Kasuga and Hashimoto (2005) implemented neural oscillators to simulate the movement of the robot in physical human-robot interaction. The neural oscillator made use of the synchronization of movements during the interactions. In this approach, the applied forces and torques were used as inputs to determine the trajectory of the shoulder and elbow joints of a robot arm. By adjusting the parameters of this system, the passive behavior of the robot’s handshake was adjusted. From computer simulations and experimental validation, results showed that the proposed neural oscillator control method was better than the conventional impedance control method.

Extending the work of Kasuga and Hashimoto (2005), Jindai et al. (2006) proposed the use of a second-order lag element to simulate the reaching movement of the handshake receiver. The proposed reaching movement was a weighted combination of the reaching movement of the initiator and a following movement of the initiator’s hand. The value of the weighting coefficient changed as the movement progressed such that the movement switched from the former to the latter. A handshake experiment was performed to evaluate the proposed method. The velocity plots of the reaching movement of the receiver and the one obtained by applying this method were similar, which showed the acceptability of the procedure.

Yamato et al. (2008) proposed a preshaking movement to add to the reaching movement proposed by Jindai et al. (2006) and to the handshaking movement proposed by Kasuga and Hashimoto (2005). However, this led to modifying the model of the reaching movement by adding a dead-time element to the transfer function. The proposed preshake movement was hypothesized to exist as a leading initiative by the receiver to start the handshake. This movement was simply a quarter of a handshake cycle that was directed upward or downward, or was absent (i.e., the initiator led the shaking movement). These three conditions were tested in a second handshake experiment between the participants and a robot system. The authors reported that the upward preshake movement was the most acceptable of the three. A third experiment was conducted to determine the best out of the three models: the selected upward model, a height-based movement direction model, and a force direction model. The height-based model selected the direction of the movement based on the height at which contact was made. The force direction model moved in the direction that matched the direction of the force applied by the handshake initiator. The height-based model was reported to be the best out of the three models.

Jindai et al. (2012) proposed a model for the reaching movement of the handshake initiator. The proposed model was based on a combination of fast and slow movement instances of Hogan (1984)’s model. This approach was utilized to obtain a skewed bell-shaped velocity profile, which was the reaching movement profile. A handshake experiment between the participants and a small robot system was conducted to determine the best value of the parameters of the lag and dead-time elements of the control system. It was determined that the receiver's movement that lagged behind the initiator’s movement and incorporated a dead-time period was preferred.

In Wang et al. (2008), they proposed a model for the handshaking contact wherein the modelling procedure started from acquiring numerous handshake data. Then, the desired trajectories were generated by a planner and were synthesized by a motion synthesis module. Finally, new control methods were employed to achieve a satisfactory robot handshake. The controller design made use of force-based impedance control.

In Tagne et al. (2016), they studied handshake in the context of various greetings (i.e., hello, congratulations, sympathies). They found that the context has an effect on the strength and duration of the handshake. Similarly in Melnyk and Henaff (2019), they found that there is a difference in the duration of handshake in the context of handshake for greetings and that for consolations.

Avraham et al. (2012) proposed three handshake leader and follower methods: the Tit-for-Tat model, λ model, and iML-Shake model. The Tit-for-Tat model was based on the assumption that the shaking movement involved a leader and a follower. The leader imposed his/her handshake style while the follower conformed to and imitated it. Thus, the Tit-for-Tat model involved recording and repeating the shaking movement of the leader. This required either prior knowledge of the shaking movement (when taking the leader’s role) or recording a portion of the movement and repeating or following it (when taking the follower’s role).

The λ model was based on the assumption that the hand alternates between two threshold positions during the handshaking movement and the smoothness of the resulting path is a result of the physiology and biomechanics of the muscles. This model required instantaneous data of the participant’s hand position, an understanding of the biomechanics of the arm movement, and an estimation of movement parameters.

