We modeled the shoulder collision of two humans as a collision between two spherical rigid bodies with three major assumptions:

1. Mass of the human body: The colliding bodies are assumed to be two spherical bodies of lumped mass of m/2 each. Assuming that the average mass of the human body in a crowd is 60 kg, which is equally divided between the two shoulders due to symmetry, with mass M₁ = M₂ = 30 kg.

With this simple model of a shoulder collision, the collision force could be estimated using the principle of the conservation of momentum. The walking speed of a person in an aggressive or busy crowd is estimated to be V_1i = 1.7 m/s (Murtagh et al., 2021). With an average shoulder cross section of length l = 16 cm (Wysiadecki et al., 2014), the duration of contact ( δ t ) is calculated to be approximately 188 ms. With this assumption, the minimum impact or impulsive collision force can be calculated using the following formula: Collision force = F = M 1 . V 1 i . Cos θ δ t .

Therefore, the minimum impact or impulsive force, as a result of the collision, is estimated to be F₂ = 23.618 N. We used this estimated collision force to design a collision haptic device, as described in Section 3.2.3.

Our hardware consists of three different haptic modules, namely, “linear actuator (LA),” “eccentric rotating mass (ERM),” and “collision haptic device (CHD),” to generate three varieties of touch stimuli. All the three haptic modules are attached to a common baseplate that could be fitted to the user’s shoulder or arm using a shoulder band (Supplementary Figure S2). The aim of our investigation is to contrast the types of haptic stimuli for different VR contexts.

A crowd was simulated with a 360-degree video rendering of a real crowd in a Meta Quest 2 headset (Aggressive Crowd ¹ and Casual Crowd ² ). The 360-degree video was captured using an Insta360 Pro camera ³ . An open, crowded place was recorded using the camera lens adjusted and positioned at the average height of a person at 155 cm. A circle of radius 50 cm was drawn, and the camera was placed in the center of the circle to avoid artifacts from being very close. The crowd environment was recorded at a 4 K resolution at 30 FPS (Figure 3). The Casual Crowd was differentiated from the Aggressive Crowd by varying two parameters: crowd density (number of participants in the scene) and the rate of crossing the camera (speed) (for further details, see Supplementary Table S2) (Koilias et al., 2020b). The run time of each VR scene is 45 s.

Each haptic cue was synchronized with the virtual collision in the VR crowd. The VR scene was designed using Unity 3D ⁴ with a pre-recorded 360-degree crowd video, wrapped onto a 3D sphere (game object) using a material created with a normally flipped shader. The main camera was disabled, and the OVR Camera Rig was used as a camera. The ratio of the dimensions of the 3D sphere (where the 360-degree videos are projected) to the field of view of the OVR Camera Rig was set at 10:7 to maintain a realistic scaling of the VR environment compared with the real environment (Škola et al., 2020). The game scene in Unity was streamed wirelessly to the Meta Quest 2 connected to a PC via an air link. The participants experience the virtual crowd with the haptic prototype attached to their shoulder, as shown in Supplementary Figure S2. The total weight of the prototype is 520 g. A tight shoulder band was used to firmly hold and press the prototype over the shoulder of the participant. The Timeline function in Unity 3D was used to synchronize a visual collision event in the VR scene with the actuation of haptic devices via Unity–Arduino serial communication, as shown in Figure 4.

All participants were provided with an information sheet about the experiment and were also requested to sign an informed consent form. Each participant visited the laboratory at prearranged times. After completing a demographics questionnaire, they were fitted with the HMD along with the haptic devices on their shoulders before the experiment started. Out of the 20 subjects, 10 experienced the Casual Crowd scene first, followed by the Aggressive Crowd scene, and the remaining 10 experienced the Aggressive Crowd scene first, followed by the Casual Crowd scene after a 10-min break. For each crowd scene, the participants experienced different haptic conditions in a counterbalanced order. Each haptic condition was tested three times. To ensure a counterbalanced order, the sequences of the three haptic conditions were varied in a way such that each condition was experienced after the other two haptic conditions. The sequences were 1-2-3-1-3-2-1-2-3-1 / 3-1-2-3-2-1-3-1-2-3/2-3-1-2-1-3-2-3-1-2, where 1 = No Haptic (NH), 2 = Haptic Stimulus, and 3 = Tactile Stimulus. For example, the sequence 1-2-3-1-3-2-1-2-3-1 means that the participant experiences No Haptic (NH) first, followed by Haptic Stimulus and Tactile Stimulus, followed by No Haptic, Tactile Stimulus, and Haptic Stimulus, then by No Haptic, Haptic Stimulus, and Tactile Stimulus, and, finally, by No Haptic. The experiment lasted for approximately 24 min in total, including a 10-min break between the crowd conditions.

