## 1 Introduction
### Handover Timing Prediction and Fluency of Robots  
In the context of assembly tasks during which robots hand over parts to human partners, the handover path should be as close as possible to the expectations of the human partners, whereas the time point must be estimated as accurately as possible to enhance the interactive confidence and minimize the waiting time, thus improving the efficiency. To calculate paths and time points, a path-planning algorithm that accounts for human factors must first be designed [34,35]. [PERSON] et al. constructed robot movement paths on the basis of the distance between operators and robots and the operators' safety and subjective perceptions [17]; subsequently, human movement and operational constraints were incorporated [36]. Regarding the tools used for establishing a path-planning model, some scholars have employed statistical learning methods [37] and the hidden Markov model [38]. Numerous methods can be used to predict human activity trajectories. [PERSON] et al. conducted task-level analysis by using the Markov decision process to predict the next steps of an operator [39]. Some scholars have also used knowledge bases and decision-making procedures to predict human operations [40]. [PERSON] and [PERSON] simultaneously inferred time and causality in a Bayesian network to assist robots in determining which tasks and when the tasks should be implemented [41]. [PERSON] et al. used the partially observable Markov decision-making process to reduce the interference caused by the nature of human-robot coworking spaces and to improve the fluency and efficiency of HRI during tasks [42]. In the context of human-robot collaboration within assembly tasks, [PERSON] and [PERSON] employed timed Petri nets to model and control robots through language, fixation, gestures, and manipulation [43]. The results demonstrated shorter reaction delay of the robots and are subjectively considered by participants to be satisfactory working partners. [PERSON] et al. used a task-level robot plan execution system, chaski, that selects and schedules the robot's actions and adapts to the robot's human partner [30]. The system reduced the idle time of the human partner by 85% compared with the robot being verbally commanded by a human teammate. Similar low-order robot motion planning has been used to improve team fluency and human security [1,44,45]. The method-time measurement approach (MTM) is often used in the industrial engineering field as a tool for predicting assembly times. [PERSON] et al. compared four methods (including the MTM) and discovered that the Kalman filter, which uses Bayesian probability, was more adaptable to assembly operations with complex changes than MTM, which was more suitable for stable assembly [24]. Stable predictions could still be made when the operator changed the assembly time for various reasons. The Kalman filter is capable of predicting complex systems and filtering measurement noise; it is thus widely used in applications such as robot navigation that require correction after prediction. Whereas the MTM can be characterized as stable but inflexible (without dynamic response to changing operation parameters (operator's speed, precision, etc. ), the other end of the scale is the trigger sensor method that features a collaborative robot that responds to the operator's specific movement, for example crossing a plane or passing by a sensor. Thus, in contrast to the other two predictive handover models, this is a reactive handover model. Its application in actual production systems is limited. First, the trigger sensor must be relatively complicated if it is to instantly detect an operator's hand movements and position, which is difficult to implement on production lines due to complexity and cost considerations. Compared with a trigger sensor, the MTM uses the standard cycle time determined beforehand. Moreover, when the Kalman filter is executed on an actual production line, the only system input required is the interval between the removal time of previous and current objects.