Analysis of Three-Dimensional Circular Tracking Movements Based on Temporo-Spatial Parameters in Polar Coordinates

Abstract

Motor control characteristics of the human visuomotor control system need to be analyzed in the three-dimensional (3D) space to study and imitate human movements. In this paper, we examined circular tracking movements on two planes in 3D space from a motor control perspective based on three temporospatial parameters in polar coordinates. Sixteen healthy human subjects participated in this study and performed circular target tracking movements rotating at 0.125, 0.25, 0.5, and 0.75 Hz in the frontal or sagittal planes in three-dimensional space. The results showed that two temporal parameter errors on each plane were proportional to the change in the target velocity. Furthermore, frontal plane circular tracking errors without depth for a spatial parameter were lower than those for sagittal plane circular tracking with depth. The experimental protocol and data analysis allowed us to analyze the motor control characteristics temporospatially for circular tracking movement with various depths and speeds in the 3D VR space.

1. Introduction

We studied and imitated human motion control mechanisms using a visually guided motor control system in the three-dimensional (3D) space. To understand the visually guided motor control of humans accurately, we need to analyze visually guided tracking movements in 3D space directly and analyze important 3D space motor control characteristics such as depth perception. This is vital for workspace distance determination and motion establishment. However, in previous target-tracking movement studies, no technology or system has provided an accurate visual target representation [1,2,3,4,5,6,7,8,9,10].

Recently, we developed a 3D visuomotor control evaluation system in a virtual reality (VR) environment [11]. This system enabled the analysis of VR space circular tracking movement to the millimeter level accuracy. We compared 3D circular tracking movement visuomotor control between monocular and binocular vision. As reported by Melmoth et al. [12], reaching and grasping movement accuracy in binocular vision had a 2.5 to 3.0 times advantage over monocular vision in the real environment. Our previous study obtained a similar result, where the circular tracking movement accuracy in binocular vision showed approximately 4.5 times the advantage over monocular vision on both frontal and sagittal planes in a 3D VR environment.

Depth estimation is an equally significant control metric for both motor control and depth perception in real and virtual 3D spaces. We analyzed two circular target-tracking movement types on the frontal and sagittal planes (relative to the subject). However, only the Cartesian coordinate spatial error was used to analyze the tracking movement accuracy in our previous study. The temporospatial relationship between the tracer and target should be investigated for a comprehensive study of the motor control characteristics of circular tracking movements. In this study, we redesigned the experiments to evaluate the impact of various target speeds.

Three polar coordinate kinematic parameters (ΔR, Δθ, and Δω) are widely used in circular tracking movement analysis [13,14]. Our previous study analyzed the motor control and impact of speed and visual target feedback in 2D tracking movements based on these parameters [14]. In other words, ΔR allows us to examine spatial motor control characteristics in polar coordinates as a circular movement performance evaluation. However, Δθ and Δω allow us to analyze motor control temporal characteristics in polar coordinates as a circular tracking movement evaluation of the positional and velocity-control precision. This inspired us to examine two planar circular tracking movements in 3D space from a motor control perspective based on temporospatial parameters.

Therefore, in this study, we analyzed the motor control characteristics of circular tracking movements in 3D space using three kinematic parameters in polar coordinates: difference in fixed pole distance, ΔR; position angle difference, Δθ; and angular velocity difference, Δω. We investigated the parameter differences between circular tracking movements relative to the subject on the frontal and sagittal planes. We also examined parameter-based changes in motor control for four different target speeds.

2. Materials and Methods

2.1. Subjects and Experimental Setup

The subjects were 16 males, with a mean age of 20.1 ± 0.62 years (see

Table 1. Characteristics of 16 participants.

ID	Age	Sex	Dominant Hand	Dominant Eye
1	20	M	L	R
2	20	M	R	R
3	20	M	R	R
4	20	M	R	L
5	20	M	R	R
6	20	M	R	R
7	19	M	R	R
8	21	M	R	R
9	21	M	R	R
10	19	M	R	R
11	21	M	R	R
12	20	M	R	R
13	20	M	R	R
14	21	M	R	R
15	20	M	L	R
16	20	M	L	R

). Three subjects were left-handed, and 13 subjects were right-handed. Fifteen subjects were right-eye dominant, and one subject was left-eye dominant. All had normal or corrected-to-normal vision. None had previously participated in similar studies. All subjects gave written informed consent before their participation. All experiments were conducted in accordance with relevant guidelines and regulations. The protocol was approved by the ethics committee of the National Institute of Technology, Gunma College.

