Perceptual Haptic Spectrum Modeling for Fine Texture Rendering on Virtual Object Surfaces in Virtual Reality

Abstract

To enhance immersion in virtual reality (VR) environments and improve the fidelity of virtual tactile interaction, this study proposes a perceptually grounded haptic-rendering framework for fine surface-texture simulation. The framework is centred on a Perceptual Haptic Spectrum Model (PHSM), which maps virtual surface attributes, including hardness, elasticity, roughness, friction, and microtexture periodicity, to multi-band tactile targets in perceptual frequency space. A Just Noticeable Difference (JND)-inspired parameterisation strategy is used as a design guideline to avoid imperceptible or redundant actuation, while region-specific response functions adapt the output to the fingertip centre, finger pad, and lateral edge. To improve reproducibility, the revised manuscript now specifies the flexible thin-film force/strain-sensor cell, array quantity, 320 Hz per-cell acquisition setting, signal-conditioning pipeline, contact-state classification rules, delay budget, and dual-actuation scheduling logic. The sensing design is based on a commercial flexible piezoresistive force-sensor cell with microsecond-level response time and a 12-bit ADC acquisition chain that provides a sufficient aggregate sampling margin for a 7–21 cell array. Manufacturer-supported sensor performance and prototype-level acceptance criteria are reported for response time, linearity, repeatability, hysteresis, drift, SNR, contact-state detection, latency, and durability. The system remains a proof-of-concept platform rather than a completed large-scale psychophysical validation. Within these boundaries, the results show coherent integration of perceptual modelling, multi-rate sensing, state monitoring, predictive feedforward control, and coordinated haptic actuation for fine VR texture rendering.

1. Introduction

Recent advances in haptic gloves have enabled meaningful progress in force-feedback actuation, electrical stimulation, vibrotactile output, and pneumatic feedback [1,2]. Nevertheless, reproducing fine tactile qualities in dynamic VR interaction remains challenging. Existing interfaces often struggle to combine spatially localised feedback, low-latency state recognition, and perceptually meaningful signal encoding; as a result, tactile output may feel delayed, spatially diffuse, or weakly related to the virtual material being touched.

A first limitation concerns spatial resolution. Many glove or sleeve interfaces rely on sparse actuator layouts that cannot produce localised, region-specific responses consistent with the heterogeneous physiology of the fingertip. Touching an edge with the fingertip centre, sliding over a rough boundary with the lateral finger surface, and stroking with the finger pad should evoke different tactile patterns, but homogeneous actuator outputs often blur these distinctions [3,4].

A second limitation concerns neural and perceptual coding. Human tactile perception involves coordinated mechanoreceptive channels with distinct spatial and temporal sensitivities [5,6,7]. Coarse surface features are often associated with broader spatial deformation, whereas fine textures can elicit skin vibrations whose temporal patterns contribute to perceived roughness [6]. A haptic-rendering model therefore needs to organise output not only by actuator type but also by the perceptual role of frequency, contact region, and motion state.

A third limitation concerns dynamic contact recognition. Many systems trigger feedback only after sensor signals exceed fixed thresholds. Although such reactive control is sufficient for basic contact notification, it is less effective for light touch, stroking, pressing, and rapid slip transitions. Because visual-haptic asynchrony can reduce perceived realism, the sensing stream, classification logic, and actuation scheduler must be designed as one timing-sensitive pipeline rather than as independent modules [8].

Commercial systems such as bHaptics and SenseGlove demonstrate the feasibility and market relevance of wearable haptics, including vibrotactile and force-feedback products [9,10]. Recent deep learning approaches such as TactGAN and GAN-based image-to-friction generation further show that tactile signals can be generated from learned or cross-modal representations [11,12]. However, these advances do not by themselves solve the joint problem of fingertip-region sensing, contact-state estimation, perceptually organised multi-band rendering, and low-latency dual-actuation coordination.

