Analysis of Visuo Motor Control between Dominant Hand and Non-Dominant Hand for Effective Human-Robot Collaboration

The human-in-the-loop technology requires studies on sensory-motor characteristics of each hand for an effective human–robot collaboration. This study aims to investigate the differences in visuomotor control between the dominant (DH) and non-dominant hands in tracking a target in the three-dimensional space. We compared the circular tracking performances of the hands on the frontal plane of the virtual reality space in terms of radial position error (ΔR), phase error (Δθ), acceleration error (Δa), and dimensionless squared jerk (DSJ) at four different speeds for 30 subjects. ΔR and Δθ significantly differed at relatively high speeds (ΔR: 0.5 Hz; Δθ: 0.5, 0.75 Hz), with maximum values of ≤1% compared to the target trajectory radius. DSJ significantly differed only at low speeds (0.125, 0.25 Hz), whereas Δa significantly differed at all speeds. In summary, the feedback-control mechanism of the DH has a wider range of speed control capability and is efficient according to an energy saving model. The central nervous system (CNS) uses different models for the two hands, which react dissimilarly. Despite the precise control of the DH, both hands exhibited dependences on limb kinematic properties at high speeds (0.75 Hz). Thus, the CNS uses a different strategy according to the model for optimal results.


Introduction
Human-robot collaboration has been emerging with the recent advances in smart manufacturing [1][2][3][4]. The human-robot collaboration is challenging owing to the different mechanisms used by humans and current robots. A robot controls an end effector with a position control mechanism based on absolute coordinates, whereas a human controls limbs with a predictive-control mechanism and feedback-control mechanism based on body coordinates [5][6][7][8]. Humans use a combination of feedback and predictive-control mechanisms. The dominant control mechanism depends on the periodicity of the target [9][10][11][12][13][14][15]. The difference in the mechanism leads to the human control of the upper limb with low precision and accuracy compared to the robot. To achieve an effective collaboration in smart manufacturing, the characteristics of human control mechanisms need to be analyzed for robots' planning, identification, and classification of the human movement (how people react to spatio-temporal changes of the target).
The human controls the upper limb based on the sensory-motor integration system in body coordinates, which helps humans achieve goals and well adapt to spatio-temporal changes [16][17][18]. The upper-limb control, achieved by a complex muscle coordination, entails a combination of a

Subjects and Experimental Setup
Thirty healthy subjects (21 males and 9 females) participated in the experiments. Their average age was 24.8 years (22-35 years). None of the subjects had participated in similar studies. The DH was evaluated according to the Oldfield handedness inventory before the experiment [62]; 28 subjects were right-handed, whereas two subjects were left-handed. All subjects received sufficient explanation about the experimental procedure and provided written informed consent prior to the experiment. The protocol was approved by the ethics committee of the National Institute of Technology, Gunma College.
We used a quantitative evaluation system for visuomotor control in the 3D VR space to record the movement of each hand at 90 Hz [55]. The system displays the 3D circular tracking movement using the HTC VIVE head-mounted display (HMD). The hand-held controller is a synchronized real-time VIVE tracer. The system can perform visually guided 3D circular tracking tasks with a target and tracer. The target from the HMD is a virtual red ball with a radius of 1.5 cm, while the handle of the controller is a virtual white stick with a length of 20 cm against a black background. The tracer is yellow, has a radius of 1 cm, and is attached to the top of the virtual stick. The tracer position was synchronized with the subject's hand movements. The controller direction was also synchronized with the virtual stick. The subjects were asked to track the target using a virtual tracer. The target moves along an invisible circular orbit with a radius of 15 cm. Cartesian 3D coordinate data were derived from the position of the controller.

Experimental Task
We performed the experiment using circular tracking movements in the 3D VR frontal plane for each hand to quantify the 3D visuomotor control performance. The subjects sat on a chair designed for the experiment and wore an HMD. The upper body of the subject was fixed for a motion analysis of the upper limb. We ran a calibration to locate the optimal initial target position for the subject's arm length and height to minimize the effects of different anthropometric parameters on the experimental results, as shown in Figure 1A. To avoid a subject learning effect, the experiment was performed with random counterbalance.
The target's circular orbit was symmetrical along a body-centered coordinate system. The target circled along the orbit at 0.125, 0.25, 0.5, and 0.75 Hz. Before the experiment, the subjects repeated the exercise of placing a tracker on a calibrated target three times. As shown in Figure 1, the subjects were then asked to perform 3D circular tracking movements. In total, 48 experimental trials were performed (six trials × four speeds × two hands) by each subject.