The subjects were asked to perform a visually guided tracking task in a 3D VR environment [11], which involved tracking a target with a tracer (see Figure 1). The subjects held a hand-held controller of the HTC Vive HMD to move a tracer in the 3D VR space. The subjects used the tracer (visualized as a yellow ball) to track the target (visualized as a red ball) moving circularly in the clockwise direction. The green lines indicate the target path in the 3D VR space. The two graphs in the second trace show the target path as seen from the front (left) and side (center) from the subject’s viewpoint. Insets in the second trace of (A) and (B) show how three outcome measures (ΔR, Δθ, and Δω) were derived from the target (or the tracer) path data for each plane. The three lower graphs show a typical trial of the target path (green line) and the tracer path (black line) for each axis versus time. The target path was not displayed to the subjects during the experiment. The target was a virtual red ball with a radius of 1.5 cm. Instead of their own hands or HMD’s controller, the subjects perceived a 20-cm-long virtual stick. The controller direction was synchronized with the virtual stick. Circular tracking was performed without the 3D hand and arm displayed in VR in this study; therefore, the virtual stick with the virtual tracer presents the hand position and direction information. The tracer was a virtual yellow ball of 1 cm radius, placed at the tip of the stick. The tracer position was synchronized with the subject’s hand movements. In the experiment, the target moved continuously along an invisible circular orbit with a 15 cm radius. The rotational axis was set to two orientations based on experimental requirements.

2.2. Movement Task

For this study, we performed an experiment to evaluate 3D visuomotor control quantitatively, using circular tracking movements for the frontal and sagittal planes relative to the subject in the VR space (see Figure 1). The subjects were seated on a chair built for the experiment and wore an HMD. Prior to the experiment, we orally confirmed that each subject could properly perceive stereoscopic vision. Subjects were asked to hold the physical controller in their dominant hand. We ran a calibration to locate the target’s initial position optimized for the subject’s arm length and height to minimize the different anthropometric parameter impacts on experimental results. The target rotated at 0.125, 0.25, 0.5, or 0.75 Hz along the orbit after a 3 s countdown with a sound effect. The subjects were asked to move the tracer to the target position during the countdown and then perform a circular tracking movement. The target stopped after three loops. At the end of each trial, the target stopped for 1 s and played a sound. Four trials each were performed with the target rotating in the frontal (ROT(0) in Figure 1A) and sagittal planes (ROT(90) in Figure 1B). The first trial for each plane was a practice run and was excluded from the analysis. Therefore, 32 experimental trials were performed (4 trials × 4 speeds × 2 planes) for each subject. To avoid a subject learning effect, the experiment was performed with random counterbalance.

2.3. Data Analysis

For data analysis, we transformed the Cartesian (X, Y, Z) data to radial displacement, angular displacement, and angular velocity on polar coordinates; R, θ, and ω, respectively.

$$\Delta R\left[\mathrm{mm}\right]=\frac{{{\displaystyle \sum }}_{t=1}^{n}abs\left(R_{tracer}\left(t\right)-R_{target}\left(t\right)\right)}{n},$$

(1)

where ΔR is defined as the radial position difference absolute value between the target and tracer from the origin.

$$\Delta \theta \left[\mathrm{deg}\right]=\frac{{{\displaystyle \sum }}_{t=1}^{n}abs\left({\theta }_{tracer}\left(t\right)-{\theta }_{target}\left(t\right)\right)}{n},$$

(2)

where Δθ represents the angular displacement difference absolute value between the target and tracer.

$$\Delta \omega \left[\frac{\mathrm{deg}}{\mathrm{s}}\right]=\frac{{{\displaystyle \sum }}_{t=1}^{n}abs\left({\mathsf{\omega }}_{tracer}\left(t\right)-{\mathsf{\omega }}_{target}\left(t\right)\right)}{n},$$

(3)

where Δω denotes the angular velocity difference absolute value between the target and tracer. These parameters were normalized with total time n of three trials for each target speed.

The units of ΔR, Δθ, and Δω are mm, deg, deg/s, respectively. We calculated the absolute difference averages of ΔR, Δθ, and Δω on three trials for each subject. Next, the mean (M) and standard deviation (SD) were calculated by using the ΔR, Δθ, and Δω averages for the 16 subjects.

