Proactive Risk Perception Module

• The module is defined as a system that anticipates risk by leveraging continuous sensor inputs, shared LSTM state, and lightweight neural layers.
• It maps agent–human distances into continuous risk scores across danger, warning, and safe zones to enable early, socially compliant maneuvers.
• Integration with social navigation policies improves personal space compliance and reduces collisions, validating its real-time, anticipatory safety benefits.

A Proactive Risk Perception Module encapsulates the ability of an autonomous system, agent, or collective to anticipate and quantify imminent risks—typically before those risks manifest or are queried explicitly—by leveraging continuous perception, context modeling, and forward-looking inference mechanisms. In the context of social navigation, autonomous decision making, or large-scale opinion dynamics, such a module forms the backbone of intelligent, safety-critical reasoning and adaptation.

1. Core Architectural Elements

A typical Proactive Risk Perception Module, as implemented in egocentric social navigation settings (Xiao et al., 9 Oct 2025), operates as an auxiliary neural subnetwork coupled to the main policy or decision layer. Its key architectural features include:

• Inheritance of Shared Perceptual State: The module accesses high-dimensional, temporally aggregated state representations (for instance, the LSTM hidden state δ_R in Falcon (Xiao et al., 9 Oct 2025)) encoding both spatial and temporal environmental features.
• Lightweight Feedforward Layers: The risk prediction logic is constructed as a two-layer fully connected neural network, using learned weight matrices (W₁, W₂), a rectified linear unit (ReLU), and sigmoid activation:

$$\phi_\text{risk}(\delta_R) = \sigma( W_2 \cdot \text{ReLU}( W_1 \cdot \delta_R ) )$$

• Risk Signal Output: For each nearby human agent (indexed by $i$), the module produces a continuous risk score $r_i \in [0, 1]$, corresponding to collision likelihood or personal space violation.

This design enables the module to operate with minimal added computation, leveraging the shared representation to provide real-time, risk-aware feedback during navigation.

2. Distance-Based Collision Risk Modeling

The foundation of the proactive risk signal is an explicit, continuous mapping from agent–human distance to collision risk:

• Zone Assignments:
  • Danger Zone ($d_i < d_\text{danger}$): Risk is maximal, $r_i^\text{true} = 1$.
  • Warning Zone ($d_\text{danger} \leq d_i < d_\text{safe}$): Risk decreases linearly: $$r_i^\text{true} = \frac{d_\text{safe} - d_i}{d_\text{safe} - d_\text{danger}}$$.
  • Safe Zone ($d_i \geq d_\text{safe}$): Risk is zero.

$$r_i^\text{true} = \begin{cases} 1.0, & d_i < d_\text{danger} \ \frac{d_\text{safe} - d_i}{d_\text{safe} - d_\text{danger}}, & d_\text{danger} \leq d_i < d_\text{safe} \ 0.0, & d_i \geq d_\text{safe} \end{cases}$$

where $d_\text{danger} = 2.0$m and $d_\text{safe} = 4.0$m (Xiao et al., 9 Oct 2025).

This parametrization provides a continuous, dense supervisory signal during learning. Unlike event-triggered (sparse) penalties for collision only at impact, this risk map enables early avoidance—enabling anticipatory, socially compliant policy updates.

3. Integration with Social Navigation Policy

The risk module is integrated into the broader navigation learning objective via a composite loss function:

$$\mathcal{L}_\text{total} = \beta_\text{main} \cdot \mathcal{L}_\text{main} + \beta_\text{aux} \cdot (\mathcal{L}_\text{count} + \mathcal{L}_\text{pos} + \mathcal{L}_\text{traj}) + \beta_\text{risk} \cdot \mathcal{L}_\text{risk}$$

Here, $\mathcal{L}_\text{risk}$ penalizes deviation between the predicted risk score and the continuous, distance-based ground truth risk. The weighting constant $\beta_\text{risk}$ modulates the influence of proactive risk awareness relative to other objectives (Xiao et al., 9 Oct 2025).

• Sensor Input & Policy Backbone: RGB-D images are encoded via ResNet-50 and odometry is fused into the state representation processed by a 2-layer LSTM. The proactive risk perception module consumes the post-LSTM output, ensuring consistent information sharing between modules.
• Joint Training: The risk module is trained end-to-end with the main policy and auxiliary prediction heads (i.e., human count, human position, motion forecasting), ensuring that risk awareness influences feature selection and trajectory planning.

4. Impact on Social Navigation and Benchmark Results

The module's explicit risk encoding substantially augments the ability of autonomous agents to maintain social norms in crowded, dynamic environments:

• Personal Space Compliance (PSC): With proactive risk perception, the agent maintains a safe buffer (≥0.5m) to humans for a larger proportion of timesteps, resulting in higher PSC metrics.
• Collision Rate (H-Coll): Explicit risk scoring reduces the frequency of physical collisions with human agents.
• Task Success and Path Efficiency: The module preserves high success rates (SR) and success weighted by path length (SPL), showing that proactive risk awareness does not compromise task completion or path optimality.

On the Social-HM3D benchmark, the enhanced system achieved PSC ~0.86 and H-Coll ~0.33, with SR ~0.66 and SPL ~0.60, culminating in a composite score ranking 2nd among 16 teams (Xiao et al., 9 Oct 2025).

5. Mathematical Formulation and Supervisory Design

The mathematical structure of the proactive risk module enables differentiable, gradient-based optimization due to:

• Continuous Supervision: $r_i^\text{true}$ as a piecewise-linear function provides a stable learning target across a wide range of agent–human proximities.
• Dense Temporal Feedback: Unlike sparse event rewards, the module provides at every timestep a scalar risk signal, directly shaping the agent's policy toward anticipatory avoidance.
• Ease of Joint Optimization: The use of a shared hidden representation ($\delta_R$) allows multitask learning (navigation, human counting, localization, and proactive risk) without architectural redundancy.

This approach suggests that proactive risk awareness can be universally integrated into social navigation agents operating on purely egocentric, sensor-based inputs.

6. Applicability, Limitations, and Potential Extensions

Proactive risk perception, as exemplified by this module, generalizes across dynamic, uncertain environments where forward-looking social or safety constraints are essential:

• Applicability: Human–robot social navigation, mobile robotics in human-populated environments, and other tasks with dynamic, safety-critical agent–human interactions benefit directly from continuous, anticipatory risk modeling.
• Limitations: Static parameterization of risk thresholds ($d_\text{danger}$, $d_\text{safe}$) may not optimally generalize across diverse cultures, contexts, or agent morphologies. Further, risk is modeled solely as a function of physical proximity; A plausible implication is that richer behavioral models (e.g., accounting for human intent or group behaviors) could improve proactive policy adaptation.
• Extensions: Dynamic or adaptive risk thresholds, integration with semantic understanding (activity, attention), and the extension to multi-agent or non-holonomic systems are suggested areas of future research.

7. Broader Implications in Proactive Risk Perception

The formalization and empirical validation of proactive risk perception modules mark an important development in socially intelligent autonomous systems. By quantifying risk before adverse events, such modules enable both robust safety compliance and enhanced human–robot interaction fluency, setting a technical precedent for embedding anticipatory safety into embodied AI (Xiao et al., 9 Oct 2025).