The iML-Shake model is a machine-learning model that was based on the concept that human movements can be viewed as a function that takes positions as inputs and produces forces as outputs. The model required the collection of movement data and performing linear regression to estimate the parameters of the model. The position of the interrogator’s hand was also required when performing the handshake test. The Tit-for-Tat and the iML-Shake models were considered to be more humanlike than the λ model. The authors suggested developing a model that captured the advantages of all of the proposed models.

Jouaiti et al. (2018) introduced the Hebbian plasticity in central pattern generator controllers to facilitate self-synchronization for human-robot handshaking. With this mechanism, they showed that the synchronization had a transitory phase and the permanent phase. In the transitory phase, the system adapts and learns the handshake conditions while in the permanent phase, the system retained the learning.

Mura et al. (2020) proposed a handshake robot system that implemented an extended Kalman filter (EKF) to learn from a human handshaking partner and to mimic the handshake. The EKF was designed to observe the intention of the human and turn this into an appropriate control reference for the robot arm. For the handshake movement, a sinusoidal function of unknown time-varying amplitude and frequency were implemented. The robot arm and hand system was able to synchronize with the human motion and to anticipate an active, leading behavior.

The models proposed in Kasuga and Hashimoto (2005); Jindai et al. (2006); Yamato et al. (2008); Wang et al. (2008) and the Tit-for-Tat model (Avraham et al., 2012; Mura et al., 2020) were based on collecting movement data from the handshake partner. This approach leads to replicating or imitating the performed movement and removes any differences in handshake characteristics that normally exist between two individuals who are performing a handshake. Moreover, in certain situations, a warm greeting (e.g., when welcoming a guest) or a firm one (e.g., in an interview) is expected from one side.

Without the ability to collect the movements from the handshake partner, these types of handshakes will be impossible to perform. The iML-shake model proposed in Avraham et al. (2012) introduced a machine learning strategy whereby the participants’ behavior data related to their positions and grasping forces were used as an input-output function of their algorithm. According to the authors, it assumed little about the handshake movement, which made it more useful, because any unknown biomechanical features will be included. However, this feature is its main weakness. Ideally, a model like the λ model (Avraham et al., 2012) should be sought such that the important features of a movement are included and the weak or random influences are removed.

The reason this model did not perform that well could be due to the observation of Nelson (1983) wherein he stated that dynamic models are not enough to describe human movement alone and a form of optimization should be sought to compliment them. This approach was utilized in developing the model proposed in Jindai et al. (2012) by building on Hogan’s jerk minimization model (Hogan, 1984). The present paper builds on these results to develop an improved model for a smooth human-to-human handshake, which can then be replicated in human-robot handshakes.

An experimenter was selected to wear a set of motion and force sensors and was trained to perform the handshakes. Due to the long duration required for wearing and calibrating the sensors and the training time for the experimenter, only one participant played the role of the experimenter. Another five participants were selected to shake hands with the experimenter, who were naive about the hypothesis of the research study. All the participants selected were right-handed males and their hand dimensions were close to the 50th percentile as compared to the anthropometrical dimensional data [i.e., 19.3 cm hand length, 8.9 cm width; (Man-Systems Integration Standards, 1995)].

The data of the experimenter and participants are summarized in Table 1. They did not report any neuromuscular or neurological disease that might interfere with motor function. Approval for the handshake experimental protocol was granted by the Institutional Review Board of the National University of Singapore and the procedures involved in this study were in accordance with the World Medical Association’s Code of Ethics (Declaration of Helsinki). Data were stored and analyzed anonymously. All participants gave their written informed consent.

There is substantial benefit in replicating human motion to inspire behaviors in robots (Kulic et al., 2012; Maeda et al., 2017; Cini et al., 2019). In such approaches, visual trackers and sensors are often employed to capture and learn from human movements. In the present work, the experimenter wore two sets of sensors. Motion trackers (Fastrak, Polhemus Inc, VT, United States) were mounted proximally to the shoulder, elbow, and wrist joints (Figure 1A). The trackers recorded the 3D position in the xyz axes of each sensor relative to transmitter of the trackers (Figure 2A). The transmitter was positioned on top of a desk behind the experimenter and serves as the reference frame for the motion trackers. Figure 2B shows the experimenter and participant in the positive xyz plane.