The objective of this study was to investigate the contribution of quality or type of haptics to eliciting emotional responses in crowded VR scenarios. We carried out a 2 × 3 within-group factorial experiment with the factors Crowd and Haptics. The Crowd factor has two levels, Casual Crowd and Aggressive Crowd, and refers to the type of social interaction between the participant and a depicted surrounding crowd. Under the Casual Crowd condition, the crowd members casually passed by the participant, whereas under the Aggressive Crowd condition, passers-by occasionally brushed/collided with the participant’s shoulder. The Haptics factor has three levels and refers to the type or quality of haptic feedback that the participants received from passers-by based on the haptic design implementation. This consists of “Tactile Stimulus,” “Haptic Stimulus,” and “No Haptic” (See Section 3.4 for details on haptic device design). The haptic devices were actuated in synchronization with the collision with the crowd in the scene visually. Twenty participants experienced each of these six factors three times, in a counterbalanced order, resulting in 18 repetitions for each participant.

The main study was approved by the Institutional Ethics Committee of IIT Madras (IEC/2022-01/MM/03/11). Twenty healthy adult participants aged 20–35 years took part in the experiment (the participants were distinct to those in the pilot study). The participants had correct or corrected vision and were recruited by advertising around the Department of Applied Mechanics at the Indian Institute of Technology Madras. Most of them were comparable across different parameters, such as prior experience of VR, knowledge of computers and programming, and the time they spent on playing video games (Table 1 and Supplementary Figure S4). Overall, the participants had a high level of prior computer and programming knowledge but were unlikely to have used VR before and were not computer game players.

After each of the 18 trials (2 crowd scenes × 3 haptic conditions × 3 repetitions), the participants were requested to complete the questionnaire shown in Table 2. The responses were provided on a Likert 1–7 scale, where 7 indicated maximum agreement and 1 indicated least agreement. Here, we were interested to examine whether the factors (haptics conditions and crowd scenes) influenced these responses.

The questions in Table 2 are divided into three categories (apart from identification): 1) haptic assessment (touchcomfort and touchreal), 2) negative emotional responses (nervous, judged, and rejected), and 3) positive emotional responses (comfortable, friendly, and pleasant). The box plots for each of these categories are shown in Figure 5.

Figure 5A suggests that identification with the crowd increases with Haptic Stimulus, regardless of whether the crowd is Casual or Aggressive. For touchcomfort, Figure 5A shows that Tactile Stimulus is rated to be greater than Haptic Stimulus, implying that participants are more comfortable with Tactile Stimulus than Haptic Stimulus. Under the Casual condition, there is little difference between Tactile Stimulus and Haptic Stimulus. Under the aggressive condition, touchcomfort is rated higher for the Tactile Stimulus (since this concerns comfort, this is not surprising). However, touchreal is greater for the Haptic Stimulus than Tactile Stimulus under both conditions, with the difference being more pronounced in the Aggressive case; the entire interquartile range (IQR) of Haptic Stimulus is greater than the upper quartile of Tactile Stimulus.

Figure 5B shows the negative emotional responses. In the Casual condition, nervous clearly increases with Haptic Stimulus, and this is more pronounced in the Aggressive condition. For judged, there is a little increase with Haptic Stimulus under the Casual condition, although the maximum median score is still only 4, and there is little difference under the Aggressive condition. For rejected, no effect of any type of haptics is observed under the Casual condition, and there is some hint of an increase under the Aggressive condition, but the scores are low.

Figure 5C suggests that the No Haptic condition has the highest positive emotional responses and Haptic Stimulus has the least. Again, this is not surprising because it is presumably more comfortable to have No Haptic on the arm compared to the other conditions.

The aforementioned descriptive analysis provides some insights into the effects of the touch stimuli, and we discuss the formal statistical inference in this section. Since all the responses are ordinal on a 1–7 scale, we cannot use parametric statistics that assume continuous response variables. Instead, we use ordered logistic regression on each of the nine variables shown in Table 2, which correctly treats the responses as ordinals.

