Responsible Robot Judgment OS: Multi-Universe Gate Control for Physical-World Autonomous Decision Systems

1. Introduction

The boundary between digital and physical autonomy is collapsing. Warehouse robots move 400-kilogram pallets at 2 meters per second. Surgical robots manipulate tissue with sub-millimeter precision. Delivery drones navigate urban canyons with pedestrians, cyclists, and children sharing the same airspace. Agricultural robots apply herbicides centimeters from food crops. In every case, the robot makes hundreds of decisions per second, and each decision carries physical consequences that cannot be undone with a database rollback.

Digital agent governance systems — including MARIA OS in its current form — operate under assumptions that do not hold in the physical world. Digital gates can afford 300-millisecond evaluation times because the worst case is a delayed API call. Physical gates must complete within the robot's control loop period, typically 1-10 milliseconds, because the worst case is a collision, a surgical perforation, or a pedestrian strike. Digital agents operate on clean, structured data with well-defined schemas. Physical robots operate on noisy sensor streams — LiDAR point clouds with occlusions, camera images with motion blur, force-torque signals corrupted by vibration. Digital agent conflicts are abstract (budget allocation vs. timeline pressure). Physical robot conflicts are concrete and lethal (shortest path vs. safety distance, speed vs. noise in a hospital corridor).

Yet the fundamental governance principle remains identical: every autonomous action must pass through responsibility-bounded evaluation before execution, and the system must fail closed when evaluation is uncertain. The question is whether this principle can be maintained under the extreme constraints of physical-world robotics.

This paper answers affirmatively and provides the mathematical, architectural, and experimental foundations. Our contributions are:

• Robot Gate Engine (Section 3): A real-time Multi-Universe evaluation architecture with formal latency guarantees, where five parallel evaluation universes — Safety, Regulatory, Efficiency, Ethics, and Human Comfort — score every action candidate and a fail-closed aggregation gate halts actuators when any universe score is below threshold.
• Real-Time Conflict Heatmap (Section 4): A continuous ConflictScore function over physical-world decision spaces that identifies and visualizes trade-offs between competing objectives in real-time, enabling predictive conflict avoidance rather than reactive conflict resolution.
• Embodied Ethics Calibration Model (Section 5): A responsibility-constrained reinforcement learning framework that detects ethical drift in learned robot policies — the gap between the robot's stated ethical constraints and its practiced behavior — and corrects it through constrained policy optimization.
• Robotic Responsibility Protocol (Section 6): A quantitative responsibility allocation framework that decomposes every decision node into Human, Robot, System, and Environment responsibility shares, enabling precise accident attribution and continuous responsibility monitoring.
• Layered Robot Judgment Architecture (Section 7): A concrete integration design that layers MARIA OS Multi-Universe evaluation, Gate control, and Conflict detection on top of the ROS2 middleware stack, with zero modification to existing ROS2 node interfaces.

The remainder of this paper is structured as follows. Section 2 reviews related work across robot safety, ethical AI, responsibility frameworks, and ROS2 governance. Sections 3-7 present our five technical contributions. Section 8 describes the integration architecture for Physical-Capital Multi-Universe and Autonomous Industrial Holding scenarios. Section 9 details experimental design. Section 10 presents results. Section 11 discusses implications, limitations, and future directions. Section 12 concludes. References follow.

2. Related Work

2.1 Robot Safety Standards and Functional Safety

The IEC 61508 standard [1] defines Safety Integrity Levels (SIL 1-4) for safety-related electronic systems, with SIL 3 requiring a probability of dangerous failure per hour between 10^{-8} and 10^{-7}. ISO 13482:2014 [2] extends safety requirements to personal care robots, mandating risk assessment per ISO 12100 [3] with explicit consideration of reasonably foreseeable misuse. ISO/TS 15066:2016 [4] specifies collaborative robot safety requirements including force and pressure thresholds for human-robot contact. These standards establish the safety envelope within which our Robot Gate Engine must operate, but none of them address the responsibility attribution problem: when a robot causes harm within its safety envelope due to a judgment error rather than a component failure, the standards provide no framework for determining who is responsible.

2.2 Ethical AI and Machine Ethics

The field of machine ethics [5, 6] has produced theoretical frameworks for encoding ethical reasoning in autonomous systems, from Asimov's Three Laws through deontological rule engines [7] to consequentialist utility maximizers [8]. Wallach and Allen [9] distinguish between operational morality (ethics built into design), functional morality (ethics the machine can reason about), and full moral agency (not yet achievable). Our Embodied Ethics Calibration Model targets functional morality: the robot does not derive ethical principles but must detect when its learned behavior deviates from externally specified ethical constraints and correct the deviation. This aligns with the constrained optimization approach of Amodei et al. [10] for AI safety, extended to embodied agents with physical actuators.

2.3 Responsibility and Accountability in Robotics

Matthias [11] articulated the responsibility gap: as machines become more autonomous and unpredictable, traditional responsibility attribution breaks down. Sparrow [12] argued that neither the programmer, the commanding officer, nor the robot itself can bear moral responsibility for autonomous lethal decisions. Our Robotic Responsibility Protocol takes a different approach: rather than seeking a single responsible party, we decompose responsibility into quantitative shares across Human, Robot, System, and Environment factors, where the shares must sum to 1.0 at every decision node. This is closer to the distributed responsibility model of Coeckelbergh [13] but formalized mathematically for engineering use.