Wearable force sensors (Finger TPS, Pressure Profile Systems, CA, United States) were also worn to measure the normal contact forces exerted during the handshake. The force sensors were positioned on seven locations: the middle phalanges of the middle, ring, and little fingers, the proximal phalange of the little finger, the distal phalange of the thumb, and the volar and dorsal sides of the hand, as shown in Figure 1B. These locations were selected because these are the locations with high skin compliance and where the maximum handshake contact forces occur (Cabibihan et al., 2006a, 2011). The motion trackers and force sensors have a sampling rate of 30 Hz.

With the experimenter trained to give a neutral handshake, he was further instructed to keep his grasping force to a minimum while allowing the receiver to apply his natural handshake grasp and motion. This was similar to the protocol in Chaplin et al. (2000) where they determined the relationship between handshakes and personality. In a neutral handshake, the experimenter extended his right hand to initiate a handshake. Upon contact with the experiment participant, the experimenter grasped the other person’s hand, but waited for the other to initiate the grip and the upward and downward shaking. Moreover, the experimenter was instructed to relax the grasp once the partner relaxed his grasp.

The participants were introduced to the experimenter and were told to respond naturally to the experimenter’s handshake. The experimenter and each participant were instructed to stand face-to-face within 1 m from each other. After starting the data acquisition, the experimenter was instructed to initiate the handshake. Data acquisition continued for at least 1 min after finishing the handshake. Each participant performed only one handshake with the experimenter to avoid any learning effects that could influence the data, such as those reported in Jindai et al. (2006).

The human upper limb consists of the hand, forearm, and upper arm with 7 DOFs that are made possible by the wrist, elbow, and shoulder joints (Kim et al., 2011). The pronation/supination of the hand, which originates from the forearm (Taylor and Schwarz, 1955), and the fine finger movements were not investigated in this experiment since those require separate analysis. Analyses were done on the contact forces recorded for each sensor location, differences in the handshake phases in human-human handshakes, and differences among the various handshake models.

When the hand is grasped during handshakes, the forces on the fingers oppose the forces on the palm. We expect that the sum of the normal forces exerted by the fingers is equivalent to the sum of the normal forces exerted by the palm to counterbalance the forces. We want to determine whether the selected locations of the sensors were appropriate. If our sensor placements are correct, the sum of the normal forces must be equal to zero where the normal forces from the fingers are equal and opposite to ones on the palm (Eq. 1): ∑ f = 1 5 F f = ∑ p = 1 2 F p (1) where the subscript f denotes the sensors positioned on the fingers and p denotes the sensors on the palm (Figures 1B,E).

To determine whether there was a difference among the handshake phases, the two-sample t-test has been conducted between all possible combinations of the phases. However, this only has been used for the ones that could be assumed to have equal variances. Moreover, Welch’s t-test has been used for the non-equal variance. Furthermore, the F-test has been first used to test if the assumption of the equal variance could be applied or not. We found that the assumption of equal variances could be applied only between the reaching and return phases based on the conducted F-test. That indicates that the two-sample t-test (equal variance t-test) would be used to investigate the mean difference between reaching and return phases, while the others would use Welch’s t-test (non-equal variance t-test). All statistical analyses were performed using a statistical package (Minitab v17, Minitab, LLC, PA, United States). A p-value of ≤0.05 was considered statistically significant. Furthermore, our model was compared with other handshake models in earlier physical human-robot interaction works. Only the contact phase was similar among them. Thus, the contact phase was compared using the percentage difference equation.

The motion was divided into three main phases. We first developed the model for the contact phase because this was the commonly modeled phase for handshakes. After that, a different model was used for both the reaching and return phases.

Unlike the vertical motion, the horizontal motion was consistent across the datasets. Thus, the mean values for the key states and durations of the phases were obtained and were used in the modelling process.

