Introduction

Sensing the motion of the world and its objects is a fundamental task of our visual system, a concept introduced over 70 years ago by James Gibson1. When an observer translates or rotates through the environment, the pattern of light reflected from objects undergoes a lawful continuous perspective transformation, resulting in global motion patterns known as optic flow2,3. On a flat screen, optic flow can create the same retinal image as a real three-dimensional (3D) scene4. This effect can be produced by visual stimuli, such as patterns of moving dots, creating a sense of self-motion, or “vection,” even in the absence of physical movement. This phenomenon can influence human behavior and control certain actions, although most previous studies have been confined to the laboratory. However, a recent study demonstrated that optic flow can also affect human behavior and control actions in natural, real-world environments5. It is now feasible to incorporate optic flow into real motor behaviors, such as precision throwing (including dart throwing), using augmented reality (AR) technology. Precision throwing is a uniquely human, skilled ability6. Although the combination of optic flow and AR holds potential for enhancing motor control and skill acquisition, there have been no reports of the generation of optic flow or other perceived motions using AR.

Optic flow serves several functions for observers in motion. It allows them to perceive their direction of movement and provides visual guidance for various actions such as steering toward a target, maintaining balance and posture, and avoiding or achieving collisions2. Both humans and monkeys tend to rely heavily on optic flow to generate actions7. Additionally, optic flow is essential for perceiving object shapes and the layout of the environment8. However, the most widely accepted theory suggests that optic flow is primarily used to guide locomotion toward a target of interest9. In most previous studies, optic flow has been induced through random-dot motion, in which dots are generated at random locations on a screen and displayed for random durations within a specified time frame. This random-dot optic flow more convincingly induces vection—a sense of self-movement—than virtual environments replaying real-life scenes, such as riding in a vehicle10. Head-mounted displays (HMDs) used for AR or virtual reality (VR) may offer an advantage in inducing strong effects because vection may vary with field size and immersion level11. In a study using an HMD, optic flow induced different head displacement responses depending on vection direction and whether participants were sitting or standing12. However, few studies have investigated optic flow generated through HMDs, and it remains unclear how AR-based optic flow affects motion perception. Several studies have shown that the strength of motion perception is influenced by optic flow parameters on conventional displays. For example, vection strength depends on motion direction and is weaker in oblique than in cardinal directions13. Moreover, the speed of optic flow significantly contributes to vection strength14.

VR technology has been used to simulate sports activities15, facilitate the learning of complex sports movements16, and improve the understanding of intricate tactics in ball games17,18. VR-based simulators providing feedback have shown greater effectiveness than practicing with real balls under a coach’s supervision15,19. In particular, AR systems have been used to enhance sports training by offering visual or auditory feedback20. These systems have been applied to various types of physical training, including golf ball striking21 and ballet22. Additionally, AR HMDs that present an ideal shot trajectory have demonstrated benefits in basketball free-throw training23,24. A previous literature review categorized various feedback approaches but failed to identify the ideal method for presenting feedback20. Studies have used various feedback types for dart-throwing tasks with HMDs, such as third-person perspectives25 and dart trajectories26. However, these studies did not identify the optimal type of feedback to improve dart-throwing performance, similar to the findings of studies of other skill-based activities27,28.

This study evaluated the effects of AR-based optic flow and other types of motion stimuli, randomly generated through moving spheres, on dart-throwing performance. Six motion patterns of the random spheres were displayed on an AR HMD (Microsoft HoloLens 2; Microsoft Corp., Redmond, WA, USA); their effects on aiming motor skill in dart throwing were examined in two groups of young, healthy participants, with a non-random-sphere presentation serving as a control (Fig. 1). Experiment 1 initially tested three patterns: random motion, radial expansion motion from the dartboard center (i.e., the bull’s eye), and a combination of random and radial expansion motions (Fig. 1a). The random motion tested the effects of random-sphere presentation as noise for visual perception, while radial expansion motion induced optic flow toward the center, simulating forward locomotion. These motions were expected to reduce aiming errors based on a previous study showing greater attraction for these motion types compared to radially contracting motions29, except in young children30. If expansion affected aiming performance, we assumed that the combined motion would induce a similar but weaker effect because of the reduced coherence at 50%, compared to the full coherence of 100% in the pure expansion motion31. Experiment 1 showed that only the expansion motion altered aiming performance, shifting darts upward and reducing vertical errors, while other motions showed no significant differences compared to the control condition. We then performed Experiment 2 to examine the remaining three motion patterns: leftward motion, radial contraction motion toward the bull’s eye, and diagonal radial expansion motion from the left (Fig. 1b). Leftward motion was assumed to shift darts to the left32,33. The radial contraction motion, simulating backward locomotion, was expected to induce effects opposite to those of expansion, shifting darts downward. Diagonal radial expansion motion was anticipated to shift darts leftward and upward because optic flow is generated when the observer looks straight ahead but heads to the left34. Experiment 2 demonstrated that leftward motion shifted darts to the left, as expected, but the other two motions produced unexpected results. The contraction motion did not have an effect opposite to expansion; instead, it reduced lateral variance. Diagonal expansion motion showed no significant effect. Thus, the effects of AR-based perceived motion on dart-throwing performance appear more complex than initially anticipated. Nonetheless, the experimental results imply that certain types of AR-based motion stimuli could enhance motor performance by reducing error and variance.