Experimental Task
Cartesian coordinate data (x, y, z) were acquired with the 3D VR system at a sampling rate of 90 Hz. Each graph shown in Figure 1B,C represents a typical example in this experiment. The red line represents the movement of the target, while the black line indicates the movement of the tracer ( Figure 1B,C). We calculated the radial position (R), phase position (θ), acceleration (a), and DSJ. R and θ are utilized for analyzing the tracking performance.
∆R is the mean absolute radial position error, i.e., the absolute difference between the tracer's radial position and target's radial position, ∆θ is the mean absolute phase error, i.e., the absolute difference between the phase of the tracer and that of the target, Sensors 2020, 20, 6368 4 of 14 ∆a is the mean absolute acceleration error, i.e., the absolute difference between the acceleration of the tracer and that of the target. The acceleration data were filtered with a Butterworth low-pass filter at a cut-off frequency of 7.5 Hz.
DSJ was calculated as: where D is the total distance between the end effector and final point, and v peak is the maximum speed during the movement, i.e., the maximum value of v expressed by: DSJ, which is a jerk without dimensions, measures the smoothness of movement. A lower DSJ implies a smoother movement path. The initial and final points of DSJ are based on each target position at 0 • and 180 • by means of the acceleration direction change in the y axis. The units of ∆R, ∆θ, and ∆a are mm, degree, and mm/s 2 , respectively. DSJ is dimensionless. The data visualization was implemented in Matlab (MathWorks, Natick, MA, USA).  Δa is the mean absolute acceleration error, i.e., the absolute difference between the acceleration of the tracer and that of the target. The acceleration data were filtered with a Butterworth low-pass filter at a cut-off frequency of 7.5 Hz.
DSJ was calculated as: where D is the total distance between the end effector and final point, and vpeak is the maximum speed during the movement, i.e., the maximum value of expressed by: DSJ, which is a jerk without dimensions, measures the smoothness of movement. A lower DSJ implies a smoother movement path. The initial and final points of DSJ are based on each target position at 0° and 180° by means of the acceleration direction change in the y axis. The units of ΔR, Δθ, and Δa are mm, degree, and mm/s 2 , respectively. DSJ is dimensionless. The data visualization was implemented in Matlab (MathWorks, Natick, MA, USA).

Statistical Analysis
To statistically analyze each parameter, we used a two-way repeated-measure analysis of variance (ANOVA) on hand factors (hand level: DH, NDH) and speed factors (V1, V2, V3, and V4). The main effect and interaction effect of each parameter were computed using a repeated-measure function in SPSS Statistics V.26 (IBM, Chicago, IL, USA). A posthoc test was performed using pairwise comparisons with Bonferroni correction.
Additionally, we calculated the mean (M), standard error (SE), and standard deviation (SD) of the data. A Mauchly's sphericity test was performed to validate the ANOVA results. In Supplementary Tables S1-S4, we considered differences as statistically significant for p < 0.05 and highly significant for p < 0.01. The effect sizes in Supplementary Tables S1-S4 were estimated using Cohen's D.

Differences in Control Outcomes between the DH and NDH in the Circular Tracking Movement
We used two parameters (ΔR and Δθ) to represent the control error of the human upper extremity during the circular tracking movement (a typical example is shown in Figure 2; ΔR for A1 and A2; Δθ for B1 and B2). The control error (ΔR and Δθ) tended to increase with the target speed.

Statistical Analysis
To statistically analyze each parameter, we used a two-way repeated-measure analysis of variance (ANOVA) on hand factors (hand level: DH, NDH) and speed factors (V 1 , V 2 , V 3 , and V 4 ). The main effect and interaction effect of each parameter were computed using a repeated-measure function in SPSS Statistics V.26 (IBM, Chicago, IL, USA). A posthoc test was performed using pairwise comparisons with Bonferroni correction.
Additionally, we calculated the mean (M), standard error (SE), and standard deviation (SD) of the data. A Mauchly's sphericity test was performed to validate the ANOVA results. In Supplementary Tables S1-S4, we considered differences as statistically significant for p < 0.05 and highly significant for p < 0.01. The effect sizes in Supplementary Tables S1-S4 were estimated using Cohen's D.