Statistical analysis and data visualization were performed by SPSS Statistics V26, IBM and MATLAB, MathWorks. In general, Cronbach’s α indicates the overall data reliability; it is understood that a value around 0.8 is respectable [15]. The reliability analysis for ΔR, Δθ, and Δω data was measured by Cronbach’s α (Reliability Analysis function in SPSS Statistics, IBM), with values of 0.87, 0.82, and 0.84, respectively.

This study verified a relationship between the target speed and depth in 3D target-tracking movements. Therefore, we investigated the parameter differences of ΔR, Δθ, and Δω between frontal and sagittal plane circular tracking movements. In addition, we examined the visuomotor control differences for four different parameter-based target speeds. For the analysis of circular tracking movement differences based on ΔR, Δθ, and Δω, we carried out a two-way repeated-measures analysis of variance (ANOVA), with a two-level plane factor (ROT(0), frontal plane; and ROT(90), sagittal plane) and a four-level speed factor (V1: 0.125 Hz, V2: 0.25 Hz, V3: 0.5 Hz, and V4: 0.75 Hz; each with n = 16). The total sample size was 128, calculated by a priori power analysis [16]. The main impacts and interaction of plane and speed factors in ΔR, Δθ, and Δω parameters were assessed by the Repeated Measures function in SPSS Statistics, IBM. We performed Mauchly’s sphericity test to validate the ANOVA results. When sphericity was assumed (p > 0.05), the values corrected with Sphericity Assumed were used. When sphericity was not assumed (p < 0.05), the values corrected with Greenhouse–Geisser were used.

A posthoc test was conducted by pairwise comparison of the Bonferroni corrections. Except where noted, we describe data using M and SD; considering comparisons yielding p < 0.05 as statistically significant and those yielding p < 0.01 as highly significant differences. This analysis corresponds to the statistical tests shown in Tables S1–S3.

2.4. Power Analysis

We conducted the priori power analysis using G*Power software 3.1.9.4, determining the minimum required sample size in ANOVA: Repeated measures, within-between interaction [16]. With effect size = 0.25, alpha = 0.05, number of groups = 8, power = 0.80, number of measurements = 4, and nonsphericity correction = 1, the analysis showed that the sixteen participants were required to detect an actual power of 0.8.

Furthermore, to estimate the power of the two-way repeated-measures ANOVA used in this research, we conducted a post hoc power analysis using G*Power software 3.1.9.4. As shown in Item A in Tables S1–S3, the power values were approximately 1.0. We can be confident that the 16-participant sample size achieves enough power to detect the main effects and interactions.

3. Results

The following sections analyze motor control characteristics of circular tracking movements in 3D space based on each of the three polar coordinate parameters.

3.1. Differences in Circular Tracking Movement Based on ΔR in 3D VR Space

Figure 2 shows typical circular tracking movement examples at four target speeds (V1: 0.125 Hz, V2: 0.25 Hz, V3: 0.5 Hz, and V4: 0.75 Hz; each with n = 16). Figure 2A1,A2 show the circular tracking movement ΔR on the frontal and sagittal planes at each target speed. For the circular tracking movement on both the frontal and sagittal planes, the difference between target trajectories and the tracer tended to increase as the target speed increased. Further, there is a higher sagittal plane difference compared to the frontal plane at each target speed, as shown in Figure 2A1,A2. Hence, we examined the 3D space circular movement at the four target speeds using ΔR.

Two-way repeated-measures ANOVA on the ΔR performance differences revealed significant key impacts for the plane, F(1,15) = 47.53, p = 0, partial η² = 0.76, and speed, F(1.43,21.46) = 76.15, p = 0, partial η² = 0.835, as well as an interaction between the plane and speed factors, F(3,45) = 7.4, p = 0, partial η² = 0.33 (item A in Table S1). This indicates that the plane and speed factors affected the circular tracking movement ΔR. Further, the interaction between the target speed and depth in 3D target-tracking movements would affect the ΔR performance in estimating the spatial motor control characteristics in the task.

Therefore, we performed a pairwise comparison to analyze the speed factor between ROT(0) and ROT(90). As shown in Figure 3A, there was a statistically significant ΔR difference between ROT(0) and ROT(90) (item B in Table S1). The results show that the subjects found it particularly difficult to track the sagittal plane target radius (M = 11.77 mm, SD = 5.2 mm) than that on the frontal plane (M = 8.93 mm, SD = 3.90 mm) at target speeds of 0.25 Hz and higher (p = 0, r = 0.656; item C in Table S1).