Motivated by these challenges, this paper presents a perceptually grounded framework for fine texture rendering on virtual object surfaces. The main contributions are fourfold. First, a PHSM is proposed to map physical surface properties onto multi-band perceptual targets. Second, region-specific response functions adapt tactile rendering to anatomical sub-regions of the fingertip [13]. Third, a contact-aware control strategy combines flexible thin-film sensing, noise-aware state classification, rule-based channel allocation, and short-horizon predictive feedforward control. Fourth, a dual-actuation prototype coordinates glove-based force support with local high-frequency texture augmentation. The revised manuscript explicitly treats the work as a prototype framework and scenario-based demonstration; statistically powered psychophysical validation [14] is defined as future work rather than claimed as a completed outcome.

2. Materials and Methods

2.1. Perceptual Haptic Spectrum Model

The proposed framework is grounded in human tactile-perceptual mechanisms and in the physical properties governing surface–finger interaction [15]. Virtual surface attributes, including hardness, elasticity, roughness, friction coefficient, viscoelasticity, and microtexture periodicity, are treated as the physical input space [16]. These attributes are transformed into a structured perceptual representation, namely the PHSM, in which tactile events are described by temporal, spatial, and spectral components.

Within the PHSM, each contact event is represented not as a single vibration or force value but as a composite tactile signal distributed across perceptual frequency bands. In the present prototype, three practical rendering bands are used: 0–20 Hz for macroscopic force cues such as pressing resistance and compliance-related deformation; 20–200 Hz for texture-related microvibrations and frictional variation; and 200–400 Hz for fine microtexture and sliding-induced tremor cues. These boundaries are derived from the general frequency-dependent behaviour of cutaneous mechanoreception and from the bandwidth of the selected sensing and actuation hardware [17]. They are not claimed to be universally optimal; rather, they provide a transparent and reproducible partition for the current prototype.

By computing the spectral position and amplitude of each contact event within the PHSM, a multilayered haptic-feedback target set is generated. These targets are mapped to physically actuated components in the haptic glove and finger sleeve, allowing low-frequency force support and high-frequency texture cues to be coordinated. This process establishes an end-to-end mapping from perceptual intention to physical actuation and shifts the design philosophy from “how available actuators are driven” to “what perceptual response should be evoked”. Figure 1 presents the perceptual-to-actuation workflow.

2.2. Perceptual Spectrum Parameterisation and Calibration Basis

To operationalise the PHSM, the physical attributes of each virtual contact event are converted into spectral parameters describing amplitude, dominant frequency, bandwidth, and temporal envelope. Gross compliance and normal resistance are mapped mainly to the low-frequency band, whereas fine roughness, friction modulation, and boundary-induced oscillation are mapped to the mid- and high-frequency bands. This conversion is deliberately conservative: it favours perceptual consistency and temporal stability over aggressive high-gain actuation.

A JND-inspired quantisation strategy is used to prevent imperceptible or redundant output. In this manuscript, the JND principle is used as a perceptual design guideline rather than as a completed user-specific psychophysical calibration [13,14,15]. Each frequency band is assigned a sensitivity interval intended to keep tactile variations within perceptually meaningful ranges while avoiding unnecessary actuation. For a new user, calibration would involve three steps: (i) estimating baseline detection thresholds for low-, mid-, and high-frequency stimulation; (ii) scaling regional intensity and frequency parameters around the individual threshold; and (iii) checking the tuned parameters during short pressing, stroking, and slip sequences.

The parameters alpha_i, lambda_i, beta_i, phi_i, and gamma_i(t) (see

Table 1. Parameter-selection basis and sensitivity interpretation.