Differences in Control Outcomes between the DH and NDH in the Circular Tracking Movement
We used two parameters (∆R and ∆θ) to represent the control error of the human upper extremity during the circular tracking movement (a typical example is shown in Figure 2; ∆R for A1 and A2; ∆θ for B1 and B2). The control error (∆R and ∆θ) tended to increase with the target speed. The two-way Sensors 2020, 20, 6368 6 of 14 repeated-measure ANOVA on the ∆R performance differences revealed significant effects of the hand factor to 14.95 ± 4.33 mm. ∆R of the NDH was larger than that of the DH at all speeds, except for V 1 ( Figure 3B,C). Except for V 1 and V 2 for the DH, the difference in the main effects of the speed factor between the DH and NDH was highly statistically significant (F(2.153, 30.148) = 118.052, p < 0.001, partial η 2 = 0.803, item B in Supplementary Table S1). However, no statistically significant interaction between the hand factor and speed factor was observed (F(2.827, 81.993) = 1.843, p = 0.149, partial η 2 = 0.060, items C and D in Supplementary Table S1).
Sensors 2020, 20, x FOR PEER REVIEW 6 of 14 The two-way repeated-measure ANOVA on the ΔR performance differences revealed significant effects of the hand factor to 14.95 ± 4.33 mm. ΔR of the NDH was larger than that of the DH at all speeds, except for V1 ( Figure 3B,C). Except for V1 and V2 for the DH, the difference in the main effects of the speed factor between the DH and NDH was highly statistically significant (F(2.153, 30.148) = 118.052, p < 0.001, partial η2 = 0.803, item B in Supplementary Table S1). However, no statistically significant interaction between the hand factor and speed factor was observed (F(2.827, 81.993) = 1.843, p = 0.149, partial η2 = 0.060, items C and D in Supplementary Table S1).  The two-way repeated-measure ANOVA on the ∆θ performance-based differences revealed a significant main effect for the hand (F(1, 29) = 27.291, p < 0.001, partial η2 = 0.485, item A in Supplementary Table S2). ∆θ of the DH increased from 2.10 ± 0.76° at V1 to 6.72 ± 2.04° at V4. For the NDH, it changed from 2.09 ± 0.54° at V1 to 7.95 ± 2.55° at V4. Thus, Δθ of the NDH was larger than that of the DH at all speeds except for V1 ( Figure 4B,C). A highly statistically significant effect of the hand factor on ∆θ was observed at V3 and V4 ( Figure 4A; item B in Supplementary Table S2). The main effect of the speed factor was highly statistically significant (F(1.389, 40.281) = 170.424, p < 0.001, partial η2 = 0.855, item B in Supplementary Table S2). The interaction between the hand and speed factors was also highly statistically significant (F(1.933, 56.050) = 12.718, p < 0.001, partial η2 = 0.305, items C and D in Supplementary Table S2). The maximum error of ∆θ in the task was 1.231° at the target speed of V4.
In summary, the DH can exhibit relatively precise movements at high speeds (V3, V4), although no difference in control between the DH and NDH was observed at low speeds (V1, V2). Additionally, the accuracies of the hands were different only at a particular speed (V3). These findings indicate that the feedback mechanism of the DH enables reaction to a wider spectrum of target speeds. The two-way repeated-measure ANOVA on the ∆θ performance-based differences revealed a significant main effect for the hand (F(1, 29) = 27.291, p < 0.001, partial η 2 = 0.485, item A in Supplementary Table S2). ∆θ of the DH increased from 2.10 ± 0.76 • at V 1 to 6.72 ± 2.04 • at V 4 . For the NDH, it changed from 2.09 ± 0.54 • at V 1 to 7.95 ± 2.55 • at V 4 . Thus, ∆θ of the NDH was larger than that of the DH at all speeds except for V 1 (Figure 4B,C). A highly statistically significant effect of the hand factor on ∆θ was observed at V 3 and V 4 ( Figure 4A; item B in Supplementary Table S2). The main effect of the speed factor was highly statistically significant (F(1.389, 40.281) = 170.424, p < 0.001, partial η 2 = 0.855, item B in Supplementary Table S2). The interaction between the hand and speed factors was also highly statistically significant (F(1.933, 56.050) = 12.718, p < 0.001, partial η 2 = 0.305, items C and D in Supplementary Table S2). The maximum error of ∆θ in the task was 1.231 • at the target speed of V 4 .