2.4 ROS2 and Robot Operating Systems

ROS2 [14] provides the de facto middleware for robot software, with a DDS (Data Distribution Service) communication layer, lifecycle-managed nodes, and quality-of-service (QoS) policies. The Nav2 [15] navigation stack and MoveIt2 [16] manipulation stack provide high-level planning capabilities. However, ROS2 has no native concept of governance gates, responsibility attribution, or multi-criteria evaluation of action candidates. Actions are either permitted by the planning stack or rejected due to kinematic/dynamic infeasibility — there is no mechanism for halting a kinematically feasible action because it fails an ethical or comfort evaluation. Our Layered Robot Judgment Architecture adds this missing governance layer without modifying ROS2 core interfaces.

2.5 Multi-Objective Robot Decision Making

Multi-objective optimization in robotics has been studied extensively for path planning [17, 18], task allocation [19], and human-robot interaction [20]. Pareto-optimal approaches identify trade-off surfaces but do not enforce hard constraints on individual objectives. Constrained optimization approaches [21] enforce constraints but treat all constraints equally rather than organizing them into a priority hierarchy. Our Multi-Universe architecture organizes evaluation criteria into distinct universes with configurable priority ordering and independent fail-closed thresholds, providing both Pareto analysis (via the ConflictScore) and hard constraint enforcement (via gate thresholds).

2.6 MARIA OS and Digital Agent Governance

MARIA OS [22, 23, 24] provides a Multi-Universe evaluation framework for digital AI agents, where each action candidate receives scores from multiple evaluation universes and a max_i aggregation gate computes the composite risk. The fail-closed gate design [23] ensures that actions are halted when risk exceeds threshold. The responsibility decomposition framework [24] attributes responsibility across six continuous variables per decision node. This paper extends all three capabilities — Multi-Universe evaluation, fail-closed gates, and responsibility decomposition — to the physical-world robotics domain, addressing the hard real-time, sensor noise, and embodied ethics challenges that digital-only governance does not face.

3. Responsibility-Bounded Robot Decision Architecture

3.1 Research Question

The central research question of this section is: Can fail-closed gate evaluation be maintained within the hard real-time constraints of physical-world robot control loops? Specifically, can a Multi-Universe evaluation that spans Safety, Regulatory, Efficiency, Ethics, and Human Comfort complete within 10ms — the typical control loop period for industrial and service robots — while preserving the mathematical properties of responsibility-bounded judgment?

3.2 Five Evaluation Universes for Robotics

We define five evaluation universes, each corresponding to a distinct evaluation dimension with its own scoring function, threshold, and failure semantics. Within the MARIA OS coordinate system, these universes occupy positions G1.U_k for k in {1, ..., 5} under a dedicated Robotics Galaxy.

• U_S (Safety Universe, G1.U1): Evaluates physical safety — collision risk, force limits, stability margins, obstacle proximity. Score s_S in [0,1] where 0 = maximally dangerous and 1 = maximally safe.
• U_R (Regulatory Universe, G1.U2): Evaluates compliance with applicable standards (ISO 13482, ISO/TS 15066, local regulations, facility-specific rules). Score s_R in [0,1] where 0 = total non-compliance and 1 = full compliance.
• U_E (Efficiency Universe, G1.U3): Evaluates operational efficiency — energy consumption, time-to-completion, throughput contribution. Score s_E in [0,1] where 0 = maximally wasteful and 1 = Pareto-optimal efficiency.
• U_Eth (Ethics Universe, G1.U4): Evaluates ethical alignment — fairness of resource allocation, respect for human autonomy, proportionality of force, privacy protection. Score s_Eth in [0,1] where 0 = ethically unacceptable and 1 = ethically exemplary.
• U_HC (Human Comfort Universe, G1.U5): Evaluates human comfort and psychological safety — noise level, movement predictability, personal space maintenance, perceived intent clarity. Score s_HC in [0,1] where 0 = maximally distressing and 1 = maximally comfortable.

Each universe maintains an independent evaluation pipeline that receives the same action candidate and produces its score in parallel. The universes do not communicate during evaluation — they produce independent assessments that are aggregated only at the gate layer.

3.3 The Robot Gate Engine

$ G(s_S, s_R, s_E, s_{Eth}, s_{HC}) = \begin{cases} \text{PERMIT} & \text{if } \forall k: s_k \geq \tau_k \text{ and } \Phi(\mathbf{s}) \geq \tau_\Phi \\ \text{ESCALATE} & \text{if } \exists k: \tau_k^{\text{esc}} \leq s_k < \tau_k \text{ and } \nexists j: s_j < \tau_j^{\text{halt}} \\ \text{HALT} & \text{otherwise} \end{cases} $

where tau_k is the threshold for universe k, tau_k^{esc} is the escalation threshold (tau_k^{halt} < tau_k^{esc} < tau_k), tau_k^{halt} is the hard halt threshold, and Phi(s) is the composite gate function.

The composite gate function uses a max_i scoring strategy consistent with MARIA OS conventions:

$ \Phi(\mathbf{s}) = 1 - \max_{k \in \{S,R,E,Eth,HC\}} w_k \cdot (1 - s_k) $

where w_k are universe weights satisfying w_S >= w_R >= w_Eth >= w_HC >= w_E and sum_k w_k = 1. The max_i formulation ensures that the worst-performing universe dominates the composite score — a robot action that is efficient but unsafe cannot achieve a high composite score regardless of its efficiency.

Theorem 1 (Fail-Closed Correctness). Under the Robot Gate Engine, if any universe score s_k < tau_k^{halt}, the gate output is HALT regardless of all other universe scores. Formally:

$ \exists k: s_k < \tau_k^{\text{halt}} \implies G(\mathbf{s}) = \text{HALT} $

Proof. By the case definition of G, the HALT case applies when neither the PERMIT condition (requires all s_k >= tau_k) nor the ESCALATE condition (requires no s_j < tau_j^{halt}) is satisfied. If s_k < tau_k^{halt} for any k, then the ESCALATE condition's exclusion clause is triggered (there exists j = k with s_j < tau_j^{halt}), and the PERMIT condition fails (s_k < tau_k^{halt} < tau_k). Therefore G(s) = HALT. QED.

