WaveWalkerClone: VR Sensing & Pilot-Wave Simulation

• WaveWalkerClone is a dual system integrating a camera-free radar-based VR obstacle sensing platform with a computational simulation of bouncing droplets driven by pilot-wave hydrodynamics.
• The VR module utilizes mmWave radar, GPS/IMU sensor fusion, and edge computing to achieve centimeter-level obstacle detection and real-time environmental mapping.
• The pilot-wave simulation applies the damped Mathieu equation and impulse-driven wave dynamics to recreate non-Markovian behavior and quantum-like phenomena.

WaveWalkerClone refers to two distinct technical systems in contemporary research: (1) a camera-free, radar-based obstacle sensing and visualization system for outdoor virtual reality (VR) environments; and (2) a computational reproduction of the hydrodynamic “walker” system, where bouncing fluid droplets self-propel through feedback with sub-threshold Faraday waves. Both implementations exemplify state-of-the-art techniques for detecting, modeling, and interactively visualizing dynamic environments—one in embodied computing, the other in macroscopic pilot-wave hydrodynamics. This article systematically details both interpretations and their core methodologies.

1. Radar-Based Outdoor VR: System Architecture and Sensing Platform

WaveWalkerClone, as realized in outdoor VR research, constitutes a multimodal real-time sensing pipeline built to maintain user safety and preserve environmental awareness during fully immersive VR experiences without cameras or explicit environment mapping (Nargund et al., 1 Feb 2026).

At its core, the system integrates:

• Millimeter-Wave (mmWave) Radar: Texas Instruments IWR6843AOP FMCW radar, operating at $f_c \approx 60\,\text{GHz}$, with $B \approx 4$ GHz bandwidth yielding range resolution $\Delta R = c/(2B) \approx 3.75$ cm. The field of view spans $\pm70^\circ$ azimuth and $\pm15^\circ$ elevation, with a 10 Hz obstacle detection update rate and a region of interest (ROI) of $\pm3$ m lateral by 8 m forward.
• GPS/IMU Fusion: A Google Pixel 8 (L1/L5 GNSS, 1–2 m accuracy) alongside a 3-axis MEMS accelerometer and gyroscope. Sensor fusion is performed via an Error-State Kalman Filter (ESKF) on an NVIDIA Jetson Nano, with state $$\mathbf{x} = [\mathbf{p}, \mathbf{v}, \mathbf{q}]^T$$ for global pose estimation.
• Edge Computing: NVIDIA Jetson Nano, running ROS, processes radar data (range/Doppler FFT, beamforming, CFAR detection, DBSCAN clustering, tracking), fuses GNSS and IMU, and transmits obstacle/pose data to a Meta Quest 3 headset across 2.4 GHz Wi-Fi at 20 Hz.

The data flow follows: radar and GNSS + IMU $\rightarrow$ Jetson Nano (sensing, fusion, clustering) $\rightarrow$ Unity application on headset (visualization).

2. Sensing, Signal Processing, and Obstacle Tracking

The perception pipeline derives spatial and kinematic information through a layered process:

• Radar Signal Processing: Range FFT produces range bins ($N_r$), Doppler FFT estimates velocity bins ($N_d$), followed by angle-of-arrival estimation using beamforming (MVDR or Delay-and-Sum). CFAR (Constant False Alarm Rate) detection thresholds are set as $T = \alpha P_{noise}$, with $P_{noise}$ adaptively estimated.
• Clustering & Tracking: DBSCAN clusters are defined by points within $\epsilon = 0.3$ m and minPts = 5. Cluster centroids initialize tracked obstacles. A constant-velocity Kalman filter with state $\mathbf{s} = [x, y, \dot{x}, \dot{y}]^T$ propagates predicted states via transition matrix

$$F = \begin{bmatrix} 1 & 0 & \Delta t & 0 \ 0 & 1 & 0 & \Delta t \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{bmatrix}$$

Observation-model update uses measurement matrix $H = [1\ 0\ 0\ 0; 0\ 1\ 0\ 0]$.