Differences in Circular Tracking Movement Based on ∆a and DSJ
We analyzed ∆a to indirectly assess the movement of muscles according to the control strategy used by the subjects (typical examples are shown in Figure 2C1,C2). The main effect of the hand factor was statistically significant (F(1, 29) = 11.381, p = 0.002, partial η2 = 0.282, item A in Supplementary Table S3; Figure 5A). A statistically significant effect of the speed factor was also observed (F(1.157, 33.564) = 248.442, p < 0.001, partial η2 = 0.895, item B in Supplementary Table S3). The interaction between the hand and speed factors was also statistically significant (F(1.615, 46.848) = 3.474, p = 0.049, partial η2 = 0.107, items C and D in Supplementary Table S3). The maximum error of ∆a in the tasks was 183.011 mm/s 2 at V3. ∆a of the NDH was higher than that of the DH at all speeds. In addition, ∆a tended to increase according to the speed of the target for both hands.
DSJ is utilized to analyze the smoothness of a movement. The two-way repeated-measure ANOVA was used to assess DSJ at four speed levels (V1, V2, V3, V4) for both hands (DH, NDH). The main effect of the hand factor was statistically significant (F(1, 29) = 20.868, p < 0.001, partial η2 = 0.418, item A in Supplementary Table S4; Figure 6A). DSJ tended to decrease with the increase in the target speed, as shown in Figure 6B,C. The main effect of the speed factor was statistically significant (F(1.002, 29.047) = 85.913, p < 0.001, partial η2 = 0.748, item B in Supplementary Table S4). The interaction between the hand factor and speed factor was also statistically significant (F(1.002, 29.047) = 20.156, p < 0.001, partial η2 = 0.410, items C and D in Supplementary Table S4). A statistically significant difference between the hands at speeds of 0.125 and 0.25 Hz was observed. The ratios of the mean DSJ, representing the DSJ ratio of the DH and NDH, were 2.78, 2.58, 1.10, and 1.07 ( Figure 6D). In summary, the DH can exhibit relatively precise movements at high speeds (V 3 , V 4 ), although no difference in control between the DH and NDH was observed at low speeds (V 1 , V 2 ). Additionally, the accuracies of the hands were different only at a particular speed (V 3 ). These findings indicate that the feedback mechanism of the DH enables reaction to a wider spectrum of target speeds.