Fig. 1
figure 1

Augmented reality (AR)-based motion stimulus. Patterns of motion used in (a) Experiment 1 (Supplementary Materials S1–3.mp4) and (b) Experiment 2 (Supplementary Materials S4–6.mp4). The size, density, speed, and lifetime of the spheres remained constant across all motions.

Results

The effects on aiming accuracy were compared with a non-sphere presentation condition in 40 participants, categorized into two groups. Experiment 1 was conducted with 20 participants, followed by Experiment 2 with another 20 participants. Each group evaluated three different sphere motion patterns in Experiment 1 (Fig. 1a) and Experiment 2 (Fig. 1b). The size (1-cm radius), density (177.8 spheres/m3), speed (0.44 m/s), and lifetime (50–250 ms) of the spheres remained constant across all conditions, except for the control condition. The participants were instructed to throw 30 darts for each pattern, aiming for the bull’s eye, resulting in a total of 120 darts thrown per participant. The Mann–Whitney U test showed no significant differences for participants in Experiment 1 and Experiment 2 compared to the control condition (Table 1).

Table 1 Mann–Whitney U test comparing dart performance in non-sphere presentation condition between Experiments 1 and 2. There was no statistically significant difference, using a p-value threshold of < 0.05.

To evaluate the effects of the AR-based motion stimulus, we calculated the mean errors relative to the target and the variance in dart-throwing performance using one-way repeated-measures analysis of variance (ANOVA). If significant differences were found, Dunnett’s test was used to evaluate the effects of the motion stimulus relative to the control condition through multiple post-hoc comparisons.

Experiment 1

In Experiment 1, random, expansion, and combined motions were compared with the control condition (Fig. 2). Although the expansion motion resulted in smaller absolute error (Fig. 2a) and total variance (Fig. 2d) than the other conditions, there were no significant differences (Table 2). The lateral errors and variance were nearly equal across conditions, with no significant differences (Fig. 2b, e). For vertical error and variance (Fig. 2c, f), the expansion motion led to smaller error and variance. However, the error showed a significant difference (Table 2). Dunnett’s multiple comparison test revealed a significant difference between the expansion motion and the control condition (p = 0.044; Fig. 2c). Conversely, random motion and the combination of random and expansion motion did not significantly differ from the control condition (p = 1.0 and p = 0.93, respectively).

Fig. 2
figure 2

Dart-throwing performance in Experiment 1. Top row shows the (a) absolute, (b) lateral, and (c) vertical errors of darts stuck on the dartboard. Bottom row shows the (d) total, (e) lateral, and (f) vertical variances. The small gray dots represent data from individual participants, and the bars indicate means across participants. The vertical whiskers are the 95% confidence intervals. The horizontal line indicates a significant difference, with p-values above the line.

Table 2 Results of one-way repeated-measures ANOVA for Experiment 1. p < 0.05 was considered indicative of statistical significance. Significant effects are shown in bold.

Experiment 2

In Experiment 2, the leftward, contraction, and diagonal expansion motions were compared with the control condition (Fig. 3). The absolute error and total variance were similar among these conditions (Fig. 3a, d), with no significant differences (Table 3). However, significant differences were found in the lateral error and variance among the motion patterns (Table 3). According to Dunnett’s multiple comparison tests, the leftward motion induced significantly smaller lateral errors compared to the control condition (p = 0.013; Fig. 3b). However, the contraction and diagonal expansion motions did not significantly differ from the control condition (p = 0.32 and p = 0.79, respectively). Additionally, the contraction motion induced significantly smaller vertical variance compared to the control condition (p = 0.029; Fig. 3e). Conversely, there were no significant differences in the leftward motion (p = 0.92) or diagonal expansion motion (p = 0.99) compared to the control condition. While the contraction motion resulted in larger vertical errors and variance (Fig. 3c, f), these differences were not significant (Table 3).