3.4 Real-Time Latency Analysis

The Robot Gate Engine must complete evaluation within one control loop period T_ctrl. We analyze the worst-case execution time (WCET) of each component.

$ T_{\text{gate}} = \max\left(T_{U_S}, T_{U_R}, T_{U_E}, T_{U_{Eth}}, T_{U_{HC}}\right) + T_{\text{agg}} + T_{\text{halt}} $

where T_{U_k} is the WCET for universe k evaluation (parallel execution), T_agg is the aggregation time for the composite gate function, and T_halt is the time from HALT decision to actuator stop command.

For the parallel universe evaluation, each universe operates on pre-computed features extracted from the sensor processing pipeline. We bound each universe's WCET:

• T_{U_S} <= 2ms (collision checking against pre-built occupancy grid, O(log n) kd-tree query)
• T_{U_R} <= 1ms (rule lookup against compiled regulatory constraint table)
• T_{U_E} <= 1ms (efficiency scoring from pre-computed trajectory cost)
• T_{U_Eth} <= 2ms (ethical constraint evaluation against behavioral policy bounds)
• T_{U_HC} <= 2ms (comfort model inference from pre-computed human state estimates)

The aggregation function Phi(s) is a scalar computation: T_agg <= 0.01ms. The halt propagation through the real-time safety bus: T_halt <= 1ms (SIL-3 certified safety relay).

Therefore: T_gate <= max(2, 1, 1, 2, 2) + 0.01 + 1 = 3.01ms, which is well within the 10ms control loop budget. Even with a 2x safety margin for WCET estimation uncertainty, T_gate <= 6.02ms < 10ms.

Theorem 2 (Real-Time Schedulability). Given a control loop period T_ctrl >= 8ms and the Robot Gate Engine WCET bounds above, the gate evaluation is schedulable under Rate-Monotonic Scheduling (RMS) alongside the sensor processing task (WCET 3ms) and trajectory planning task (WCET 4ms).

Proof. Under RMS, three tasks with periods P_1 = P_2 = P_3 = T_ctrl and WCETs C_1 = 3ms, C_2 = 4ms (non-gate tasks combined), C_3 = 3.01ms are schedulable if the utilization satisfies:

$ U = \sum_{i=1}^{3} \frac{C_i}{P_i} = \frac{3 + 4 + 3.01}{T_{\text{ctrl}}} = \frac{10.01}{T_{\text{ctrl}}} \leq n(2^{1/n} - 1) $

For n = 3 tasks: 3(2^{1/3} - 1) = 3(0.2599) = 0.7798. At T_ctrl = 13ms: U = 10.01/13 = 0.770 < 0.7798. With parallel universe evaluation reducing effective gate WCET, the actual utilization is lower. For T_ctrl = 10ms with the parallel architecture: U = (3 + 4 + 3.01)/10 = 1.001, which marginally exceeds the RMS bound but is schedulable under Deadline-Monotonic Scheduling (DMS) with priority assignment Safety > Gate > Planning > Sensor, since the gate task completes before the sensor task's next release. QED.

3.5 Sensor Noise and Gate Robustness

Physical-world sensors introduce noise into universe scores. Let the true score be s_k and the measured score be s_k = s_k + eta_k where eta_k ~ N(0, sigma_k^2) is Gaussian sensor noise. The gate must be robust to this noise — specifically, the probability of a false PERMIT (allowing a dangerous action due to noise inflating the score) must be bounded.

$ \hat{\tau}_k = \tau_k + z_\alpha \cdot \sigma_k $

where z_alpha is the z-score corresponding to the desired confidence level (z_{0.001} = 3.09 for 99.9% confidence that a true sub-threshold score is not permitted).

Theorem 3 (Noise-Robust Fail-Closed Property). Under the noise-robust threshold hat_tau_k, the probability of false PERMIT is bounded by:

$ P(G(\mathbf{s}) = \text{PERMIT} \mid \exists k: s_k^* < \tau_k) \leq \alpha^K $

where K is the number of universes with s_k* < tau_k.

Proof. For each universe k with s_k < tau_k, a false PERMIT requires s_k >= hat_tau_k, i.e., s_k + eta_k >= tau_k + z_alpha sigma_k. Since s_k < tau_k, this requires eta_k > z_alpha sigma_k + (tau_k - s_k) > z_alpha sigma_k. Therefore P(s_k >= hat_tau_k | s_k < tau_k) < P(eta_k > z_alpha * sigma_k) = alpha. Since universe evaluations are independent, the joint probability of all K sub-threshold universes producing false PERMITs is alpha^K. QED.

For alpha = 0.001 and K = 1 (single universe failure): false PERMIT rate < 0.1%. For K = 2: < 10^{-6}. This demonstrates that the Multi-Universe architecture provides exponential noise robustness.

4. Physical-World Conflict Mapping

4.1 The Nature of Physical Conflicts

In digital agent governance, conflicts are abstract: budget allocation vs. timeline pressure, accuracy vs. response time, compliance vs. user experience. In physical robotics, conflicts are concrete and have spatial-temporal extent. A warehouse robot choosing between the shortest path to a pickup location and a path that maintains 2-meter safety distance from human workers faces a conflict that occupies a specific region of physical space and a specific window of time. A hospital delivery robot choosing between fast delivery (high motor speed, loud noise) and quiet operation (slow speed, low noise) faces a conflict whose resolution depends on whether it is passing an ICU ward or an empty corridor.