We employ a Bayesian model, which has the advantage of allowing multiple response variables to be examined simultaneously in one overall model, allowing for multiple inferences across various response variables. This also avoids the problem of multiple comparisons, diminishing the validity of significance levels in null hypothesis significance testing. Therefore, a Bayesian logistic regression was performed on all of the nine questionnaire response variables in one overall model that included all nine variables. Moreover, taking into account the fact that each participant had 18 trials, allowing for differences between individuals is essential. The individuals are treated as random effects, and the factors and other variables are treated as fixed effects. For each response, the linear predictor is given in the following form: Individual + Aggressive + Tactile + Haptic + Sex + Aggressive × Tactile + Aggressive × Haptic + Aggressive × Sex + Sex × Tactile + Sex × Haptic .

Here, Aggressive = 1 for the Aggressive Crowd and 0 for the Casual Crowd.

Tactile = 1 for Tactile Stimulus and 0 otherwise.

Haptic = 1 for Haptic Stimulus and 0 otherwise.

Hence, No Haptic corresponds to Tactile = Haptic = 0.

Sex = 1 for female and 0 for male.

The remaining terms are interaction terms.

The major focus of interest is on the interaction terms, Crowd-Type × Tactile, and Crowd-Type × Haptic, and the other terms are only used to account for variations in the sample.

The formal linear predictor for the model is given as u i d i + β 1 A g g r e s s i v e i + β 2 T a c t i l e i + β 3 H a p t i c i + β 4 S e x i + β 5 A g g r e s s i v e i ∙ T a c t i l e i + β 6 A g g r e s s i v e i ∙ H a p t i c i + β 7 A g g r e s s i v e i ∙ S e x i + β 8 S e x i ∙ T a c t i l e i + β 9 S e x i ∙ H a p t i c i i = 1,2 , … , N = 360 . Here, i d i is the identifier (1, 2…,20) of the participant in the ith trial (1, 2…, 360) (20 subjects × 18 trials) and therefore the same within each participant. Hence, u i d i is the effect on the ith participant, which is a different random variable for each participant.

The β j values are different for each response variable, replaced by the coefficients indicated in the first column of Table 2 for the nine different response variables. The main focus of interest is on β 5 and β 6 .

The prior distribution for each coefficient was taken to be normal (mean = 0, SD = 10), hence, the prior 95% credible intervals were −20 to 20. The logistic model needs cut points, and the prior distributions were also assigned normal values (mean = 0; SD = 10). According to Gelman et al. (2006) and Lemoine and Lemoine (2019), these prior distributions are weakly informative or appropriate probability distributions with high variances that reflect substantial uncertainty.

The analysis was carried out using Stan ⁵ (Stan Development Team, 2011–2019) through the R interface ⁶ . A total of 2,000 iterations were used over four cores. All models converged satisfactorily.

Tables 3–5 show the resulting posterior distributions of the parameters of the model. If a β j value has a high probability of being positive, then the corresponding factor positively influences the response; if it is negative, then it negatively influences the response; and if it is not clearly different from 0, then there is little evidence of an effect. Here, both the 95% credible interval and the probability of being positive (or negative) should be considered. For example, if the credible interval does not include 0 or if 0 is at the extreme of the interval, then this indicates an effect. We consider each variable in turn.

identification : The interaction term between Aggressive Crowd and Haptic Stimulus has a high probability of being positive (0.996); the mean of the distribution is positive (1.26), and the 95% credible interval does not include 0 (Table 3). Therefore, the evidence supports the finding that identification is positively influenced for Aggressive Crowd with Haptic Stimulus, as shown in Figure 5A.

touchcomfort : Only the main effects of Aggressive Crowd with Tactile Stimulus indicate a positive effect. It is same for the Haptic Stimulus (Table 3).

touchreal : Both Tactile Stimulus and Haptic Stimulus have a positive effect (Table 3).