Parameter	Prototype Range	Selection Basis	Observed Sensitivity in Local Sweep
alpha_i	0.2–1.0	Regional intensity scaling adjusted around JND-inspired amplitude intervals	±10% changes intensity without changing contact state; ±20% may alter salience
lambda_i	1–10	Spatial concentration parameter linked to sensor pitch and sub-region size	High values sharpen R1/R3 localisation but may reduce smoothness
beta_i	20–400 Hz	Mapped to low/mid/high perceptual bands and actuator bandwidth	Most perceptible in texture roughness; robust state labels within ±10%
phi_i	0-pi	Phase offset used to sequence multi-region slip cues	Affects lateral motion continuity during slip rendering
gamma_i(t)	0.0–2.0	Dynamic gain modulated by contact-state classifier	Dominant factor in transitions; cross-fading mitigates abrupt changes

) are therefore representative prototype settings rather than universal constants. Their influence was assessed through a local sensitivity sweep in which each parameter was perturbed by ±10% and ±20% while all other parameters were held fixed. The qualitative contact state remained stable under ±10% perturbation, whereas larger perturbations mainly changed perceived intensity and slip sharpness. This analysis defines a preliminary robustness boundary for the current configuration; it does not replace personalised psychophysical optimisation.

2.3. Flexible Strain-Sensor Layout, Sampling, and Noise Processing

A flexible thin-film force/strain-sensor array (see

Table 2. Prototype flexible strain-sensor and acquisition parameters.

Item	Prototype Setting	Role in Contact Detection
Array layout	7–21 flexible thin-film sensing cells; the demonstrated index-finger layout uses 2 + 3 + 2 cells	Estimates contact centroid, active area, and regional pressure distribution while allowing denser sleeve coverage when required
Single sensing cell	Tekscan FlexiForce A101 (Tekscan, Inc., Norwood, MA, USA)-equivalent miniature piezoresistive thin-film sensor; 3.8 mm sensing-area diameter; thickness 0.203 mm; response time < 5 microseconds	Provides a commercially available sensing unit whose mechanical/electrical response is far faster than the 320 Hz acquisition setting
Covered regions	R1 fingertip centre; R2 finger pad; R3 lateral edge	Supports region-specific response functions and channel allocation
Nominal pitch	1.0–1.2 cm in the distal-to-proximal direction	Defines spatial resolution for centroid and area estimates
Per-cell sampling rate	320 Hz per sensing cell; 3.125 ms frame period; 2.24–6.72 kS/s aggregate rate for 7–21 cells	Provides temporal granularity for slip detection and remains below the capacity of the selected ADC readout
Acquisition resolution/readout	12-bit MCP3208-class SPI ADC, up to 100 kS/s at 5 V; three 8-channel ADCs can cover a 21-cell sleeve	Provides sufficient aggregate throughput and resolution for the pressure-envelope and derivative features
Noise processing	Per-channel baseline subtraction; 3-sample median filter; fourth-order Butterworth low-pass envelope filter; derivative smoothing for slip	Suppresses impulsive noise and reduces false slip triggers
Interference handling	Z-score normalisation, shielded/short leads where possible, ground-referenced readout, and cross-channel consistency checks	Improves robustness to drift, cable motion, and isolated sensor spikes
Sensing-actuation boundary	The flexible cells are used only for sensing; 200–400 Hz texture cues are generated by separate sleeve actuators	Avoids confusing the 320 Hz sensing stream with the high-frequency tactile actuation signal

) is integrated into the index-finger sleeve to detect contact location, pressure magnitude, contact area, and temporal change. The sensing layer is functionally separated from the local tactile-actuation layer: the sensors measure pressure and deformation for classification, whereas independent vibration-based or piezoelectric elements generate texture output. To ensure that the sensing hardware can support a 320 Hz acquisition stream, each cell is specified as a commercial flexible piezoresistive force-sensor unit, represented by the Tekscan FlexiForce A101 [18] or an equivalent miniature thin-film cell. The A101 is Tekscan’s smallest standard piezoresistive force sensor and has a 3.8 mm sensing-area diameter, 0.203 mm thickness, 15.6 mm body length, 7.6 mm body width, a response time below 5 microseconds, linearity error below ±3% full scale, repeatability below ±2.5%, hysteresis below 4.5%, drift below 5% per logarithmic time scale, and durability of at least 3 million actuations [18].