These physical conflicts have properties that digital conflicts lack:

• Spatial locality: The conflict exists in a region of physical space and affects entities within that region.
• Temporal urgency: The conflict must be resolved within the robot's planning horizon, typically 0.1-5 seconds.
• Irreversibility gradient: Some resolutions are more reversible than others (slowing down is more reversible than accelerating; detouring is more reversible than proceeding through a narrow gap).
• Sensory observability: The parameters of the conflict are measured through noisy sensors, not queried from a database.

4.2 ConflictScore Formalization

$ CS(a) = 1 - \prod_{(j,k) \in \mathcal{P}} \left(1 - \text{tension}_{jk}(a)\right) $

where P is the set of all universe pairs {(j,k) : j < k, j,k in {S,R,E,Eth,HC}} and tension_{jk}(a) in [0,1] is the pairwise tension between universes j and k for action a.

The pairwise tension is defined as the degree to which improving universe j's score necessarily worsens universe k's score:

$ \text{tension}_{jk}(a) = \max\left(0, -\frac{\nabla_a s_j \cdot \nabla_a s_k}{\|\nabla_a s_j\| \cdot \|\nabla_a s_k\|}\right) $

This is the negative cosine similarity of the score gradients, clamped to [0,1]. When the gradients point in opposite directions (improving j worsens k), tension is high. When they point in the same direction (both improve together), tension is zero. This formulation has the following properties:

Proposition 1. CS(a) = 0 if and only if all universe pairs have zero tension (all objectives are aligned for action a).

Proposition 2. CS(a) approaches 1 as more universe pairs exhibit high tension (the action is deeply conflicted across multiple dimensions).

Proposition 3. CS is differentiable with respect to action parameters wherever the universe scoring functions are differentiable, enabling gradient-based conflict avoidance.

4.3 Concrete Conflict Examples

Conflict Type 1: Shortest Path vs. Safety Distance.

Consider a warehouse robot at position p_0 navigating to goal position p_g with a human worker at position p_h. Let a = (v, theta) be the velocity and heading angle. The Efficiency universe scores the action based on progress toward the goal:

$ s_E(v, \theta) = \frac{v \cdot \cos(\theta - \theta_{\text{goal}})}{v_{\max}} $

The Safety universe scores based on minimum distance to the human:

$ s_S(v, \theta) = \sigma\left(\frac{d_{\min}(v, \theta, p_h) - d_{\text{safe}}}{\delta}\right) $

where d_min is the minimum distance along the trajectory, d_safe is the required safety distance, delta is a scaling parameter, and sigma is the sigmoid function. The tension between these two universes is:

$ \text{tension}_{SE}(v, \theta) = \max\left(0, -\frac{\nabla_{(v,\theta)} s_S \cdot \nabla_{(v,\theta)} s_E}{\|\nabla_{(v,\theta)} s_S\| \cdot \|\nabla_{(v,\theta)} s_E\|}\right) $

When the human is positioned between the robot and the goal, this tension approaches 1.0 — the direct path maximizes efficiency but minimizes safety. The ConflictScore for the direct path is high, triggering either an alternative action search or an ESCALATE decision.

Conflict Type 2: Efficiency vs. Noise (Hospital Corridor).

A hospital delivery robot must traverse a corridor adjacent to an ICU ward. Motor speed v produces noise level N(v) = N_0 + kv^2 decibels. The Efficiency universe favors high speed. The Human Comfort universe penalizes noise:

$ s_{HC}(v) = \max\left(0, 1 - \frac{N(v) - N_{\text{ambient}}}{N_{\text{threshold}} - N_{\text{ambient}}}\right) $

The tension between Efficiency and Human Comfort is constant along the speed axis in this scenario (improving one always worsens the other), yielding ConflictScore close to 1.0 for any speed. The resolution requires a meta-decision: either accept a slow, quiet traversal (Human Comfort wins) or route through an alternative corridor (spatial resolution of the conflict). This meta-decision is itself evaluated by the Robot Gate Engine.

4.4 Real-Time Conflict Heatmap

The ConflictScore can be computed over the robot's action space and projected onto physical space to create a Real-Time Conflict Heatmap.

$ H(x, y, t) = \max_{a \in A(x,y)} CS(a, t) $

where A(x,y) is the set of action candidates that bring the robot to position (x,y) within one planning horizon. The heatmap shows the maximum conflict the robot will encounter at each position, enabling predictive conflict avoidance — the robot's planner can route around high-conflict regions before entering them.

Computational Complexity. For a discretized workspace of N_x times N_y cells and M action candidates per cell, the naive computation cost is O(N_x N_y M |P|) where |P| = 10 (number of universe pairs). For a 100x100 grid with 20 actions per cell and 10 pairs, this is 2 10^6 tension evaluations. At 100ns per evaluation (gradient dot product), the total computation time is 200ms — too slow for real-time operation at 10ms control rates.

We address this with three acceleration techniques:

• Hierarchical evaluation: Compute the heatmap at coarse resolution (20x20) first, then refine only high-conflict regions to fine resolution (100x100). Typical speedup: 5-10x.
• Incremental updates: Between control cycles, only recompute cells where sensor measurements have changed significantly (human positions moved, obstacle map updated). Typical update fraction: 10-20% of cells.
• GPU parallelism: The tension computation is embarrassingly parallel. On a modest embedded GPU (NVIDIA Jetson Orin), the full 100x100 grid completes in 1.2ms.

With these optimizations, the conflict heatmap update completes within 2ms, well within the control loop budget.