The displacement data from the sensor at the wrist was plotted in a three-dimensional graph (Figure 3A). Only the displacements for the x-coordinate position (i.e., horizontal movement) and the y-coordinate position (i.e., vertical movement) were considered. The panning movement (i.e., z-coordinate position) had a small change with respect to time and was thus neglected in our analysis. Moreover, our own experiences tell us that excessive movements along the z-plane during the handshake oscillation is not usual.

From Figure 3A, it can be observed that there is a rapid rate of increase in the vertical movement during the reaching phase (14.16 cm s⁻¹). During the contact phase, the vertical displacement changed to a damped oscillation. There can be around 2-4 oscillations during handshake. Lastly, there was a slower rate of decrease in the vertical displacement during the return phase to complete the handshake (−9.78 cm s⁻¹).

The states, phases, durations of phases, subphases, calculated coefficients of the models, and illustrations of the states and phases were summarized. For ease of understanding, the reader is referred to the handshake phases in Figure 3B, which consists of the reaching, contact, and return. The y-coordinate position and x-coordinate position models were further presented with the summary of the coefficients. Both models have a reaching phase at the start and return phase at the end. The contact phase can be further divided into subphases. For the y-coordinate position, the contact phase has preshake, main shake, postshake, and no motion subphases. For the x-coordinate position, the contact phase has motion and no motion subphases.

Figure 3C shows the state conditions for the displacement, velocities and accelerations for the y and x-coordinate positions. An arrowhead pointing outward indicates that the data were obtained from the phase (i.e., these served as outputs to other phases as conditions). An arrowhead pointing inward to the column of numbers indicates that the data were used to determine the phase (i.e., as state conditions).

The hand movement models provided a description of the handshake kinematics. During the reaching phase (State 1), the wrist moved from its default position at the hips to a position of about 13.4 cm upward and 27 cm forward (Figure 3C). Once contact with the other hand was detected, there was an increase of around 1.3 cm [State 2 (14.7 cm)–State 1 (13.4 cm)] to reach the peak of the y-coordinate displacement of the handshake. In other words, before the main handshake occurs, the hands are first raised to the peak vertical values before the handshake oscillations commence. During the contact phase, the hand accelerated and started the handshaking movement while the hand relaxed slightly backward to −6.3 cm [subphase d (20.7 cm)–subphase b (27.0 cm)]. This meant that a position correction was done from the initial overshoot of the reaching movement.

The handshaking motion decreased in amplitude as it progressed with about three to four oscillations (Figures 3A, 4A). The hand decelerated to a stop to about 5 cm [State 2 (14.7 cm)–State 3 (9.7 cm)] lower than its position at the start of the handshake. Moreover, the handshaking motion was mainly a feature of the vertical hand movement. This was shown on the y and x axis displacement results. During the return phase, the hand moved downward (Figure 4A) and backward (Figure 4D) towards its initial neutral position, which cleared all the grasping forces and movements that remained after contact (also refer to Figures 1C,D).

From the coefficients of the main handshake subphase model (Figure 3B), the following can be stated. Since the handshake experiment was done approximately at a similar height, the low variability of the intercept (A _V3) can be expected. The low variability of the angular frequency (ω) obtained in the conducted experiment indicates that the handshake is mostly performed at an angular frequency of 17.7 (SD = 2.4) rad s⁻¹. The high variability of A _V2 of 16.2 (SD = 2.1) and γ of 1.8 (SD = 1.2) signify that the features they represented (downward trend and exponential decay, respectively) were not norms. In this work, their mean values were used in the handshake model. However, one may want to use smaller or larger values and recalculate the affected phases and subphases to arrive to a different vertical hand motion model. This can be investigated further to impart personalities for robot handshakes.

The proposed hand movement models agreed well with the experimental datasets (Figures 4A–F). The general trend of the handshake positions in the y and x-axes were achieved by the model (Figures 4A,D), but there were marked differences in the displacement values. The velocities and accelerations in the y and x-axes were likewise represented.