The sleeve can be configured with 7–21 sensing cells depending on coverage requirements. The present index-finger demonstration uses a 2 + 3 + 2 layout (see Figure 2), while the same acquisition strategy scales to denser 15 or 21 cell layouts. The nominal sensor pitch is approximately 1.0–1.2 cm in the distal-to-proximal direction, and the spatial reference origin is placed at the distal fingertip. Each cell is sampled at 320 Hz, corresponding to a 3.125 ms frame period. For the maximum 21-cell configuration, the aggregate sampling requirement is 6.72 kS/s, which is substantially below the 100 kS/s maximum conversion rate of an MCP3208-class 12-bit ADC at 5 V [19]. Figure 2 has been annotated with the coordinate origin, a 1 mm scale bar, and dashed partition boundaries for R1, R2, and R3.

Before contact-state classification, the sensor stream is processed using a concise noise-reduction sequence. Each channel is corrected by subtracting the no-contact baseline, followed by a three-sample median filter to suppress impulsive spikes. A low-pass pressure envelope is used for contact-area and pressure-stability judgement, and a smoothed first-derivative trace is retained to support slip-transition recognition. This paragraph describes only the signal-conditioning practice required for stable use of the selected sensor array and bases on the engineering characterisation (see

Table 3. Preliminary engineering characterisation of sensing and contact-state detection.

Metric	Value Used in Revised Prototype Specification	Basis and Interpretation
Sensor response time	<5 microseconds for the A101-equivalent cell	Manufacturer-supported value for the A101 class; comfortably faster than a 320 Hz sampling period
Linearity error	<±3% full scale from 0 to 50% load	Used as the single-cell force-envelope accuracy boundary
Repeatability	<±2.5% under conditioned loading	Supports repeatable pressure-envelope estimation after calibration
Hysteresis	<4.5% full scale	Defines expected force-history error for pressing/releasing sequences
Drift	<5% per logarithmic time scale under constant load	Motivates baseline subtraction and periodic recalibration
Durability	≥3 million actuations under representative perpendicular loading	Supports short-term reliability of repeated fingertip contacts
Acquisition timing margin	21 cells × 320 Hz = 6.72 kS/s, compared with 100 kS/s ADC capability	Shows that the 7–21 cell array can be sampled at 320 Hz per cell with large throughput margin
Raw-to-filtered SNR	Prototype acceptance target: >24 dB raw and >30 dB after filtering	System-level readout/noise-processing criterion; not a standalone vendor sensor specification
Contact-state detection accuracy	Prototype acceptance target: ≥90% for scripted concentrated/distributed/slip sequences after baseline calibration	Engineering target for contact-state logic; not a psychophysical user study result
End-to-end command delay	Approximately 12–15 ms excluding mechanical settling	Compatible with short-horizon feedforward scheduling and 320 Hz sensing

).

2.4. Region-Specific Response Functions

Human tactile sensitivity is strongly heterogeneous across the finger surface. The fingertip centre, finger pad, and lateral edge differ in skin thickness, deformation behaviour, receptor density, and sensitivity to fine spatial and temporal cues. The proposed framework therefore subdivides the index-finger contact surface into three perceptual sub-regions: R1, the fingertip centre; R2, the main finger pad; and R3, the lateral edge used during sliding and boundary confirmation. The sensor array estimates which region dominates the current contact, while the actuator layer renders the corresponding feedback pattern.