4.5 Conflict Resolution Strategies

When the ConflictScore for a proposed action exceeds a threshold tau_CS, the system invokes one of four resolution strategies:

| Strategy | Condition | Action | Latency Impact |

| --- | --- | --- | --- |

| Pareto Search | CS(a) > tau_CS, alternatives exist | Search for a lower-conflict action in A | +1-3ms |

| Priority Override | CS(a) > tau_CS, safety involved | Accept safety-optimal action regardless of other scores | +0ms |

| Temporal Deferral | CS(a) > tau_CS, not time-critical | Pause and wait for conflict conditions to change | Variable |

| Human Escalation | CS(a) > tau_CS^{esc}, no resolution found | ESCALATE to human operator via responsibility gate | +seconds to minutes |

The priority ordering is: Priority Override > Pareto Search > Temporal Deferral > Human Escalation. Safety-involved conflicts are resolved immediately without searching for alternatives.

5. Embodied Ethical Learning

5.1 The Ethical Drift Problem in Embodied Agents

Digital AI agents can violate ethical principles by generating harmful text, making biased decisions, or leaking private data. These violations are discrete, detectable, and reversible — the output can be retracted, the decision can be overridden, the data can be deleted. Embodied robots face a fundamentally different ethical challenge: their ethical violations are continuous, gradual, and physically instantiated.

Consider a warehouse robot that is trained with a reinforcement learning policy pi to pick and place packages. The reward function R(s, a) includes an efficiency term (packages per hour) and a safety term (negative reward for proximity to humans). During training, the robot learns to maintain a comfortable 2-meter buffer around human workers. After deployment, the robot encounters scenarios not represented in training: dense crowds during shift changes, narrow aisles where 2-meter clearance is impossible, time pressure from delayed upstream processes. The RL policy adapts — not through retraining, but through the intrinsic generalization of the neural network policy. The buffer gradually shrinks: 1.8m, 1.5m, 1.2m. Each individual decision is locally optimal. The gradual erosion is invisible to point-in-time safety checks that evaluate against a fixed threshold.

This is embodied ethical drift: the systematic deviation of practiced behavior from stated ethical constraints, driven by the interaction between a learned policy and a non-stationary deployment environment.

5.2 Formalizing Ethical Drift

$ D_{\text{ethical}}(t) = D_{\text{KL}}\left(\pi_{\text{practiced}}(t) \| \pi_{\text{stated}}\right) = \sum_{s \in S} \pi_{\text{practiced}}(s, t) \log \frac{\pi_{\text{practiced}}(s, t)}{\pi_{\text{stated}}(s)} $

where D_KL is the Kullback-Leibler divergence and the sum is over the state space S. When D_ethical(t) = 0, the robot's behavior exactly matches its stated ethical policy. As D_ethical(t) grows, the robot's practiced behavior diverges from its stated constraints.

Theorem 4 (Drift Monotonicity Under Non-Stationary Environments). If the deployment environment distribution p_env(t) shifts monotonically away from the training environment distribution p_train, and the policy pi generalizes continuously, then D_ethical(t) is monotonically non-decreasing.

Proof sketch. Under continuous generalization, pi_practiced(t) tracks the optimal policy for the current environment p_env(t). As p_env(t) diverges from p_train, the optimal policy for p_env(t) diverges from the optimal policy for p_train, which was calibrated to satisfy pi_stated. Since KL-divergence is continuous and pi_practiced(t) is a continuous function of p_env(t), the drift D_ethical(t) is non-decreasing. The formal proof uses the data processing inequality and the monotonicity of KL-divergence under deterministic transformations. QED.

5.3 Drift Detection from Behavior Logs

We detect ethical drift by maintaining a sliding window of robot behavior logs and comparing the behavioral distribution to the stated policy. The robot operates within the MARIA OS coordinate system at a specific agent node G1.U1.P_p.Z_z.A_a, and all actions are logged to the Decision Pipeline.

$ \hat{D}(t, W) = \frac{1}{W} \sum_{i=t-W}^{t} \log \frac{\hat{\pi}_{\text{practiced}}(s_i, a_i)}{\pi_{\text{stated}}(s_i, a_i)} $

where hat_pi_practiced is estimated from the empirical action frequency in the window and pi_stated is the known stated policy. This is a sample average of the pointwise KL-divergence, which converges to D_ethical(t) as W -> infinity by the law of large numbers.

Alert condition: An alert is raised when hat_D(t, W) > epsilon_drift for a configurable threshold epsilon_drift. The alert propagates through the MARIA OS responsibility gate at the agent's zone level, triggering an ESCALATE event in the Decision Pipeline.

5.4 Responsibility-Constrained Reinforcement Learning

Once drift is detected, the robot's policy must be corrected. We use Constrained Markov Decision Process (CMDP) optimization, where the constraint is the ethical drift bound.

$ \max_{\pi} \mathbb{E}_{\pi}\left[\sum_{t=0}^{\infty} \gamma^t R(s_t, a_t)\right] \quad \text{subject to} \quad D_{\text{KL}}(\pi \| \pi_{\text{stated}}) \leq \epsilon_{\text{drift}} $

This is a standard constrained RL problem solvable via the Lagrangian relaxation:

$ \mathcal{L}(\pi, \lambda) = \mathbb{E}_{\pi}\left[\sum_{t=0}^{\infty} \gamma^t R(s_t, a_t)\right] - \lambda \left(D_{\text{KL}}(\pi \| \pi_{\text{stated}}) - \epsilon_{\text{drift}}\right) $

The optimal policy has a closed-form solution via the KKT conditions:

$ \pi^(a | s) \propto \pi_{\text{stated}}(a | s) \cdot \exp\left(\frac{Q^{\pi^}(s, a)}{\lambda^*}\right) $

where Q^{pi}(s, a) is the optimal Q-function and lambda is the optimal Lagrange multiplier determined by the constraint D_KL(pi* || pi_stated) = epsilon_drift.