Differences in Circular Tracking Movement Based on ∆a and DSJ
We analyzed ∆a to indirectly assess the movement of muscles according to the control strategy used by the subjects (typical examples are shown in Figure 2C1,C2). The main effect of the hand factor was statistically significant (F(1, 29) = 11.381, p = 0.002, partial η 2 = 0.282, item A in Supplementary Table S3; Figure 5A). A statistically significant effect of the speed factor was also observed (F(1.157, 33.564) = 248.442, p < 0.001, partial η 2 = 0.895, item B in Supplementary Table S3). The interaction between the hand and speed factors was also statistically significant (F(1.615, 46.848) = 3.474, p = 0.049, partial η 2 = 0.107, items C and D in Supplementary Table S3). The maximum error of ∆a in the tasks was 183.011 mm/s 2 at V 3 . ∆a of the NDH was higher than that of the DH at all speeds. In addition, ∆a tended to increase according to the speed of the target for both hands.
The movement of the DH was rougher at relatively low speeds (V1, V2), while the smoothness of the hands at relatively high speeds (V3, V4) were similar. The feedback-control ability of the DH was superior to that of the NDH at low target speeds (V1, V2), while it tended to be similar between the hands at high speeds (V3, V4).  DSJ is utilized to analyze the smoothness of a movement. The two-way repeated-measure ANOVA was used to assess DSJ at four speed levels (V 1 , V 2 , V 3 , V 4 ) for both hands (DH, NDH). The main effect of the hand factor was statistically significant (F(1, 29) = 20.868, p < 0.001, partial η 2 = 0.418, item A in Supplementary Table S4; Figure 6A). DSJ tended to decrease with the increase in the target speed, as shown in Figure 6B,C. The main effect of the speed factor was statistically significant (F(1.002, 29.047) = 85.913, p < 0.001, partial η 2 = 0.748, item B in Supplementary Table S4). The interaction between the hand factor and speed factor was also statistically significant (F(1.002, 29.047) = 20.156, p < 0.001, partial η 2 = 0.410, items C and D in Supplementary Table S4). A statistically significant difference between the hands at speeds of 0.125 and 0.25 Hz was observed. The ratios of the mean DSJ, representing the DSJ ratio of the DH and NDH, were 2.78, 2.58, 1.10, and 1.07 ( Figure 6D). The movement of the DH was rougher at relatively low speeds (V 1 , V 2 ), while the smoothness of the hands at relatively high speeds (V 3 , V 4 ) were similar. The feedback-control ability of the DH was superior to that of the NDH at low target speeds (V 1 , V 2 ), while it tended to be similar between the hands at high speeds (V 3 , V 4 ).

Discussion
We analyzed the visuomotor control characteristics of the 3D circular tracking movement in the VR space. It can be a representative of a steady-state response. ΔR and Δθ are the control outcomes derived from the circular tracking movement described in the polar coordinate system. The control outcomes (ΔR and Δθ) and Δa were directly proportional to the speed of the target. However, for DH, ΔR was not statistically significantly different between V1 and V2. For V3, ΔR was statistically significantly different between the hands. Therefore, the DH has a wider speed spectrum range in its feedback mechanism capability. In other words, the CNS sustains control of the DH through a feedback-control mechanism at higher target speeds than those for the NDH.
Overall, the data show that the control outcomes (ΔR and Δθ) at low speeds (V1, V2) were similar between the DH and NDH, considering the negligible differences in ΔR and Δθ between the hands. All values of Δa for the DH were smaller than those for the NDH. Furthermore, all values of ΔR for the DH were smaller than those for the NDH except at V1. The subjects moved their DHs more frequently for correcting errors at low speeds (V1, V2) because of the value of DSJ. Thus, the DH can be controlled with a smaller amount of total energy as (1) the muscle contributes to the acceleration