Each sub-region is assigned an independent response profile controlling maximum feedback intensity, spatial attenuation, dominant frequency, phase offset, and dynamic gain. The original region-based response function is retained as the haptic-output model, as defined below:

Ψ(x,t) = ∑_i=1ⁿ [α_i · (1 − e^(−λ_i · |x − μ_i|)) · cos(2π · β_i · t + φ_i) · γ_i(t)]

(1)

where Ψ(x,t) denotes the integrated feedback intensity to be output by the system at spatial coordinate x and time t. The index i represents the sub-perceptual region, with n = 3 in the present prototype. The parameter α_i is the static feedback-intensity factor for region i; λ_i is the spatial attenuation parameter centred on the region; μ_i is the central coordinate of region i; β_i is the feedback-frequency factor in Hz; φ_i is the initial phase used for synchronisation or phase offset; and γ_i(t) is the time-varying gain term associated with contact behaviour. For example, slip contact can assign a higher dynamic gain to the lateral-edge region, whereas distributed contact can reduce local high-frequency emphasis.

2.5. Contact-State Classification and Predictive Feedforward Control

Three contact states are considered in the present prototype: concentrated contact, distributed contact, and slip contact. Concentrated contact is characterised by a small active area with a high local pressure peak; distributed contact is characterised by a broader and more stable pressure distribution; and slip contact is characterised by rapid centroid displacement and short pressure pulses associated with sliding or boundary traversal. These states are intentionally simple so that the control logic remains transparent and reproducible.

The thresholds of 15 cm/s and 100 ms are heuristic prototype values selected from scripted exploratory motions and are now explicitly labelled as such. They should be recalibrated for different sensor pitches, sleeve materials, or user populations. At a 320 Hz per-cell sampling rate, the sensing frame is 3.125 ms, which provides more than 30 samples across a 100 ms pulse window and sufficient temporal granularity for the stated slip criterion. A threshold sensitivity sweep showed that slip labels were stable for velocity thresholds from 12 cm/s to 18 cm/s when pulse duration remained below 100 ms; outside this range, false positives increased during fast but stable stroking.

The control logic uses state estimates to allocate haptic channels according to task relevance. Concentrated contact prioritises local high-frequency texture rendering at the dominant sub-region; distributed contact shifts emphasis toward broader low-frequency support; and slip contact reduces normal support while increasing phase-modulated local texture cues. Conflict resolution follows a fixed priority order: safety and stability constraints, slip cues, concentrated local texture, and distributed force support.

The short-horizon predictive feedforward mechanism (see Appendix A) is implemented as rule-based kinematic estimation using recent motion trajectory, contact-centroid movement, and acceleration to anticipate the next contact state within a 5–10 ms horizon. The predicted state pre-arms the relevant actuator channel, but the final command is gated by the current measured state to reduce erroneous pre-activation. A learning-based predictor is discussed as future work rather than claimed as a validated module in the present prototype.

The delay-budget components are shown in Figure 3. Under the 320 Hz per-cell sensing configuration, the expected tactile command delay is approximately 12–15 ms before mechanical settling. This estimate includes the sensing-frame interval, filtering, rule-based classification, predictive scheduling, and communication to the drive layer. It is reported as an engineering timing budget rather than as a new control equation, and it identifies the most important bottlenecks for future hardware optimisation.

2.6. Dual-Actuation Hardware Architecture

To address the bandwidth limitations of a single actuator type, the system adopts a dual-actuation cooperative architecture (see

Table 4. Functional roles of the main sensing and actuation components.

Component	Physical Role	Signal Domain	Main Function in the Framework
HaptX Gloves G1	Primary actuation	Low-frequency force support	Provides gross pressure, resistance, and compliance-related cues
Flexible strain-sensor array	Sensing	Pressure/deformation measurement	Detects contact location, area, pressure distribution, and temporal change
Local sleeve actuators	Secondary actuation	Mid-/high-frequency texture output	Deliver local roughness, boundary, and slip-related tactile cues
Motion-capture/VR tracking	Kinematic sensing	Pose, velocity, acceleration	Supports short-horizon predictive feedforward control
Control scheduler	Resource coordination	State-dependent allocation	Resolves timing conflicts and assigns actuator dominance

). The primary actuation layer is the glove-based force-feedback unit, represented in this prototype by the HaptX Gloves G1 (HaptX, Inc., Redmond, WA, USA). This layer provides macroscopic, low-frequency cues such as support, resistance, and compliance-related deformation. The secondary actuation layer is embedded in the finger sleeve and consists of local texture actuators placed near the sensing region. These actuators provide higher-frequency cues associated with fine roughness, granularity, edge transitions, and slip-related pulses; they are separate from the flexible sensing cells described in Section 2.3.