Theorem 5 (Convergence of Embodied Ethics Calibration). Under standard regularity conditions (finite state-action space, ergodic MDP, bounded rewards), the Lagrangian relaxation converges to a policy pi that satisfies D_KL(pi || pi_stated) <= epsilon_drift and achieves the maximum expected return among all policies satisfying the drift constraint.

Proof. This follows from strong duality in convex optimization over the policy simplex. The policy space is a compact convex set (probability distributions over actions). The KL-divergence constraint defines a convex feasible set (KL-balls are convex). The expected return is linear in pi. Therefore Slater's condition is satisfied (any policy strictly inside the KL-ball is a strictly feasible point), and strong duality holds. The KKT conditions yield the stated closed-form solution. Convergence follows from the convergence of policy iteration in the Lagrangian. QED.

5.5 Online Correction Protocol

The correction operates as a feedback loop integrated with the MARIA OS Decision Pipeline:

1. Monitor: Continuously compute hat_D(t, W) from the decision log at the agent's coordinate. 2. Detect: When hat_D(t, W) > epsilon_drift, raise an ESCALATE event at the zone-level responsibility gate. 3. Diagnose: Identify which behavioral dimensions contribute most to the drift (safety distance, speed, force application) by decomposing D_KL along state features. 4. Correct: Run constrained policy optimization with the identified behavioral dimensions, producing an updated policy pi satisfying the drift bound. 5. Validate: Evaluate pi in simulation (digital twin) against the stated policy before deploying to the physical robot. 6. Deploy: Update the robot's policy through the MARIA OS agent update channel, with a responsibility gate requiring human approval for the policy change. 7. Verify: Monitor hat_D(t, W) post-deployment to confirm drift has been corrected.

Each step produces an audit record in the Decision Pipeline, ensuring full traceability of the ethical correction process.

6. Human-Robot Responsibility Matrix

6.1 The Responsibility Attribution Problem

When a robot causes harm, the question 'who is responsible?' is legally, ethically, and technically complex. Current practice assigns responsibility through ad-hoc legal analysis: the manufacturer if it is a design defect, the operator if it is a misuse, the owner if it is a maintenance failure. This binary assignment fails for autonomous robots where the harm results from the interaction of multiple factors: the robot's learned policy, the human operator's supervision, the system's sensor quality, and the environment's unpredictability.

We propose a quantitative framework that distributes responsibility continuously across four factors at each decision node, enabling both real-time responsibility monitoring and post-hoc accident analysis.

6.2 The Four Responsibility Factors

$ \mathbf{\rho}_i = (\rho_H^i, \rho_R^i, \rho_S^i, \rho_E^i) \in [0,1]^4 $

where:

• rho_H^i = Human responsibility share: the degree to which a human operator had oversight, could have intervened, and was informed.
• rho_R^i = Robot responsibility share: the degree to which the robot's autonomous decision was the proximate cause.
• rho_S^i = System responsibility share: the degree to which the system infrastructure (sensors, communications, planning software) contributed.
• rho_E^i = Environment responsibility share: the degree to which environmental conditions (lighting, obstacles, human behavior) were beyond design parameters.

Constraint: The responsibility shares must sum to unity at every decision node:

$ \rho_H^i + \rho_R^i + \rho_S^i + \rho_E^i = 1 \quad \forall i $

This constraint ensures complete responsibility attribution — no portion of responsibility is unassigned.

6.3 Responsibility Computation

Each responsibility share is computed from observable quantities at the decision node.

Human Responsibility:

$ \rho_H^i = \alpha_H \cdot h_i \cdot \text{inform}_i \cdot \text{intervene}_i $

where h_i in [0,1] is the human-in-the-loop factor (1 if the gate required human approval, 0 if fully autonomous), inform_i in [0,1] is the information sufficiency (was the human provided with adequate information to make the decision?), intervene_i in [0,1] is the intervention capability (could the human have intervened in time?), and alpha_H is a normalization constant.

Robot Responsibility:

$ \rho_R^i = \alpha_R \cdot a_i \cdot \text{conf}_i \cdot (1 - e_{\text{novelty}}^i) $

where a_i in [0,1] is the automation level, conf_i in [0,1] is the robot's confidence in its decision, e_novelty^i in [0,1] is the environmental novelty (how far the current situation is from the training distribution), and alpha_R is a normalization constant. The (1 - e_novelty) term captures the principle that robot responsibility decreases when the robot is operating in situations it was not designed for.

System Responsibility:

$ \rho_S^i = \alpha_S \cdot (1 - \text{sensor\_quality}_i) \cdot (1 - \text{comm\_quality}_i) \cdot (1 - \text{plan\_quality}_i) $

where sensor_quality, comm_quality, and plan_quality measure the quality of the sensor data, communication links, and planning outputs at the decision node. System responsibility increases when infrastructure degrades.

Environment Responsibility:

$ \rho_E^i = \alpha_E \cdot e_{\text{novelty}}^i \cdot (1 - \text{predict}_i) $

where predict_i in [0,1] is the predictability of the environment (was the environmental condition foreseeable?). The normalization constants alpha_H, alpha_R, alpha_S, alpha_E are determined by the unity constraint:

$ \alpha_H, \alpha_R, \alpha_S, \alpha_E \text{ are set such that } \rho_H^i + \rho_R^i + \rho_S^i + \rho_E^i = 1 $

This is achieved by computing unnormalized shares rho_tilde and normalizing: rho_k^i = rho_tilde_k^i / sum_k rho_tilde_k^i.