Fig. 3
figure 3

Dart-throwing performance in Experiment 2. Top row presents the (a) absolute, (b) lateral, and (c) vertical errors of darts stuck on the dartboard. Bottom row shows the (d) total, (e) lateral, and (f) vertical variances. The small gray dots represent the data from individual participants, and the bars indicate the means across participants. The vertical whiskers are the 95% confidence intervals. Horizontal lines indicate significant differences. P-values are shown above the lines.

Table 3 Results of one-way repeated-measures ANOVA for Experiment 2. p < 0.05 was considered indicative of statistical significance. Significant effects are shown in bold.

Discussion

We investigated the effects of AR-based perceived motion in 3D space using a random-sphere motion stimulus on aiming motor skill in dart throwing. Randomly generated spheres moved according to six motion patterns: random, expansion, combination of random and expansion, leftward, contraction, and diagonal expansion. Effects on aiming accuracy were compared with a non-sphere presentation condition in 40 participants. The participants were categorized into two groups: one group assessed the effects of random, expansion, and combined motions, whereas the other group evaluated leftward, contraction, and diagonal expansion motions. We found significant effects only for the expansion, leftward, and contraction motions. The expansion motion affected vertical errors, leftward motion influenced lateral errors, and contraction motion reduced lateral variance. These effects were observed in different experiments with different participant groups. However, the results exhibited sufficient statistical power (≥ 0.95) and there were no significant differences between the groups.

Before conducting the experiments, we assumed that the contraction motion induces an effect opposite to that of the expansion motion. However, while the expansion motion reduced vertical error, the contraction motion reduced lateral variance. This raised the question of whether the effects varied depending on the motion direction. We hypothesize that expansion motion influences dart-throwing speed and force, making the distance to the dartboard feel shorter, whereas contraction motion focuses the gaze on the target without altering the perceived distance to the dartboard. For the dart-throwing task, it is necessary to determine a combination of dart launch angle and speed35. There is a trade-off between speed and accuracy, as higher dart speeds increase uncertainty due to motor noise36. Learning to throw darts can be best described as an iterative process of finding the optimal solution, in line with optimal control theory37,38,39. The uncertainty compounds over the distance and time until the dart sticks to the board. Thus, optimal combinations involve low speed with a steep launch angle for distant targets and high speed with a flat angle for nearer targets. If a player perceives the dartboard as closer, a high dart speed and low trajectory may induce vertical error, as darts generally tend to stick lower than the target. In contrast, radial contraction optic flow guides the direction of gaze without misperceiving the distance, resulting in a stabilized gaze that could reduce lateral variance.

On the other hand, the combined random and expansion motion did not exhibit a significant effect, despite the assumption that it would attenuate the effect of expansion using random-dot motion stimuli31. It was hypothesized that a threshold of visual motion discriminability higher than that in our setting (i.e., 50% coherence) was required. In this study, it was possible that participants could not distinguish and perceive the expansion motion within the combined motion. The diagonal expansion motion also showed no significant effects, likely due to reduced stimulus strength. Altogether, these findings imply that optic flow in 3D space requires higher stimulus strength.

This study had several limitations. First, the AR HMD had a narrow horizontal field of view (FOV) of 43°. A horizontal FOV of < 60° is considered insufficient for speed perception, leading to underestimation40. It has also been reported that occlusion of as little as the central 10° of the visual field induces a systematic overestimation of visual speed40, potentially due to an inhibitory effect of central optic flow on the peripheral field41. We did not allow any displays around the dartboard to avoid obstructing the target. However, this might have compensated for the underestimation of speed perception due to the narrow FOV. Second, we did not consider parameters of random-sphere motion, such as sphere size, velocity, density, and coherence. Although this study used solid spheres without shadows, spheres with shadows might induce greater effects. There are numerous options for setting motion stimulus parameters; however, this study focused on simple effects using basic forms of motion. Further research is needed to explore these parameters in greater detail. Third, we did not consider interactions or combined effects of different motion patterns33 within the same participants, based on the assumption that each motion stimulus would have independent effects on aiming performance. Examining differences among motion stimuli within each participant may provide further insights. Finally, this study had a gender imbalance among participants for which there was no adjustment, because it was hypothesized that aiming performance would not differ between genders.

In summary, the radial expansion and lateral motions of the random spheres influenced directional biases in dart throwing, whereas the radial contraction motion reduced lateral variance. These findings imply that AR-based motion stimuli have the potential to improve motor skills. Although there may be other effective combinations of parameters for random sphere, such as sphere size or speed, our results provide a basis for further research on AR-based illusions of motion perception.