The two actuator layers are scheduled as a resource-coordination problem. Broad pressing and stable exploration favour the primary force-feedback channel, whereas fast local sliding and boundary confirmation favour the secondary texture channel. When both layers are active, amplitudes are cross-faded over 20 ms to avoid abrupt transitions. From a system perspective, this coordination is aligned with recent work emphasising robust collaborative allocation, resilience, and long-term availability in engineered networks [20].

3. Results: Prototype Demonstration in a Virtual Fabric Task

This section reports a proof-of-concept operating scenario (see Figure 4) for the proposed system. We intend to illustrate how the framework behaves during representative texture exploration in VR. It should therefore be read as a prototype demonstration and preliminary engineering characterisation rather than as a completed controlled user study with inferential statistical analysis.

In the demonstration scenario, the user explores a virtual fabric sample in VR and attempts to identify tactile characteristics such as roughness, boundary variation, and brushing resistance. The right index finger is used as the main exploratory finger. Three typical actions are considered: pressing with the fingertip centre, stroking with the finger pad, and rapid lateral sliding with the finger edge.

3.1. Prototype Platform and Demonstration Conditions

The haptic glove serves as the primary actuation layer and provides stable macroscopic force cues during contact with the virtual fabric. The finger sleeve hosts both the flexible thin-film sensing array and the local tactile actuators. In the prototype, each sensing cell is sampled at 320 Hz to estimate contact pressure, active area, and centroid movement, while the local actuators deliver higher-frequency texture signals at the index finger. The sensor stream therefore supports state detection, whereas the actuator stream generates the 200–400 Hz tactile texture cues.

The index finger is pre-segmented into three perceptual sub-regions: R1, the fingertip centre for fine tactile inspection; R2, the main finger pad for broad-area stroking; and R3, the lateral edge for sliding-based boundary confirmation. Representative parameter ranges are alpha_i in [0.2, 1.0] for intensity scaling, beta_i in [20, 400] Hz for frequency allocation, lambda_i in [1, 10] for spatial concentration, phi_i in [0, pi] for phase control, and gamma_i(t) in [0.0, 2.0] for dynamic gain modulation. These values are used for demonstration and are not presented as universal settings.

3.2. Demonstration of Concentrated Contact

A representative concentrated-contact case occurs when the user presses the virtual fabric with the central fingertip. The detected pressure peak is located near x = mu_1 = 3.5 cm, and the measured force is approximately 0.65 N at t = 1.2 s. A representative parameter set is then assigned as follows: R1 = {alpha_1 = 0.9, lambda_1 = 7, mu_1 = 3.5 cm, beta_1 = 320 Hz, phi_1 = 0.2 pi}, gamma_1(1.2 s) = 1.8; R2 = {alpha_2 = 0.5, lambda_2 = 4, mu_2 = 5.0 cm, beta_2 = 160 Hz, phi_2 = 0.4 pi}, gamma_2(1.2 s) = 0.7; and R3 = {alpha_3 = 0.3, lambda_3 = 6, mu_3 = 6.5 cm, beta_3 = 260 Hz, phi_3 = 0.6 pi}, gamma_3(1.2 s) = 0.4.

Under these conditions, the controller places primary emphasis on R1. The local texture actuator near the fingertip is driven at 320 Hz to represent fine roughness cues, while the glove-based force-feedback channel provides stable resistive support. The outputs of R2 and R3 are reduced toward their minimum thresholds to avoid unnecessary actuation. This mode is intended to increase local texture salience during high-acuity fingertip inspection.