Next, we examined the ΔR circular tracking movement on each plane at the four target speeds. Figure 3B shows that the pairwise comparison had a significant ΔR difference for ROT(0) phase target speeds (item D in Table S1). The values of ΔR were 6.01 ± 3.53, 6.95 ± 3.24, 9.67 ± 1.72, and 13.11 ± 2.36 mm for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. This indicates that ΔR increased significantly on the frontal plane (ROT(0)) as the target speed increased.

As shown in Figure 3C, there was a significant ΔR difference in target speeds for the ROT(90) phase (item E in Table S1). The values of ΔR were 7.35 ± 3.23, 8.62 ± 2.54, 13.25 ± 2.45, and 17.86 ± 4.19 mm for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. No significant ΔR difference between V1 and V2 was noted on the sagittal plane (ROT(90)) (t(15) = 2.143, p = 0.29, r = 0.484). This suggests that the subjects found it more difficult to track the sagittal plane (ROT(90)) target radius for speeds over 0.25 Hz.

We found that the circular tracking movement that maintains a constant distance from the circle center can be more accurately tracked on the frontal plane (ROT(0)) compared with that on the sagittal plane (ROT(90)).

3.2. Circular Tracking Movement Differences Based on Δθ in 3D VR Space

Figure 2B1,B2 show Δθ at the four target speeds on the frontal and sagittal planes, respectively. First, we compared Δθ between the frontal and sagittal planes at each target speed to investigate the impact of depth (distance from the subject) on Δθ. Two-way repeated-measures ANOVA on Δθ performance-based differences revealed significant main impacts for the plane, F(1,15) = 156.89, p = 0, partial η² = 0.913, and speed, F(1.07,16.12) = 64, p = 0, partial η² = 0.81, as well as plane and speed interaction factors, F(1.542,23.13) = 6.72, p = 0.008, partial η² = 0.309 (item A in Table S2). This shows that the plane and speed factors affected Δθ in circular tracking movements. Also, the interaction between the frontal and sagittal planes at each target speed affected the Δθ performance in evaluating the precision of circular tracking movement position control.

Therefore, we performed a pairwise comparison analyzing the speed factors of ROT(0) and ROT(90). As shown in Figure 4A, there was a statistically significant difference in Δθ between ROT(0) and ROT(90) (item B in Table S2). Unlike ΔR, Δθ has a significant difference with respect to circular tracking accuracy on ROT(0) and ROT(90) over 0.125 Hz. This indicates that the subjects found it more difficult to synchronize the target and tracer positions on the sagittal plane (M = 7.48°, SD = 5.81°) than on the frontal plane (M = 5.52°, SD = 4.44°) at all target speeds (p = 0, r = 0.845; item C in Table S2).

Next, we examined the relationship between Δθ and target speed for each plane. Figure 4B shows that the pairwise comparison had a significant Δθ difference in target speeds for the ROT(0) phase (item D in Table S2). The values of Δθ were 1.95 ± 0.74°, 2.79 ± 0.85°, 5.84 ± 1.91°, and 11.51 ± 4.26° for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. As is the case with ΔR, Δθ increased significantly on the frontal plane (ROT(0)) as the target speed increased. This indicates significant difficulty in circular tracking movement position control on the frontal plane (ROT(0)) as the speed increases.

Next, as shown in Figure 4C, there was a significant Δθ difference in target speeds for the ROT(90) phase (item E in Table S2). The values of Δθ were 2.95 ± 0.95°, 4.12 ± 1.2°, 7.93 ± 2.19°, and 14.91 ± 6.46° for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. Also, with increased target speed, Δθ increased significantly on the sagittal plane (ROT(90)).

The results indicate that as the speed increased, the subjects had substantially more difficulty with circular tracking movement position control on the sagittal plane (ROT(90)) compared with the frontal plane (ROT(0)).

3.3. Circular Tracking Movement Differences Based on Δω in 3D VR Space

Figure 2C1,C2 show Δω on the frontal and sagittal planes, respectively, at each of the four target speeds.