• Coordinate Frame Alignment: Radar-frame detections $p_r = [x_r, y_r, z_r, 1]^T$ are transformed into the world frame using successive homogeneous transforms:

$$p_w = T_{GNSS \to W} \, T_{IMU \to GNSS} \, T_{Radar \to IMU} \, p_r$$

with $T_{Radar \to IMU}$ specified by fixed rotation $R$ and translation $t$ from calibration.

As a result, real-time, fused obstacle locations are rendered in reference to the tracked headset pose.

3. Visualization Strategies: Embedding Obstacles in VR

WaveWalkerClone investigates three visualization modalities for radar-tracked obstacles within VR, rendered in Unity (2022.3) using OpenXR on Meta Quest 3 (Nargund et al., 1 Feb 2026):

• Diegetic Alien Avatars: Low-poly, thematic aliens integrated with virtual narrative. Scaling with distance $d$ follows $\text{avatar\_scale} = s_0 (1 - e^{-d/d_0})$, $d_0 = 4$ m, and emissive tint transitions from blue (far) to green (near), $$color(d) = \text{lerp}(\text{blue}, \text{green}, \text{clamp}(1-d/8, 0, 1))$$.
• Non-Diegetic Human Avatars: Neutral gray, human-mesh proxies animated using filtered real-world velocity; visually informative but intentionally not thematic.
• Abstract Point Clouds: Aggregated radar points from last 0.3 s, colored by height-encoded HSL with opacity function $\alpha(d) = \alpha_0 e^{-d/8}$, $\alpha_0 = 0.75$.

Each method targets a distinct trade-off between immersion, interpretability, and narrative coherence.

4. Behavioral Evaluation: User Study Design and Metrics

A within-subjects experiment ($N=18$) was conducted with moderate-experience VR users (median age 20) (Nargund et al., 1 Feb 2026). Each participant completed three conditions (Latin-square counterbalanced): alien avatars, human avatars, and point clouds, walking a 200 m outdoor route with natural bystanders as dynamic obstacles ($\approx 26.3\, \pm\, 5.3$ encounters/trial).

Primary outcomes included:

• Presence: Measured by the Igroup Presence Questionnaire (subscales: spatial presence, involvement, realness).
• Task Load & Perceived Effort: NASA-TLX overall and subscales (mental, physical, temporal, performance, effort, frustration).
• Safety: Collision Anxiety Questionnaire (CAQ; custom Perceived Safety, 1–5 Likert), walking time.
• Cross-Reality Interaction: CRIQ [Gottsacker et al., 2021].

ANOVA or Friedman tests analyzed main effects; Bonferroni correction used for pairwise comparisons; effect sizes ($\eta_p^2$) reported.

5. Key Results and Trade-Offs Across Visualization Types

Principal findings highlight nuanced performance and user preference differentials:

• Detection Timeliness: Condition effect for "noticed dynamic obstacles promptly" ($F(2,34) = 4.63$, $p=0.017$, $\eta_p^2=0.21$); post-hoc revealed point clouds were slower than alien avatars ($p=0.043$).
• Safety: No significant differences in CAQ or Perceived Safety between conditions; mean safety rating $\approx4.1/5$ robust to lighting changes.
• Presence & Task Load: No significant differences in IPQ or overall NASA-TLX ($F(2,34) = 0.59$, $p = 0.54$). Effort and frustration trended lower for avatars and point clouds, respectively.
• User Preference: Nine preferred diegetic aliens, five point clouds, four human avatars.
• Qualitative Insights: Missed radar detections undermined comfort, especially when real bystanders were audible but not visible. Point clouds conveyed group extent most clearly; avatars clarified precise obstacle positions. "Ghost tracks" from multipath artifacts startled users.