However, there are some differences that are worth noting. First, the handshake duration of the model was slightly less than that of the dataset by 0.25 s (Figures 4A,B), yet the model was able to capture the amplitude in the experimental data. Second, the model has a higher exponential damping and downward trend, which resulted in less velocity and acceleration values toward the end of the main handshake subphase. Third, even after filtering the data, the acceleration plots show some fluctuations at the reaching and return phases that prevented the observation of the trends at those regions (Figures 4B,C,E,F). This is because the experimental results were position data, which were numerically differentiated. Due to the subtractive nature of differentiation, the errors were amplified (Chapra, 2012). For one to see the velocity and acceleration trends, a better approach is to use a sensor type that matches the variable of interest.

Taken together, the vertical displacement had a mean difference of 3.3 cm (SD = 1.25 cm) in the peaks of the handshake oscillations and a mean difference of 2.3 cm (SD = 0.48 cm) in the throughs (Figure 4A). The horizontal displacement had a mean difference of 6.35 cm (SD = 0.86 cm) from the initial reach to the release of contact (Figure 4D). These differences between the model and experimental results might be tolerable variances in an actual handshake when the heights of the handshaking partners and their relative proximity to one another are considered. The velocities and accelerations in both the y and x-axes will be more perceivable during actual handshake, which our model was able to capture well.

To determine whether humanoid robots are now able to perform handshakes that are similar to humans, we plotted the vertical position plots from the jerk-minimized handshake model and the previously published results (Figure 5). The differences between the proposed model and the other models could be due to cultural differences and social norms. There were evidences that have already reported ethnic as well as gender differences in handshakes (Chaplin et al., 2000; Katsumi et al., 2017; Melnyk and Henaff, 2019).

The differences could also be due to the following reasons. First, the amplitude of the shaking motion is too large such that it is comparable in magnitude to the displacement of the hand in the reaching phase (e.g., Figure 5; 14.7 cm in Avraham et al. (2012) vs. 13 cm y-axis displacement during reaching). Second, the number of oscillations were more than 5 in Yamato et al. (2008), Avraham et al. (2012), Mura et al. (2020), while our model had 4 oscillations. Wang et al. (2008) also showed 4 oscillations. Moreover, the duration of the other handshakes exceeded 4 s while our model had less than 4 s duration for a full handshake. In Wang et al. (2008), it can be observed that the duration of the contact phase was similar to our model. In Table 11, our model had a contact time of 1.95 s while a shorter contact duration of 1.25 s was observed in Wang et al. (2008). Others had more than 3 s of contact time.

The percentage difference between the contact phase of our model and that in Yamato et al. (2008), Wang et al. (2008), Mura et al. (2020), and Avraham et al. (2012) are 39.18, 43.75, 86.46, and 87.45%, respectively. Additionally, our model, as well as that in Wang et al. (2008), exhibited exponential decay in the amplitude in the contact phase. The oscillations in Mura et al. (2020) slightly displayed this behavior while the handshake in Yamato et al. (2008) and Avraham et al. (2012) did not show this decay.

Third, other models only considered the contact phase of the handshake and not the complete reaching-contact-return phases. The handshake movement presented in Avraham et al. (2012), which was plotted such that its starting point matches the start of the contact phase, was only limited to the handshaking motion. In contrast, the model of Yamato et al. (2008) included the handshake contact movement up to the end of shaking. Post-contact handshake phases were not shown in the other models, except in our model and that in Mura et al. (2020). However, the horizontal lines in their reaching and post-contact phases were near the same level as the baseline heights of the robot arm when the participant and the robot started and completed the handshake. In Figure 5 and in Table 11, our model showed the subphase of no motion of 0.52 s just before both hands disengaged in the return phase.