We compared Δω between the frontal and sagittal planes at each target speed to investigate the impact of depth on velocity control accuracy. Two-way repeated-measures ANOVA on the performance differences based on Δω revealed significant core impacts for the plane, F(1,15) = 171.36, p = 0, partial η² = 0.92, and speed, F(1.07,16.03) = 252.33, p = 0, partial η² = 0.944, as well as an interaction between the plane and speed factors, F(1.258,18.87) = 38.1, p = 0, partial η² = 0.717 (item A in Table S3). This indicates that Δω in the circular tracking was affected by the plane and speed factors. Further, the interaction between the target speed and depth in 3D target-tracking movements would affect the Δω performance in evaluating the velocity-control precision in circular tracking movements.

As shown in Figure 5A, the pairwise comparison of the plane and speed factors revealed a statistically significant Δω difference between ROT(0) and ROT(90)) (item B in Table S3). This indicates that the subjects were more precise on the frontal plane (M = 27.53 ° s⁻¹, SD = 18.27 ° s⁻¹) than on the sagittal plane (M = 37.17 ° s⁻¹, SD = 26.24 ° s⁻¹) when synchronizing the target and tracer angular velocities (p = 0, r = 0.855; item C in Table S3).

Next, we examined the Δω and target speed relationship for both planes using pairwise comparison. As shown in Figure 5B, there was a significant Δω difference in target speeds for the ROT(0) phase (item D in Table S3). The values of Δω were 9.65 ± 1.61, 15.17 ± 2.05, 31.23 ± 4.8, and 54.07 ± 10.13 ° s⁻¹ for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. Δω increased significantly on the frontal plane (ROT(0)) as the target speed increased. In shows that it is increasingly difficult to control the frontal plane (ROT(0)) circular tracking movement velocity as the speed increases.

As shown in Figure 5C, there was a significant difference in target speeds Δω for the ROT(90) phase (item E in Table S3). The values of Δω were 12.09 ± 1.5, 19.93 ± 3.01, 42.15 ± 5.35, and 74.54 ± 18.66 ° s⁻¹ for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. Furthermore, Δω increased significantly on the sagittal plane (ROT(90)) as the target speed increased.

We found that as the speed increased, the subjects had more difficulty controlling the circular tracking movement position on the sagittal plane (ROT(90)) compared with that on the frontal plane (ROT(0)).

4. Discussion

In this study, we quantitatively evaluated motor control characteristics for circular tracking movements in 3D space. We analyzed the temporospatial relationship in 3D space between the circular tracking movements and target motion for various speeds and two different rotation axes. We measured three kinematic metrics (parameters) based on polar coordinates: differences in distance from the fixed pole, ΔR; position angle, Δθ; and angular velocity, Δω.

We found that when the target speed increased, Δθ and Δω (indicating temporal motor control characteristics in polar coordinates) increased for both the frontal and sagittal planes. This suggests that irrespective of the target rotation axis in 3D space, increasing the target speed makes it more difficult to synchronize the angle and angular velocities of the target and tracer temporally (Figure 4B,C and Figure 5B,C). Further, ΔR, which indicates spatial motor control characteristics in polar coordinates, increased for both the frontal and sagittal planes when the target speed increased. This suggests that, irrespective of the target rotational axis in 3D space, increasing the target speed over a specific velocity makes it more difficult to track the target spatially (Figure 3B,C).

To investigate the impact of the depth on motor control in 3D space, we compared the three parameters on both planes at each target speed. On the sagittal plane, Δθ and Δω were significantly higher than on the frontal plane at all target speeds (Figure 4A and Figure 5A). However, ΔR was significantly higher than that on the frontal plane over target speeds of 0.25 Hz (Figure 3A). Further, the differences between the two planes strongly increased along with the target speed (Figure 3A, Figure 4A and Figure 5A) for all parameters.

This result shows that the depth information is significant for target-tracking movements, particularly at high speeds. In the following, we discuss the impacts of the target speed and depth.

4.1. Impact of Target Speed on Circular Tracking Movement

Previous studies on motor control characteristics for circular tracking movements used Cartesian or polar coordinate parameters [13,14,17]. Three polar coordinate parameters are widely used: ΔR, Δθ, and Δω [13,14]. Based on these parameters, our previous study analyzed the motor control and impact of target speed and visual feedback about the target during 2D tracking movements [14].

In our previous study, Cartesian coordinate errors allowed us to confirm the circular tracking movement spatial accuracy (or spatial error) in terms of each axis in 3D space. However, Δθ and Δω in polar coordinates of this study enable us to analyze motor control characteristics in 3D space in terms of the position and velocity control accuracy, respectively. Our results showed that a higher target speed increases position and velocity errors as well as the circular movement spatial error.