Methods

We conducted two dart-throwing experiments in which participants wore an AR HMD displaying six patterns of motion stimuli using randomly generated spheres. These were compared to a non-sphere presentation condition.

Participants

The study included 40 participants (3 women) aged 19–28 years. Five participants were left-handed, and the remaining participants were right-handed, with normal or corrected-to-normal vision and no history of neurological or psychiatric conditions. None of the participants were expert darts players; the most experienced players practiced less than once per week. The least experienced participants were instructed to watch a 3-min introductory video on dart throwing. All participants provided written informed consent prior to inclusion in the study. They were allocated to Experiment 1 (n = 20), which included one woman, or Experiment 2 (n = 20), which included two women.

Apparatus

A commercially available soft dartboard was positioned at a height of 1.73 m, with the distance from the throwing line to the dartboard set at 2.44 m (Fig. 4a). Participants threw standard plastic-tipped darts of identical size and weight while wearing an AR HMD (HoloLens 2; Microsoft Corp.), with horizontal and vertical FOVs of 43° and 29°, respectively. The system was developed using the Unity 2020 game engine (Unity Technologies, San Francisco, CA, USA). The darts were equipped with reflective markers, and their landing positions on the dartboard were measured. The markers were tracked using a motion capture system (OptiTrack V120: Trio; NaturalPoint, Corvallis, OR, USA) that included three inline cameras.

Fig. 4
figure 4

Experimental setup. (a) The area indicated by the rectangle generated AR-based motion stimuli consisting of randomly generated white spheres moving according to a specific motion pattern. (b) Experimental procedure and trial composition. (c) Calibration of the HMD coordinate (Supplementary Material S7.mp4).

Experimental procedure

The effects of AR-based motion stimuli using randomly generated spheres on dart-throwing performance were compared to a non-sphere presentation condition. All experimental procedures were approved by the Ethics Review Board of the National Defense Academy of Japan and adhered to the Ethical Guidelines for Medical and Health Research Involving Human Subjects, as stipulated by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), the Ministry of Health, Labour and Welfare, and the Ministry of Economy, Trade and Industry of Japan.

Experiments 1 and 2 were divided into 10 blocks each (Fig. 4b). Each block consisted of four rounds, with each round involving three dart throws, resulting in a total of 120 darts per participant. Participants experienced either the control condition or AR-based motion stimuli, with three different patterns presented in each round. Conditions were randomized within each block to mitigate potential bias from previously viewed motions42, and transitions were managed by the experimenter sending commands from a laptop PC via Wi-Fi. Participants used their dominant hand to throw the darts, aiming for the bull’s eye. Darts were collected by the experimenter after each block. Before the experiment, participants adjusted the HMD coordinates through a calibration process described in the following section and completed 5–10 practice rounds to familiarize themselves with the dart-throwing task and the laboratory environment, as well as to minimize large initial errors. Participants were not informed about the specific motion stimuli patterns used in the study. If a dart did not hit or stick to the dartboard, participants were instructed to throw an extra dart because the dart’s position could not be assessed in such cases. Although this situation was rare, occasionally a soft dart failed to stick to the dartboard despite hitting it, due to issues with the apparatus (e.g., a deteriorated dartboard or dart tips).

HMD coordinate calibration

Before the experiments, participants underwent a calibration process for the AR HMD coordinate, using the user interface to adjust the coordinate system (Fig. 4c). First, the participant launched the application at the dart-throwing line and pressed a button to generate a green center cross, centered within a circle with a 1-cm radius, located 2.44 m away. The participant then adjusted the center cross to align with the center of the dartboard. After completing the alignment, the participant was instructed to turn off the signs by pressing a toggle switch on the left side. We assumed that the AR HMD had sufficient performance for the study because the participant remained stationary at the throwing line, and the reported positional accuracy of the HoloLens 2 showed less than a 0.87% deviation over the traveling distance43.

Motion stimulus

White solid spheres with a radius of 1 cm were randomly generated within a rectangular area extending from −1.0 to 1.0 m in width, −0.75 to 0.75 m in height, and 0 to 2.5 m in depth from the center of the bull’s eye (Fig. 4a). The retinal size of the spheres continuously changed by approximately 0.4–5.7° within a rectangular area while approaching or receding from the viewpoint, despite little variability for each participant depending on their height and throwing position. To ensure visibility of the dartboard and participants’ hands, spheres were not presented within a cylindrical space with a radius of 0.2 m in front of the dartboard, corresponding to an approximately 9.1° visual angle on the dartboard from the throwing line. This manipulation likely did not affect our results as the contribution of local motion processing is minimal compared to global processing, which plays a fundamental role in optic flow effects44. Sphere density was set to 177.8 spheres/m3 (i.e., 1,333 spheres always existed in the rectangular area). Each sphere disappeared after a set lifetime duration or when it moved out of the presentation area. Then, a new sphere was generated at a random position within the presentation area, with a random lifetime of 50–250 ms.

