# Efficient Reachable Workspace Division under Concurrent Task for Human-Robot Collaboration Systems
## 4 Discussion  
This paper divided the human upper-limb efficient reachable workspace based on different body and visual patterns to provide a basis for the boundaries of robot incorporation in human-robot collaboration systems. The main contributions of this paper are that it (1) summarized the movement patterns of the human body and divide the upper limb workspace into five areas; (2) divided the human body's efficient reachable workspace and found the most convenient workspace for HRC, and cooperation within this area helps improve the concurrent task completion ability; and (3) verified that adding the assistance of robotic arms in nonefficient reachable areas can significantly improve the efficiency of HRC tasks by using task completion time and concurrent task capability as indexes and precisely dividing the joining boundary of robots in HRC systems. The overall experimental and analysis procedure framework is illustrated in Appendix B. When the tasks are located in different areas, we show the human operation individually and the human-machine collaboration through videos in the Supplementary Materials. Some interesting observations will be discussed in the rest of this section. Firstly, we divided the upper-limb workspace into five areas since there is no significant difference between the angles of each area under the gaze state when the chair height is changed or when the head pitch angle is changed under non-gaze state, and there is no significant difference between the angles obtained from different participants. Therefore, the results are stable and can be generalized to the analysis of human movement capacity in nonstructural environments. We averaged the obtained angles of each area. Analysis from the right side: area I is 0\({}^{\circ}\)-44.761\({}^{\circ}\), participants could reach area I without any physical movement in gaze and non-gaze states; work in this area is extremely easy to accomplish, and neither physical nor visual limitations are sufficient to affect tasks in this area. Area II is 44.761\({}^{\circ}\)-67.578\({}^{\circ}\); work tasks in this area require head turns to be completed under the gaze state and non-gaze state. Area III is 67.578\({}^{\circ}\)-81.108\({}^{\circ}\); tasks in this area require head and body turns if in the gaze state, or just head turns in the non-gaze state. Area IV is 81.108\({}^{\circ}\)-153.173\({}^{\circ}\); in the gaze state, the work task cannot be completed in this area and requires simultaneous head turn with no visual restrictions. Area V is 153.173\({}^{\circ}\)-180\({}^{\circ}\); the body needs to be turned without visual restrictions to complete the work task. Secondly, we analyzed the task completion time and the warning frequency of the visual main task for each grasp position of the human operator. There is no significant variation in them in each area, demonstrating that changes in the target object position within each area will not have an impact on the task completion time. There were significant differences between areas, demonstrating that the patterns of human movement differed between each area, which confirms the rationality of the workspace division. As shown in Figure 6, from the area I to area V, the completion times of the human operator in phases 2 and 3 remain essentially unchanged, demonstrating that the transfer of the target ball from the grasp position to the base position and the installation is independent of the target position. However, the time of phase 1 and the warning frequency increased gradually, demonstrating that deviation from the target position could lead to slower responses when having a visual stimulus; the task becomes increasingly difficult to complete and requires increased physical DOF. Therefore, we analyzed the mean \(\pm\) SD of task completion times in phase 1 and warning frequency for human operators in areas I-V, respectively.