Discussion
We analyzed the visuomotor control characteristics of the 3D circular tracking movement in the VR space. It can be a representative of a steady-state response. ∆R and ∆θ are the control outcomes derived from the circular tracking movement described in the polar coordinate system. The control outcomes (∆R and ∆θ) and ∆a were directly proportional to the speed of the target. However, for DH, ∆R was not statistically significantly different between V 1 and V 2 . For V 3 , ∆R was statistically significantly different between the hands. Therefore, the DH has a wider speed spectrum range in its feedback mechanism capability. In other words, the CNS sustains control of the DH through a feedback-control mechanism at higher target speeds than those for the NDH.
Overall, the data show that the control outcomes (∆R and ∆θ) at low speeds (V 1 , V 2 ) were similar between the DH and NDH, considering the negligible differences in ∆R and ∆θ between the hands. All values of ∆a for the DH were smaller than those for the NDH. Furthermore, all values of ∆R for the DH were smaller than those for the NDH except at V 1 . The subjects moved their DHs more frequently for correcting errors at low speeds (V 1 , V 2 ) because of the value of DSJ. Thus, the DH can be controlled with a smaller amount of total energy as (1) the muscle contributes to the acceleration of joint dynamics [63,64], (2) the upper-limb movement for task accomplishment is the result of muscle coordination [19,20,65], and (3) owing to the energy relationship between the force and distance. The acceleration error is statistically significant for all target speeds, which indicates that the CNS recognizes each hand as a different model and reacts dissimilarly, which can be an evidence of brain lateralization [66]. These implications suggest that humans have an internal model and efficiently control circular tracking [67,68]. Furthermore, we suggest that humans are particularly proficient in controlling their hands. However, these findings are not sufficient to demonstrate that humans can efficiently control all their joints, as only hand data were analyzed.
DSJ is related to movement smoothness. A smaller DSJ implies a smoother movement [52][53][54][55][56][57][58][59][60][61]. At the target speeds of V 1 and V 2 , the degree of smoothness for the NDH was more than twice lower than that of the DH, as shown in Figure 6D. This implies that the DH actively corrects errors from control outcomes, as suggested in previous studies [36,49]. This is directly related to the superior feedback capability of the DH compared to the NDH. It is unlikely that the results are attributed to the predominance of motor learning attributed to the DH because the experiment minimized the number of tasks [69].
The DSJ ratio converged to 1 at high target speeds (V 3 and V 4 ). The movements at these speeds were also smoother. This tendency suggests that the proportion of control attributable to the predictive-control mechanism increased. When the target speed exceeded V 3 , the effects on the radial position error and phase error were statistically significant. However, at V 4 , only the phase error was statistically significantly different between the hands. Thus, the DH can be controlled more precisely owing to the phase difference. In addition, it is likely that both hands rely on the kinematic characteristics of their limbs at higher target speeds. This dependence of kinematic characteristics can represent the proficiency of the DH in muscle coordination at the high target speed.
The DH performed a circular tracking movement with less total energy and active feedback control. This is attributed to the combination of torques from the wrist, elbow, and shoulder. It is necessary to attach kinetic sensors to the wrist, elbow, and shoulder joint to identify the model (minimum torque change model, minimum jerk cost function model, or another model) used by humans for upper limbs in circular periodic tracking movements [70]. With this model, it would also be necessary to analyze the muscles that are used in circular tracking (antebrachial, biceps brachii, and deltoid muscles). The muscles used for manual tracking are the biceps brachii and deltoid, which are strongly related to typical motions in humans [65]. In addition, the dependence of kinematic characteristics can be demonstrated by utilizing kinetic sensors.
To achieve an effective human-robot collaboration, humans must use a combination of feedback and predictive mechanisms. Both hands react differently according to the target periodicity, which indicates that humans use different combinations of control mechanisms based on the speed of the target. In summary, the results suggest that the end effector of the robot should be controlled under 0.5 Hz or 471 mm/s, at which the human recognizes the target and controls its upper limb with a predictive-control mechanism. By limiting the speed of the end effector, the human-robot collaboration would be more effective, owing to the utilization of the error correction with a feedback mechanism. In addition, the speed value can be the standard setting as a safety factor. The robot can efficiently identify the human movement and control characteristics. These results could be utilized to guide studies on complex hands-over interactions and human-robot information change. We will be able to verify the efficiency of human hands by measuring brain waves with fMRI and joint movements with an inertial measure unit when each hand is used, which will lead to smoother robots for human-robot collaboration. Moreover, the human-robot collaboration can be developed into face-to-face collaboration.

Conclusions
In the human-in-the-loop technology, studies on the sensory-motor characteristics of each hand are needed for human-robot collaboration with upper limbs. We analyzed the differences in the control mechanism and outcomes between the DH and NDH during circular tracking movements in the 3D VR space. The CNS reacted dissimilarly between the hands. First, the DH had a more precise control than that of the NDH at the highest speed (0.75 Hz). Second, the DH had a wider speed spectrum in its feedback-control mechanism. However, no significant difference in the control outcomes (∆R and ∆θ) was observed at low target speeds (0.125, 0.25 Hz). Moreover, a tendency of dependence of both hands on the kinematic characteristics of the upper limb was observed when the speed of the target increased. In summary, the CNS uses different strategies, relying on the model of the particular hand, which produced optimal results in the tracking task. These results could help the robot identify and recognize the human movement, which contributes to a more efficient human cooperation with the robot.
Supplementary Materials: The following are available online at http://www.mdpi.com/1424-8220/20/21/6368/s1, Table S1: A summary of the statistical analysis of ∆R, Table S2: A summary of the statistical analysis of ∆θ, Table S3: A summary of the statistical analysis of ∆a, Table S4: A summary of the statistical analysis of DSJ (Dimensionless Squared Jerk).