)).  
There was no significant difference between the task completion time and warning frequency for each phase within each area. Thus, taking the average value for each area, as shown in Figure 6b, there was a significant difference between the task completion times of phase 3 for each area between human operators and HRC (\(p<0.5\)). The completion time of phase 1 from area I to area II, between human operators and HRC was not significant (\(p>0.5\)) and had a small increase in area III (\(p<0.01\)). There was a significant difference between area IV and area V (\(p<0.0001\)). The warning frequency in area I to area III between human operators and HRC was not significant (\(p>0.5\)), and there was a significant difference between area IV and area V (\(p<0.0001\)).