6.4 The Responsibility Matrix Over Time

For a sequence of T decision nodes leading to an outcome (e.g., a collision), the Responsibility Matrix is:

$ \mathbf{M} = \begin{pmatrix} \rho_H^1 & \rho_R^1 & \rho_S^1 & \rho_E^1 \\ \rho_H^2 & \rho_R^2 & \rho_S^2 & \rho_E^2 \\ \vdots & \vdots & \vdots & \vdots \\ \rho_H^T & \rho_R^T & \rho_S^T & \rho_E^T \end{pmatrix} \in [0,1]^{T \times 4} $

Each row sums to 1. The column averages give the aggregate responsibility shares over the decision sequence:

$ \bar{\rho}_k = \frac{1}{T} \sum_{i=1}^{T} \rho_k^i \quad \text{for } k \in \{H, R, S, E\} $

Theorem 6 (Responsibility Conservation). For any decision sequence of length T, the aggregate responsibility shares satisfy bar_rho_H + bar_rho_R + bar_rho_S + bar_rho_E = 1.

Proof. bar_rho_H + bar_rho_R + bar_rho_S + bar_rho_E = (1/T) sum_i (rho_H^i + rho_R^i + rho_S^i + rho_E^i) = (1/T) sum_i 1 = 1. QED.

6.5 Responsibility Dynamics and Early Warning

The responsibility vector rho_i evolves over time as conditions change. We define the responsibility velocity:

$ \dot{\rho}_k(t) = \frac{d\rho_k}{dt} \approx \frac{\rho_k^{i+1} - \rho_k^i}{\Delta t} $

A rapid increase in robot responsibility share (dot_rho_R > 0 sustained over multiple decision nodes) indicates that the robot is taking on more autonomous decision-making, potentially without adequate human oversight. This triggers a responsibility drift alert in the MARIA OS Decision Pipeline, analogous to the ethical drift alert in Section 5.

$ RDI(t, W) = \frac{1}{W} \sum_{i=t-W}^{t} \mathbb{1}\left[\dot{\rho}_R^i > \delta_{\text{drift}}\right] $

where delta_drift is the drift threshold. When RDI(t, W) > 0.5 (more than half the recent decisions show increasing robot responsibility), the system triggers an ESCALATE event.

6.6 Accident Attribution Protocol

When an adverse event occurs, the Responsibility Matrix provides the quantitative foundation for accident analysis:

1. Extract the decision sequence leading to the adverse event from the MARIA OS audit log. 2. Compute the Responsibility Matrix M for the extracted sequence. 3. Identify the dominant responsibility factor at the critical decision node (the node where the adverse outcome became unavoidable). 4. Trace the responsibility trajectory: how did the dominant factor evolve in the decisions preceding the critical node? 5. Determine the root cause: Was it a gradual responsibility shift (human oversight degraded over time)? A sudden system failure (sensor quality dropped to zero)? An environmental surprise (unpredictable human behavior)? 6. Recommend corrective action: Adjust gate thresholds, recalibrate the ethical policy, modify human oversight requirements, or update the environmental model.

This protocol transforms accident investigation from a blame-assignment exercise into a quantitative engineering analysis, fully traceable through the MARIA OS Decision Pipeline.

7. Robot OS x Multi-Universe Bridge

7.1 The Integration Challenge

ROS2 provides a mature, battle-tested middleware for robot software. It handles sensor driver management, inter-process communication, lifecycle management, and hardware abstraction. MARIA OS provides governance, responsibility attribution, and multi-criteria evaluation. The challenge is to combine both systems without requiring modifications to either core architecture — ROS2 nodes should not need to know about MARIA OS governance, and MARIA OS evaluation pipelines should not need to know about ROS2 communication details.

7.2 Layered Architecture

We propose a three-layer architecture that sits between the ROS2 application layer and the ROS2 middleware layer:

Layer 1: Multi-Universe Evaluation Layer. This layer intercepts action commands from ROS2 planning nodes (Nav2, MoveIt2, custom planners) before they reach the ROS2 action servers. Each intercepted command is evaluated by the five universes in parallel. The layer is implemented as a set of ROS2 lifecycle nodes that subscribe to command topics and publish evaluated commands.

Layer 2: Gate Layer. This layer receives the universe scores from Layer 1 and applies the Robot Gate Engine (Section 3.3). For PERMIT decisions, the original command is forwarded to the action server. For HALT decisions, a zero-velocity command is issued immediately via a dedicated safety-priority topic. For ESCALATE decisions, the command is held pending human approval through a MARIA OS responsibility gate.

Layer 3: Conflict Layer. This layer maintains the real-time Conflict Heatmap (Section 4.4) and provides it to the ROS2 planning nodes as a cost layer. Planners can use the conflict heatmap as an additional cost term in their objective functions, biasing plans toward low-conflict regions of the workspace.

7.3 ROS2 Integration Architecture

The integration uses ROS2's standard communication primitives — topics, services, and actions — to avoid any middleware modifications.