3.3. Demonstration of Distributed Contact

When the user transitions from fingertip pressing to broader stroking over the fabric, the contact centroid shifts toward mu_2 = 5.0 cm and the activated area expands. In the representative scenario, the activated pressure area grows from approximately 0.5 cm² to 1.2 cm², the number of engaged sensor elements increases from 3 to 7, and the mean pressure decreases from 0.65 N to 0.48 N while remaining relatively stable for more than 250 ms.

This state is classified as distributed contact. The control logic increases gamma_2(t) to 1.5 and reduces the effective texture emphasis by lowering alpha_2 and beta_2, with beta_2 reduced from 160 Hz to 120 Hz in the representative example. The primary force-support channel remains active so that the user perceives a broader, smoother brushing sensation rather than a sharply localised roughness cue. Actuation is sequenced so that low-frequency support develops first, followed by lower-amplitude texture modulation.

3.4. Demonstration of Slip Contact

A representative slip-contact case occurs when the user rapidly sweeps the lateral finger edge across a boundary of the virtual fabric to confirm edge precision. In the described demonstration, the pressure centroid shifts from approximately mu = 6.5 cm to mu = 3.9 cm within 0.12 s, corresponding to an average displacement velocity of about 22 cm/s. This motion is accompanied by short local pressure pulses and an oblique sliding trajectory across the sensor array.

The control system classifies this state as slip contact and shifts priority toward R3. In the representative parameter setting, gamma_3(t) is increased to 1.7 and beta_3 is set to 280 Hz. The local texture channel is phase-modulated with a delay of 0.3 pi to represent lateral movement across boundary features, while the normal-support channel is reduced to decrease apparent sliding resistance. This state is intended to enhance the perceptibility of boundary transitions and rapid local motion.

3.5. Summary of Demonstration Outcomes

Across the three representative interaction states, the prototype demonstrates a coherent mapping from sensed contact conditions to region-specific haptic output. Concentrated contact leads to high-acuity local texture emphasis, distributed contact leads to broader and smoother force-supported rendering, and slip contact leads to phase-modulated local texture signalling with reduced normal support. These outcomes are reported as representative system behaviours rather than statistically validated perceptual results.

4. Discussion

4.1. Perception-First Haptic Rendering

The present study proposed a perceptually grounded haptic-rendering framework for VR texture interaction, centred on the PHSM. In contrast to conventional actuator-driven strategies, the proposed approach begins from the perceptual endpoint and reconstructs the corresponding physical stimulation requirements through reverse encoding. This design logic is important because the primary challenge in VR haptics is not merely the generation of force or vibration but the generation of tactile signals that are meaningful to human perception.

4.2. Region-Specific Sensing and Actuation

The region-specific response mechanism strengthens the physiological plausibility of the framework. By dividing the fingertip into perceptual sub-regions and assigning each region distinct gain, attenuation, frequency, and phase parameters, the proposed system adapts tactile output to local sensory characteristics. The revised sensor layout makes this mechanism more concrete: a 7–21 cell thin-film array can localise the dominant contact region, while the demonstration uses a 2 + 3 + 2 configuration to represent the fingertip centre, finger pad, and lateral edge. This design remains simpler than the full spatial complexity of the human fingertip, but it provides a reproducible engineering bridge between contact sensing and region-specific rendering.

4.3. Parameter Robustness and Heuristic Boundaries

The revised manuscript clarifies that the three frequency bands, regional gains, JND intervals, and contact-state thresholds are prototype settings, not universal optima. Sensitivity analysis suggests that the contact-state logic is robust to moderate parameter perturbations, but perceived salience and slip sharpness still depend on user-specific thresholds. The selected 320 Hz per-cell sampling rate is an engineering compromise: it is far below the response capability of the selected 3.8 mm thin-film cell and the aggregate ADC throughput yet fast enough to provide multiple samples within the 100 ms slip window.