In this study, we confirmed these results for 3D space irrespective of the rotation axis (Figure 3, Figure 4 and Figure 5). In our previous study, we mapped 3D joint movements onto a 2D plane. In contrast, for this study, we directly tracked motor control characteristics in 3D space. We found that for the circular tracking movement motor control at slow target speed in 3D space, Δθ and Δω (which indicate the temporal characteristics) were more sensitive than ΔR (Figure 3, Figure 4 and Figure 5). In other words, we confirmed that in 2D and 3D spaces, tracking errors (i.e., the three parameters) increased as the target speed increased. The observed movement delay is because the brain’s neurotransmission, sensory processing, has a 200 ms delay in reaching the human visuomotor control system [18,19]. Furthermore, it is more difficult to acquire target motion visual information [20] when the target speed increases.

We also compared the frontal plane (ROT(0)) movements, similar to the 2D experiments, with those on the sagittal plane (ROT(90)), which are typical 3D movements. We quantitatively showed that circular tracking performance, position control accuracy, and velocity control accuracy in a 3D space is more difficult than in a 2D space (Figure 3A, Figure 4A and Figure 5A).

In future work, we will investigate the impact of the target visual feedback in terms of the control strategy characteristics in 3D circular tracking movements [14,21,22,23,24,25,26].

4.2. Impact of Depth on Circular Tracking Movement

Unlike 2D space, depth estimation is a significant control metric for depth perception and motor control in 3D space. In previous studies on target-tracking movements, particularly for circular tracking movements, no technology or system has been able to provide an accurate representation of the visual target. Therefore, the role of depth in 3D target-tracking movements, the relationship between target speed and depth in 3D target-tracking movements, and impact of depth on kinematic parameters, such as position, and velocity need to be explored further.

Previously, we developed a 3D visuomotor control evaluation system in a VR environment [11]. By evaluating the Cartesian coordinate spatial error, we analyzed circular tracking movements on the frontal and sagittal planes. However, the evaluation using the Cartesian coordinate spatial error in that study could not clearly show the difference between circular tracking movements on the two planes. Consequently, we did not explore the role of depth information in motor control of 3D target-tracking movements. Furthermore, we confirmed that, regarding the Cartesian coordinate spatial errors, a significant difference was observed between the two circular tracking movement types even when the target speed was increased to a higher level (see Figure 6). Accordingly, we needed to propose a new analysis method for various circular tracking movement types and speeds in a 3D environment and for exploring the role of depth information in 3D target-tracking movement motor control. In this study, based on the three polar coordinate parameters, we quantitatively showed that the depth information is significant for the performance of circular movements, position control accuracy, and velocity control accuracy in 3D movements. Furthermore, it was established that the depth information is even more significant when the target is moving faster (Figure 3, Figure 4 and Figure 5).

Target motion cognition in 3D space is significant for 3D circular tracking movement motor control. In our previous study, using a rubber hand illusion in a VR environment, we showed that depth perception is easier in left to right motion for the same depth than for different depths [27]. Also, we found that the limb position visual feedback is most accurate in the azimuth and least accurate in the depth direction [28]. Those previous studies helped us interpret our results in these studies. In other words, because target motion cognition is better on the frontal plane than on the sagittal plane, performance, position control, and velocity control are better on the frontal plane in circular tracking movements. The faster the target speed, the clearer the trend (Figure 3, Figure 4 and Figure 5). In future studies, we will quantitatively analyze the hand-arm system sensitivity as well as the impact of the target cognition level for both planes in 3D space by modifying the target visual feedback [23]. Further, we will quantitatively analyze the difference in the weight of the 3D tracking movements by experimentally recording and analyzing muscle activity.