The mean handshake duration in our experiments was 3.63 s (SD = 0.45 s) (Table 3). Previous works confirm the variability in the handshake duration (Prasad et al., 2021). Others had a minimum of 0.73 s (SD = 0.08 s) to a maximum of 4.05 s (SD = 0.53 s) duration of handshakes (Melnyk et al., 2014; Tagne et al., 2016; Melnyk and Henaff, 2019). The duration of the contact phase was observed to vary considerably when compared to the other handshake phases (Table 3). The standard deviation (SD) for the reaching and return phases were relatively small at 0.1 and 0.12 s, respectively. The SD for the contact phase was 0.46 s. The reason behind this is the variability of the handshake characteristics of each participant. For example, participants who prefered to perform two or three oscillations would generally be going to shake hands for a shorter duration than the participants who perform more oscillations.

In human handshakes, it appears that the hand undergoes planned and unplanned movements once contact has been initiated. The unplanned movement is the movement executed as the initiator and receiver correct their hand postures. This movement depends on how contact is first made. The first contact location would be the web of the hands. The accepted practice is to keep an eye to eye contact with the other person before, during, and after the handshake. In object grasping, humans gaze briefly to the affordances of an object before grasping it (Johansson et al., 2001; Juravle et al., 2015).

In handshakes, one has to estimate the location of the other person’s hand (de la Rosa et al., 2014; Fademrecht et al., 2016). If the targets were not reached correctly, perhaps due to miscalculation from peripheral vision, the handshake partners will try to correct their hand positions while proceeding with the handshake phases. This results in some randomness in the initial location that comes into contact. While the objective of this paper was to model the planned movement, it is also important to account for the unplanned movements in robot handshake algorithms with the correct estimation of the location of the handshake partner’s hands during the reaching phase.

While there are some variabilities in human-to-human handshakes, there are elements which make a handshake acceptable. Some of these were described in this work: the grasping forces, minimal movements in the z-plane, the amplitude of the handshake, the phases of movement, and the duration of each phase. Other parameters that are beyond the scope of the current paper are: the eye contact between the handshaking partners, the fingers’ micro-movements during handshake, the softness and warmth of the hands. A significant deviation in one of these parameters will be judged as an odd or unnatural handshake, which will lead to an awkward interaction (Kadambi et al., 2020).

The comparisons in Figure 5 led us to some insights toward lifelike human-robot handshakes. Across the different models, our model showed all the phases of the handshake movement from the reaching to the release. The contact phase has the subphases of preshake, handshake, postshake, and no motion. Others have only investigated the contact phase. In one model, there were up to 9 handshake oscillations. In another, the vertical hand movements showed amplitudes of 12 cm that were monotonous and do not show a decay in the vertical position. If those handshake movements were done during a human-to-human or robot-to-human interaction, these will be perceived as unnatural. We also showed a period of no motion of around half a second just before the release of contact between the handshake. Due to the multiphase modeling of the handshake phases and the subphases that we implemented, we were able to discover this no-motion behavior. This non-movement may have implications on promoting better social interactions. We will have to further test if there is such an effect in a future study.

As humanoid robots begin to collaborate and co-exist with humans (Khatib et al., 1999; Heinzmann and Zelinsky, 2003; Haddadin et al., 2009), it is conceivable that the human interaction partner will expect handshakes. Just like in human interactions, it is probable that humans will make split-second judgements on whether a humanoid robot possesses humanlike traits through a handshake (e.g., Is this robot sociable or competent enough to interact with me?). Thus, a humanoid robot should be able to know what to do when a person extends his or her hand (Cabibihan et al., 2009; Knoop et al., 2017; Avelino et al., 2018).

The validation of a realistic humanoid robotic handshake requires a human-robot experiment where a handshaking robot follows the proposed trajectory that we showed and the human’s perception of the handshake will be recorded. Our future work would be a follow-up experiment involving studies on human-robot handshake interaction, in which we have to consider what is the desired social relationship a human or robot would like so that the appropriate type of handshake can be used during an interaction (e.g., friendly, professional, acquaintance, etc.,) by the robot.

With the multiphase model revealing some of the nuances of human to human handshakes, we provide guidelines for lifelike handshakes during physical human-robot interactions.