# Efficient Reachable Workspace Division under Concurrent Task for Human-Robot Collaboration Systems
## 4 Discussion
As shown in Figure 7a, the time for area I is 2.938 \(\pm\) 0.314, area II is 3.048 \(\pm\) 0.391, area III is 4.072 \(\pm\) 0.335, area IV is 6.878 \(\pm\) 0.523, and area V is 7.892 \(\pm\) 0.611. There was no significant difference between the times of area I and area II (\(p>0.5\)), and there was a significant difference between the times for additional areas (\(p<0.01\)). The results show that human operators are highly responsive in completing tasks in areas I-II, have relatively shorter grasp times and can complete other tasks concurrently without interfering with the main visual task. Figure 7b shows the mean \(\pm\) SD of the number of ball collisions with obstacles completed by human operators in areas I-V, respectively. The number of the area I is 0.14 \(\pm\) 0.114, area II is 0.33 \(\pm\) 0.171, area III is 0.373 \(\pm\) 0.153, area IV is 2.475 \(\pm\) 0.643, and area V is 3.460 \(\pm\) 0.568. There was no significant difference between the times of area I, area II, and area III (\(p>0.5\)), and there was a significant difference between the number of additional areas (\(p<0.001\)). Due to the restriction of physical ability, the efficiency of completing the task and the ability of concurrent movement were greatly decreased when the position of the target object is located in areas IV and V; the tasks within areas IV and V are completed very slowly and the number of collisions increased significantly. In summary, we define areas I-II as the efficient reachable workspace, and the delicate manipulations that need to be done by human operators should be focused in this area. Thirdly, we analyzed the incorporation boundary of robots in HRC systems. In areas I and II, whether robotic arm assistance is added has no significant effect on the completion time of phase 1 and phase 2 of the tasks, and, due to the robotic arm needing to transfer the ball to the human operator, it leads to an increase of the task completion time in phase 3. When the target's position is located in areas III-V, the task completion time increases due to the restrictions of the human operator's physical and visual conditions, and the grasping task causes significant interference with the visual main task. Adding the assistance of the robotic arm in this area could reduce the task completion time and improve the concurrent task completion ability and efficiency. The average completion time for HRC  
Figure 7: (**a**) Mean \(\pm\) SD of task completion times for human operators in phase 1 in areas I–V. (**b**) Mean \(\pm\) SD of warning frequency for human operators in areas I–V. ** denotes \(p<0.01\), *** denotes \(p<0.001\), and *** denotes \(p<0.0001\). was 86.7% for human operators in area III and 70.1% in area IV, with the average number of warnings reduced from 2.5 to 0.4. The average completion time for HRC in area V was 59.3% for the human operator, and the average number of warnings was reduced from 3.5 to 0.5. Thus, in the HRC system, to improve the concurrent task completion capability and efficiency, the tasks in the efficient reachable workspace should be completed mainly by the human operator, on which the tasks that require high flexibility and complexity should be concentrated. In the nonefficient reachable workspace, the robotic arm is needed to assist and cooperate with the human operator to complete the task and achieve an efficient HRC system. There are still many limitations in this paper, just as the classification of each factor level is not detailed enough. However, we chose to systematically study human movement at the macro level. To conduct experiments more efficiently, environmental factors such as the size and shape of objects were not considered. In this study, we chose to focus on the human body's ability to perform concurrent tasks and, thus, chose to conduct experiments with objects that can be easily grasped with one hand.