4.3. Control Strategy and Mechanism in 3D Tracking Movements

In general, the human visuomotor control system requires approximately 200 ms to perform visually guided error correction because of the brain’s neurotransmission, sensory processing, and refractoriness in the human neuromotor control [18,19,29]. Previous studies have established theories for control strategies by considering the delay time during visuomotor processing. Intermittent feedback (FB) control and feedforward (FF) control using an internal model have been suggested as typical theories for the control strategy [21,22,23,24,30]. These studies demonstrated that control strategies (i.e., FB and FF controls) and major control parameters in kinematic features (i.e., position or velocity) for tracking movements vary irrespective of the target trajectory being random or consistent [13,17,21,22]. In other words, these studies reported that pseudorandom tracking movements are primarily controlled by intermittent FB control with position error (i.e., Δθ) reduction. In addition, periodic sinusoidal tracking movements depend on more FF control with velocity error (i.e., Δω) reduction to predict future target motion. Our previous study examined the extent of the impact of the target visual information on the periodic circular tracking task control strategy as being the same in this study [14]. We also confirmed FF controls with velocity error (i.e., Δω) reduction in target-invisible regions for the periodic circular tracking task. In other words, the target visibility allows us to examine the impact of the target visual information on the control strategy by quantitatively comparing the three temporospatial parameters (ΔR, Δθ, and Δω) relative changes during the target-visible phase responsible for stable FB control with the target-invisible phase for FF control. In our future studies, we will examine the same periodic circular tracking task with different speeds and visibility of the target based on the same ΔR, Δθ, and Δω parameters to observe control strategy changes and major kinematic feature control parameters during 3D circular tracking movement tasks.

For different movement types and target speeds, we should design different control strategies, considering cognition delay and visuomotor processing. Intermittent FB control and FF control, as an internal model, have been suggested as a suitable control strategy [13,14,15]. Based on previous studies in 2D space, FB control dominates when the target speed is slow; however, FF control dominates when the target speed is high [21,22,23,24]. In this study, similar results were found for 3D target-tracking movements. Despite adding a countdown sound to announce the start of the target movement, the initial errors were greater when the target speed was higher, indicating imprecise FF control, as observed for 2D movements (Figure 2) [25]. Our previous studies demonstrated that increasing target speed makes it more difficult to synchronize the angle and angular velocities of the target and tracer temporally. Considering our previous studies [31,32] showed the cerebellum plays an important role in the generation of motor commands for smooth velocity and position control, the method and analysis proposed in this study will apply to characterize the motor function of patients with cerebellar ataxia in the future.

Our recent study demonstrated that the smooth tracking movement of the wrist joint consists of two components with distinct motor commands for velocity and position controls [33]. In other words, the major component in a lower frequent range (named by the F1 component) of the tracking movement played the primary role to reproduce both the velocity and position of the target motion in a predictive manner. In contrast, the minor component in a higher frequency range (named by the F2 component) of the tracking movement encodes mostly the positions of small step-wise movements with intermittent FB control. In this study, the 3D tracking movement for higher target speeds and ROT(0) showed lower frequent components in two temporal parameters (Δθ and Δω). Therefore, we will quantitatively analyze the control strategy and mechanism of 3D tracking movements in the F1 and F2 components based on the predictive control and intermittent FB control in our future work.

4.4. Future Application and Limitation of Temporo-Spatial Parameters in Polar Coordinates

In this study, we adopted temporospatial parameters in an extrinsic coordinate frame to analyze motor control characteristics for two planes and various circular tracking movement speeds in a 3D environment. However, the temporospatial parameters in this study did not allow us to analyze different biomechanical constraints (i.e., arm posture of the kinematic chain, torque of each joint) in an intrinsic coordinate frame for the two planes. In other words, the different biomechanical constraints in the two planes could impact the control of the hand position (i.e., temporospatial parameters in polar coordinates) in an extrinsic coordinate frame. In the future, we will analyze the different biomechanics in an intrinsic coordinate frame between circular tracking movement on the two planes by experimentally recording and analyzing the arm posture and related muscle activities during circular tracking tasks [34,35,36].

The VR system used in this study allowed subjects to perform three degree-of-freedom visuomotor tracking movements in an immersive three-dimensional VR environment. In our future study, the proposed method and analysis parameters (i.e., temporospatial parameters in polar coordinates) can be used for evaluating the seriousness of illness and the effectiveness of rehabilitation for patients with hemiplegic upper limbs. The method can also be applied to perception studies of spatial neglect patients [37].

5. Conclusions

We examined two plane circular tracking movements in 3D space (from a motor control perspective) based on three temporo-spatial parameters. We found that errors of two temporal parameters on each plane were proportional to the change in the target velocity. Furthermore, for a spatial parameter, the errors in the circular tracking on the frontal plane (ROT(0)) without depth were lower than those in the circular tracking on the sagittal plane (ROT(90)) with depth. The experimental protocol and data analysis in this study allowed us to analyze the motor control characteristics temporospatially for circular tracking movement with various depths and speeds in 3D VR space.