comfortable : The interaction term for Aggressive Crowd with Tactile Stimulus does not contribute to the effect (the probability of being positive is 0.516) (Table 4). Then, we focus on the main effects. The main effect for Aggressive Crowd is negative (probability = 1–0.001 = 0.999), and the main effect for Tactile Stimulus is negative (probability = 1.000). The Aggressive × Haptic interaction term is positive, but the effect size (mean = 0.98) is outweighed by the main effects of Aggressive (−1.14) and Haptic (−2.80). Hence, according to Figure 5C, comfortable reduces with any type of stimulus.

friendly : Any stimulus is negatively associated with this response; there are no other effects observed (Table 4).

pleasant : Although the interaction terms are positive, these are outweighed by the negative main effects (Table 4). Thus, any type of stimulus reduces the feeling of pleasantness as participants feel unpleasantness with the crowd touch or collision.

nervous : This response (Table 5) increases with Aggressive Crowd for both Tactile Stimulus and Haptic Stimulus, with almost no difference between these two (the credible intervals are almost the same), as shown in Figure 5B.

judged : Aggressive Crowd with Tactile Stimulus shows a negative interaction term, but this is outweighed by the positive main effects. Similarly, for Aggressive Crowd with Haptic Stimulus, this is weaker than the Tactile Stimulus case (Table 5).

rejected : The interaction terms and main effects almost cancel each other out, indicating no particular effect (Table 5).

The main results from the analysis can be summarized as follows:

1. Haptic Stimulus with the Aggressive Crowd has the greatest positive influence on identification.

Overall, the results indicate that there are clear effects of the type of haptics (No Haptic, Tactile Stimulus, and Haptic Stimulus) and sensible interactions with the type of crowd (visual stimuli—Aggressive Crowd and Casual Crowd).

A major limitation of the developed collision haptic device is its inability to produce successive actuation within a 7-s timeframe. This is due to the minimum time required to reach the maximum angular momentum, which is bottle-necked by the rise time of the flywheel (that is, 7 s). However, this limitation does not affect our study, as the objective was to generate momentary collision, specifically during shoulder collisions. Despite variations in the crowd density and rates of passing-by, we were able to deliver and validate four to five actuations per crowd at an approximate interval of 7 s. This was necessary to achieve our desired impulsive force output of 25 N within a 200-ms window, accurately simulating crowd collisions for the participants. Furthermore, being a wearable haptic device, one of its main drawbacks is that both undesired action forces and desired reaction forces are delivered to the participant’s body sites, resulting in sensations felt by the participants themselves.

It is worth noting that in our study, we only considered collisions occurring at the shoulder, while real-life crowd navigation scenarios may involve collisions with other body parts. However, our haptic devices are designed to be attached to various other possible parts of the body to accommodate different scenarios, although further studies are needed to test participants’ reactions.

In our analysis, we relied on subjective questionnaires, and it is important to acknowledge the limitations of subjective analyses, which may include human errors, biased decisions, and variations in haptic perception capabilities among participants and other factors. In the future, more objective measures based on vital sign assessment, such as heart rate variability, breath rate variability (Soni and Muniyandi, 2019), electro-dermal activity (Amba and Muniyandi, 2017), and eye tracking, are needed to be included to offer better insights into emotional responses in virtual environments through haptics.

Additionally, gender differences should be explored further, as there were only six women out of 20 participants in the study. While both men and women may experience similar levels of sensory pleasantness of touch, their perceptions and attitudes toward touch differ at a higher social level. For example, research has shown that women tend to place more value on touch and express higher levels of comfort, even in interactions with less familiar (or unknown) individuals. Additionally, women tend to feel more at ease with touch directed specifically toward the forearm (Schirmer et al., 2022).

In our study, we employed a 360-degree video-based VR environment instead of 3D model-based simulated virtual environments. However, for future iterations, more immersive model-based virtual environments that incorporate realistic gait motion and facial animation of the virtual crowd would be worth exploring. Additionally, investigating the implementation of multiple haptic cues simultaneously across different parts of the body could provide valuable insights into the sense of presence and participants’ emotional responses. Presence and co-presence are not considered in this study. Tactile and haptic feedback and their impact on the sense of co-presence have been studied previously in interpersonal communication and collaboration in VR settings (Biocca and Harms, 2002; Della Longa et al., 2022). For example, Ahmed et al. (2016) showed that force-feedback actuators are perceived as being more natural and lead to better emotional interdependence and a stronger sensation of co-presence than vibrotactile touch. This study can be extended in the future to address the relationship between the intensity of the haptic devices and co-presence.