# Efficient Reachable Workspace Division under Concurrent Task for Human-Robot Collaboration Systems
## 1 Introduction
However, these studies have remained with the task-oriented approach to analysis and have not evaluated upper-limb movement capacity within the full workspace in a nonstructural environment. Therefore, we aimed to summarize human movement patterns by a quantitative index of task completion efficiency. During HRC, regardless of whether the target object is single or multiple, the robot and human focus on the same task, which is called the single task in this paper. For example, in surgery [20], the robot replaces the nurse in handing the surgical instruments to the doctor. In the process of supermarket shelf organization [21], the robot hands the products to the human, and the human operator attaches the corresponding labels and places them in the corresponding positions. In addition, single tasks are common in various scenarios, such as pathological examination [22] and daily life. In these tasks, the human and the robot have different main workspaces. Human operators perform tasks that are mostly focused on areas that can be reached quickly by both hands, such as the front of the vision, which is the workspace efficiently reachable by human bodies, and the robot transfers objects outside this area to the human operator. Thus, in dividing the efficiently reachable workspaces of the human body, finding a suitable boundary for the HRC system, and exploring areas where adding robot assistance could maximize efficiency, it can provide a reference for the robot to understand human behavior and the appropriate distribution of tasks between humans and robots. The efficiently reachable workspace for humans is highly correlated with its physical condition. When the object being manipulated is located in front of the human chest [23], human reaction speed and motion ability are at a remarkably superior level, and restrictions on body parts could lead to a decrease in upper limb capabilities. For example, in large aircraft assemblies, the interior environment is narrow, and the maintenance workers have difficulty turning their heads and bodies, making it difficult to reach certain positions with their hands. In addition, visual restrictions could also affect the movement status of the upper limbs, such as watching computer screens, reading documents, and assembling mechanical components. Under these situations, eyes are frequently in a state of gazing and central vision is anchored in a specific position. For finishing a concurrent task (getting a document, getting a water cup, or taking up an instrument), peripheral vision is required to provide movement information. The upper-limb movement performance will be greatly impaired compared to natural movement without visual restrictions [24; 25; 26]. This is also demonstrated in the driving and turning tasks of vehicles [27]. Thus, in humans, having different bodies and visual patterns in different task scenarios will have an impact on the efficient reachable workspace for their upper-limb movements. We aim to divide this workspace definitively and add robotic assistance in the nonefficient reachable workspace to increase the effectiveness of the HRC. Based on the above, the contribution of this paper is to divide the efficient reachable workspace accurately under the different physical and visual conditions and verify it in a work environment by using task completion time and the number of disturbances in the visual main task as indexes, providing a reference for quantifying the boundaries of robot incorporation in efficient HRC systems. The organization of the whole paper is as follows: Section 2 introduces the preliminary works of the experiment and experimental procedure; Section 3 presents the results of upper-limb workspace division and the comparison of HRC task completion efficiency based on an efficient workspace; and Section 4 discusses the results and applications. Finally, Section 5 summarizes the whole paper.