The random spheres moved at a speed of 0.44 m/s, corresponding to 10°/s on a plane in front of the participant’s retina at a distance of 2.5 m, almost equal to the dartboard surface. Six motion patterns of the spheres were applied. The position of a sphere pR3 with respect to the coordinates on the bull’s eye was determined as p = [xyz]T. According to the position and speed vs = 0.44 [m/s], the velocity vector vR3 was generated as the sphere motion. Patterns 1–3 and 4–6 were applied in Experiments 1 and 2, respectively.

Pattern 1: Random motion

In the random motion, each sphere moved in a random direction at a constant speed vs independent of the other spheres. The motion was generated according to the following equation of 3D polar coordinates, independent of the position:

$$ {\mathbf{v}} = v_{s} \cdot \left[ {\begin{array}{*{20}c} {\sin \theta \cdot \cos \phi } \\ {\sin \theta \cdot \sin \phi } \\ {\cos \theta } \\ \end{array} } \right] ,$$
(1)

where θ and ϕ are the angles of the velocity vector, selected from a uniform distribution between 0° and 360° for each sphere (Fig. 5a).

Fig. 5
figure 5

Motion stimulus using random spheres. (a) 3D polar coordinates to generate random motion. (b) Expansion motion. (c) Leftward motion. (d) Contraction motion. (e) Diagonal expansion motion.

Pattern 2: Expansion motion

This generated sphere motions directed from the bull’s eye to the participants as follows:

$${\mathbf{v}} = \frac{{v_{s} }}{{\left| {\mathbf{p}} \right|}} \cdot {\mathbf{p}}.$$
(2)

The velocity vector of each sphere depended on its position (Fig. 5b). However, the speed was constant.

Pattern 3: Combined random and expansion motions

This was composed of Pattern 1 random motion and Pattern 2 expansion motion. Half of the random spheres moved according to Pattern 1, whereas the remaining dots followed Pattern 2.

Pattern 4: Leftward motion

This generated a one-way directional sphere motion from right to the left by following the velocity vector (Fig. 5c):

$${\mathbf{v}} = \left[ {\begin{array}{*{20}c} { - v_{s} } \\ 0 \\ 0 \\ \end{array} } \right].$$
(3)

Pattern 5: Contraction motion

This motion concentrated on the bull’s eye and reversed the expansion motion in Pattern 2 (Fig. 5d). Thus, the velocity vector of a sphere was given by:

$${\mathbf{v}} = - \frac{{v_{s} }}{{\left| {\mathbf{p}} \right|}} \cdot {\mathbf{p}}.$$
(4)

Pattern 6: Diagonal expansion motion

The diagonal expansion motion was similar to Pattern 2. However, instead of the spheres originating from the bull’s eye, they started 1.0 m to the left of the bull’s eye (Fig. 5e). The velocity vector was adjusted to reflect this change in origin. The sphere’s position in Eq. (2) was replaced with the relative position 1.0 m to the left of the dartboard, corresponding to approximately 22° heading direction for the participants relative to the bull’s eye. Using the update position, p’ = [x – 1.0, y, z]T, the velocity vector of a sphere was defined as follows:

$${\mathbf{v}} = \frac{{v_{s} }}{{\left| {{\mathbf{p^{\prime}}}} \right|}} \cdot {\mathbf{p^{\prime}}}.$$
(5)

Data analyses

The effects of the motion stimulus were assessed by comparing aiming performance, particularly error and variance, among the different patterns of optic flow in each experiment. For each participant, means of error and variance were calculated based on 30 throws for each pattern. A standard bootstrap technique was employed to generate confidence intervals for these means. Data were resampled by a factor of 10, with Experiments 1 and 2 resampled to 200 samples. Notably, the resampled data were used solely for calculating confidence intervals.

We used a Mann–Whitney U test to confirm that there was no significant difference in dart performance between the participants grouped in Experiments 1 and 2. The Mann–Whitney U test was applied to the dart performance in the control condition. A one-way repeated-measures ANOVA was conducted to compare differences among the motion patterns within each experiment group, using an alpha level of 0.05. For post-hoc analysis, the statistical power for each effect was calculated using G*Power45, with an alpha level of 0.05. If significant differences were identified, Dunnett’s test for multiple post-hoc comparisons was used to evaluate the effects of each optic flow pattern compared to the control condition.