# Efficient Reachable Workspace Division under Concurrent Task for Human-Robot Collaboration Systems
## 1 Introduction  
\"Man owes a good part of his intelligence to his hands\" [1]. However, upper-limb movement capacity still has deficits in a variety of situations. For example, in engineering maintenance, physical activity is often restricted by the work environment, and hands cannot quickly reach certain work positions, resulting in less efficient completion of tasks and causing fatigue and injury to the operator [2]. This situation is more evident in special fields, such as aerospace and military, wherein special working conditions could make the task more difficult to complete and increase the physical burden. In addition, people often desire to improve their ability to accomplish multiple tasks at the same time [3]. In these situations, to enhance human upper-limb mobility and enlarge the human reachable workspace, it is necessary to collaborate with external devices such as exoskeletons [4], supernumerary robotic limbs [5], and collaborative robots [6; 7; 8]. Whether these external devices can find the appropriate joining boundaries to achieve physical and cognitive enhancement and accomplish natural cooperation with humans for efficient human-robot collaboration (HRC) systems are an active topic of discussion in the scientific community. Efficient HRC systems require the rational allocation of human and robot workspaces, with robots assisting at locations where humans have difficulty reaching quickly, reducingthe time to complete tasks (without interfering with the tasks being performed by human operators), and improving the ability to complete multiple tasks simultaneously [9; 10]. This also corresponds to the definition of HRC: \"State in which a purposely designed robot system and an operator work on simultaneous tasks within a collaborative workspace [11]\". It requires first recognizing the motion being performed by the human operator to explore the components that need to be incorporated by the robot. Previous studies made efforts to explore methods of machine learning to enable robots to identify human motion; some researchers implement this work through neural networks [12; 13], neuro-fuzzy inference system-based classifiers [14; 15]. For instance, the work of [16] integrated a data-driven musculoskeletal model into a robot interaction controller to recognize human movements and classified them according to the model to match the corresponding robot trajectory for application in HRC scenarios. However, these efforts are task-oriented and analyzing each movement they can perform and building datasets is impossible due to the complexity of the arm movements. Thus, for simplifying the process of recognizing upper-limb movement, we aim to find a method that classifies the type of upper-limb movements in the full workspace and find the regularity that exists between them, so that the robot can quickly perceive the position that needs to be added to optimize the efficiency of the task. [PERSON] et al. [17] introduced five work tasks on a computer assembly line and decomposed them into different parts, such as moving and holding the CPU and main board, putting the rings into the main board, and gluing the fan. They divided the fine manipulation and repetitive motions and allocated them to human operators and robots, respectively, to explore within which segments robots could be added to reduce task accomplishment time and improve task efficiency. [PERSON] et al. [18] analyzed the main characteristics of joint angles during different daily living (ADL) tasks and ultimately found patterns between human upper-limb joint angles under different motions in unstructured environments through data-driven clustering approaches and used them as a basis for robot control [19]. In conclusion, efficient HRC systems require the classification of the human movement behavior and rational allocation of the parts to be completed by the human and the robot.