# Efficient Reachable Workspace Division under Concurrent Task for Human-Robot Collaboration Systems
## 2 Method
### Reachable Workspace Division
#### 2.1.2 Experiment Protocol  
**Part A** Gaze State  
Gaze states mostly occur in desktop work scenarios, where the object to be gazed at is located in front of the eyes and the pitch angle of the head is small. Therefore, our research divided the reachable area in the gaze state in the 2D space, and then discussed the effect of height on it. Target points in 2D can be selected more densely, thus improving the experimental accuracy while ensuring that the experiment can be implemented. The participant was seated in a height-adjustable chair in front of a table of 75 cm height, with a distance of 15 cm from the participant's chest. Visual excitement was presented at a flat surface monitor at a distance of 80 cm from the table. The manipulated object was a PVC rectangular block (1.5 \(\times\) 3 \(\times\) 1), with the initial placement at the perpendicular midline of the table. It is moved to the sides along the marked lines on the table during the experiment. The participant's waist was straight, head and trunk oriented to the table, while the center of the shoulder (RSHO) is aligned with the table's center line. In the beginning, the participant's right hand was positioned in Box 1 in Figure 1. After hearing the \"Started\" prompt, the participant should use the thumb and index finger to elevate the object, then drop it, put it back on the table, and, finally, retract the hand along the initial route to the position of Box 1. The participants needed to keep their eyes fixed on the cross in the center of the screen. At the end of each grasp, the PVC block is moved in a circle, where RSHO is the center, and the length of the arm is an axis. Considering 1 or 2 times grasp error, the moving angle of the object is set to 2\({}^{\circ}\). The participants executed the mission in 3 manners: (1) maintaining the head and staying physically unmoving; (2) maintaining the physically unmoving state while the head could be turned; and (3) both the physical and head could be rotated. The experiment was performed three times, and the height of the chair was adjusted to 48 cm, 55 cm, and 62 cm, respectively. Under the different chair heights, each type was repeated 3 times. The experiments required 85 min to complete. **Part B** Non-Gaze State  
Compared to the gaze condition, most tasks in daily life occur in the non-gaze condition, and their task scenarios are not limited to desktop tasks. Therefore, this research extended the range of target points to the 3D workspace for experiments in the non-gaze state. However, if the parameter of the moving angle has remained at 2\({}^{\circ}\), the number of reachable points in the 3D workspace is enormous, and it is impossible to complete the grasping of each point in the experiment scene. The choice of the parameter is essential. Setting too large will lead to errors, and setting too small will increase the complexity of the experiment, making it difficult to complete. Therefore, by modeling and clustering the human workspace, we set the moving angle between centroids of each cluster as the distance between adjacent reachable target point positions so that it can be uniformly distributed to represent the entire workspace. The process of target points set in detail is presented in Appendix A. A 3D spherical workspace frame customized for the grasping experiment was installed, and the center of the sphere is indicated by a green dot in Figure 2, aligned with the participant's RSHO. The target points are indicated by blue crosses, corresponding to the 84 clustering centers calculated by K-means and adjusted according to each participant's arm's length. The experiment was performed at the head 60\({}^{\circ}\) upward, 30\({}^{\circ}\) upward, 0\({}^{\circ}\), -30\({}^{\circ}\) downward, and \(-60^{\circ}\) downward, respectively, maintaining a constant head pitch angle in various task types.