A summary of outcome metrics appears below:

Metric	Aliens (Diegetic)	Humans (Non-diegetic)	Point Cloud (Abstract)
Perceived Effort (NASA-TLX, mean)	30.3	37.5	41.1
Frustration (NASA-TLX, mean)	26.9	19.2	17.8
Preferred by users (count, N=18)	9	4	5

6. Design Principles and Future Directions

Evaluation of WaveWalkerClone led to the following guidelines (Nargund et al., 1 Feb 2026):

• Hybrid Representations: Combining precise avatar proxies with abstract or ground-anchored overlays improves both localization and group extent estimation.
• Semantic vs. Functional Coherence: Diegetic visual forms (narrative-syntonic) elevate immersion but may distract via anthropomorphization. Abstract representations promote interpretative clarity but reduce engagement.
• Technical Priorities: System coherence—stability, low-latency tracking, and alignment of sensory cues (audio-visual)—directly impacts user presence more than the specific visual metaphors.
• Sensor Coverage: Wider coverage (multiple radars or opportunistic recalibration) decreases "blind spots" and multipath "ghost" artifacts.
• User Customization: Enabling users to select or blend visualization strategies enhances adaptability to environment and personal comfort.
• Open Problems: Application to denser environments (vehicles, varied terrains), integration of auditory/haptic cues for out-of-field-of-view threats, and quantification of detection latencies via ROC curve analyses.

7. Pilot-Wave Hydrodynamics: Simulation Methodology

WaveWalkerClone also denotes a class of numerical reproductions of the classical "walker" system, as detailed in (Tadrist et al., 2017). The physical system consists of a droplet "walking" on a vibrated bath, self-propelled by interaction with long-lived, damped sub-threshold Faraday waves generated at each impact.

The core theoretical and numerical recipe incorporates:

• Governing Equations: The vertical surface deformation $\zeta_k(t)$ (Fourier mode $k$) for the vibrated bath is described by the damped Mathieu equation:

$$\frac{d^2 \zeta_k}{dt^2} + 2\nu k^2\,\frac{d\zeta_k}{dt} + \Big[gk + \frac{\sigma}{\rho}k^3 - \Gamma g k \cos(\Omega t)\Big]\zeta_k = 0$$

with solution structure determined by the vibration amplitude $\Gamma$, frequency $\Omega$, density $\rho$, surface tension $\sigma$, and viscosity $\nu$.

• Wave Forcing from Impacts: Each droplet kick at time $t_n$, position $\mathbf{r}_n$, applies a delta-pressure in space and time, seeding the surface wave field. The evolution after multiple impacts is constructed as a superposition of impulse responses (Green's functions).
• Memory and Spatiotemporal Persistence: The wave memory parameter $M = \Gamma/|\Gamma - \Gamma_F|$ governs the time constant $\tau_\gamma = M T_F$, with $T_F = 4\pi/\Omega$. For $\Gamma$ just below threshold $\Gamma_F$, memory can reach $M \sim 5$–$20$, supporting non-Markovian dynamics and quantum-like phenomena.
• Numerical Scheme: Discretized in time/space, the wave field is updated each step by exponential decay and subharmonic driving, with new impulsive contributions for each bounce. The horizontal force on the droplet is $-m_d g \nabla \eta(\mathbf{r}_n, t)$, integrated using explicit (e.g., Runge–Kutta) methods.
• Parameter Choices: Silicone oil ($20$ cS), frequency $f = 80$ Hz, $\Gamma \approx 3.8$–$4.2$, droplet radius $0.3$–$0.5$ mm, depth $6$ mm support walkers with $V_w\sim 10$ mm/s.

This formulation allows simulation of single-walker dynamics, multi-walker interaction, quantized orbits, and complex experiments in macroscopic pilot-wave mechanics.

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Both implementations of WaveWalkerClone illustrate the integration of real-time sensing, numerical modeling, and interactive visualization for dynamic environments, with direct implications for safety in VR and macroscopic emulation of quantum-like behaviors (Nargund et al., 1 Feb 2026, Tadrist et al., 2017).