4.4. Predictive Feedforward and Multi-Rate State Monitoring

The predictive feedforward mechanism addresses the temporal-lag limitation of VR haptics. In the current implementation (see Appendix A), prediction is a rule-based 5–10 ms kinematic estimate rather than an AI predictor. The design is related to broader multi-rate fusion and state-estimation methods, in which noisy or asynchronous measurements are combined to improve stability and reliability [21]. Future work should benchmark fractional-order Kalman fusion or lightweight neural prediction against the present rule-based module under noisy motion and rapid task switching.

4.5. Dual-Drive Collaboration and Reliability

The dual-actuation cooperative architecture is a pragmatic system contribution. The primary glove-based channel reproduces stable macroscopic force sensations, whereas the secondary finger-sleeve channel provides rapid local texture augmentation. This separation of roles helps avoid forcing a single actuator type to cover incompatible bandwidth demands. The resource-coordination perspective is consistent with engineering work on robust allocation, resilience, and lifecycle availability, although the present VR haptic prototype requires further long-duration reliability testing.

4.6. Validation Limitations

The prototype demonstration illustrates internal consistency between perceptual modelling, sensing, state classification, prediction, and actuation. However, it does not establish superiority over threshold-triggered or single-mode rendering baselines in user-level outcomes. Objective indicators such as texture discrimination accuracy and reaction time, and subjective indicators such as realism, presence, immersion, and NASA-TLX workload, remain to be measured in controlled user studies. The contribution statement has therefore been softened to avoid implying completed psychophysical validation.

5. Conclusions

This paper presented a revised and more clearly delimited description of a perceptually grounded haptic-rendering framework for fine texture interaction in VR. The PHSM maps virtual surface properties to multi-band perceptual targets, while region-specific response functions, a 320 Hz flexible thin-film sensing array, contact-aware channel allocation, short-horizon predictive control, and dual-actuation coordination together support context-sensitive tactile rendering.

The applicable conditions of the current model are now explicitly defined. The framework is intended for fingertip-level exploration of fine virtual textures under moderate contact forces, a 7–21 cell flexible sensing sleeve, and a dual-drive architecture combining low-frequency force support with local mid-/high-frequency texture cues. The present demonstration uses a 2 + 3 + 2 index-finger layout, but the hardware specification supports denser layouts when additional spatial coverage is required. The framework has not yet been validated for whole-hand manipulation, bimanual interaction, high-force grasping, wet or highly deformable materials, or users whose tactile thresholds differ substantially from the representative calibration range.

The main hardware limitations are the finite spatial resolution of the flexible sensor array, possible drift under repeated bending, actuator bandwidth mismatch, and mechanical settling that is not fully captured by the 12–15 ms electronic control delay. Individual differences in skin thickness, temperature, fingertip size, and tactile sensitivity may introduce gain and threshold errors; therefore, user-specific calibration is required before perceptual claims can be generalised.

Future work is organised into four technical routes. First, controlled psychophysical experiments with at least 15 participants should compare PHSM rendering against threshold-triggered and single-mode baselines, reporting texture discrimination accuracy, reaction time, realism, presence, immersion, and NASA-TLX workload. Second, AI prediction should be evaluated using lightweight temporal neural networks and compared with rule-based feedforward in terms of latency, false pre-actuation rate, and contact-state prediction F1 score. Third, the sensing and actuation layout should be extended from a single index finger to multi-finger and whole-hand interaction, with evaluation of inter-finger synchrony and grasp stability. Fourth, lightweight deployment should be investigated on embedded controllers, using memory footprint, update rate, energy consumption, temperature rise, and long-duration drift as engineering indicators.

Overall, the revised framework suggests that higher-fidelity virtual tactile rendering may be achieved by organising haptic control around perceptual structure rather than actuator behaviour alone. The present study provides a transparent prototype foundation, but quantitative user validation and broader hardware reliability testing remain necessary before strong claims of perceptual superiority can be made.