Subscriptions:
  /cmd_vel (geometry_msgs/Twist)           -- velocity commands
  /move_base/goal (geometry_msgs/PoseStamped)  -- navigation goals
  /arm/joint_trajectory (trajectory_msgs/JointTrajectory)  -- arm commands
  /sensor_state (maria_msgs/SensorState)   -- aggregated sensor quality
  /human_state (maria_msgs/HumanState)     -- detected human positions/states

Publications:
  /cmd_vel_gated (geometry_msgs/Twist)     -- gate-filtered velocity commands
  /gate_status (maria_msgs/GateStatus)     -- current gate evaluation result
  /conflict_heatmap (nav_msgs/OccupancyGrid)  -- conflict heatmap as cost layer
  /responsibility (maria_msgs/ResponsibilityVector)  -- current responsibility allocation

Services:
  /maria/evaluate_action (maria_srvs/EvaluateAction)  -- on-demand action evaluation
  /maria/get_responsibility (maria_srvs/GetResponsibility)  -- query responsibility matrix

Actions:
  /maria/escalate (maria_actions/Escalate)  -- human escalation with timeout

7.4 Message Flow

The message flow for a typical navigation command is:

1. Nav2 planner publishes a velocity command to /cmd_vel. 2. MARIA Bridge Node intercepts the command (subscription). 3. Layer 1 evaluates the command across five universes in parallel (2ms). 4. Layer 2 applies the Robot Gate Engine (0.01ms). 5a. If PERMIT: Bridge publishes the command to /cmd_vel_gated (0.1ms). The robot's motor controller subscribes to /cmd_vel_gated instead of /cmd_vel. 5b. If HALT: Bridge publishes zero-velocity to /cmd_vel_gated and publishes HALT status to /gate_status. 5c. If ESCALATE: Bridge holds the command, publishes ESCALATE status to /gate_status, and initiates the /maria/escalate action to contact the human operator. 6. Layer 3 updates the conflict heatmap and publishes to /conflict_heatmap. 7. Responsibility vector is computed and published to /responsibility.

Total additional latency for PERMIT path: 2.11ms. This is well within the 10ms control loop budget.

7.5 Formal Timing Model

$ T_{\text{e2e}} = T_{\text{sub}} + T_{\text{eval}} + T_{\text{gate}} + T_{\text{pub}} $

where T_sub is the subscription callback dispatch time (bounded by ROS2 executor, typically < 0.05ms), T_eval is the parallel universe evaluation time (bounded by max universe WCET, < 2ms), T_gate is the gate aggregation time (< 0.01ms), and T_pub is the publication time (< 0.1ms).

$ T_{\text{e2e}} < 0.05 + 2.0 + 0.01 + 0.1 = 2.16\text{ms} $

For the HALT path, the safety-priority publication bypasses the normal ROS2 scheduler via a dedicated real-time thread with SCHED_FIFO priority, adding at most 0.5ms:

$ T_{\text{halt}} < T_{\text{e2e}} + 0.5 = 2.66\text{ms} $

Including the safety relay actuation time (< 1ms for SIL-3 rated components), the total time from risk detection to motor stop is:

$ T_{\text{stop}} < T_{\text{halt}} + T_{\text{relay}} < 2.66 + 1.0 = 3.66\text{ms} $

This is well within the 8ms target stated in the benchmarks, even with a 2x safety margin: 3.66 * 2 = 7.32ms < 8ms.

7.6 Quality of Service Configuration

The MARIA Bridge Node uses the following ROS2 QoS configurations to ensure reliable governance messaging:

| Topic | Reliability | Durability | History | Deadline |

| --- | --- | --- | --- | --- |

| /cmd_vel_gated | RELIABLE | VOLATILE | KEEP_LAST(1) | 10ms |

| /gate_status | RELIABLE | TRANSIENT_LOCAL | KEEP_LAST(10) | 100ms |

| /conflict_heatmap | BEST_EFFORT | VOLATILE | KEEP_LAST(1) | 50ms |

| /responsibility | RELIABLE | TRANSIENT_LOCAL | KEEP_ALL | 1000ms |

The /cmd_vel_gated topic uses RELIABLE reliability with a 10ms deadline to ensure that no velocity command is dropped — a dropped command in a fail-closed system must be treated as a HALT. The /conflict_heatmap uses BEST_EFFORT because it is advisory information that does not affect safety if occasionally dropped.

7.7 Coordinate System Mapping

The MARIA OS G.U.P.Z.A coordinate system maps to ROS2 entities as follows:

| MARIA Coordinate | ROS2 Entity | Example |

| --- | --- | --- |

| Galaxy (G) | DDS Domain | G1 -> Domain 42 |

| Universe (U) | Namespace prefix | U1 -> /safety, U2 -> /regulatory |

| Planet (P) | Node group | P3 -> /warehouse/floor_3 |

| Zone (Z) | Lifecycle node | Z1 -> /warehouse/floor_3/zone_a |

| Agent (A) | Component node | A1 -> /warehouse/floor_3/zone_a/robot_01 |

This mapping enables MARIA OS governance queries to resolve directly to ROS2 entities. A governance command targeting G1.U1.P3.Z1.A1 translates to a ROS2 service call at /safety/warehouse/floor_3/zone_a/robot_01/maria/evaluate_action.

8. Integration: Physical-Capital Multi-Universe and Autonomous Industrial Holding

8.1 The Physical-Capital Convergence

The five research themes presented in Sections 3-7 address individual aspects of responsible robot judgment. In deployment, they must operate as an integrated system within larger organizational structures. We identify two integration scenarios that represent near-term deployment targets: the Physical-Capital Multi-Universe (a single facility where robots and financial systems share governance infrastructure) and the Autonomous Industrial Holding (a multi-facility enterprise where robot fleets across locations are governed by a unified judgment architecture).

8.2 Physical-Capital Multi-Universe

Consider a large warehouse operated by an e-commerce company. The warehouse contains 200 mobile robots (picking, packing, transporting), 50 human workers, and a financial management system that controls inventory procurement, labor scheduling, and shipping cost optimization. Today, the robot governance system and the financial governance system are entirely separate — the robot fleet management software has no concept of procurement cost, and the procurement system has no concept of robot utilization.

The Physical-Capital Multi-Universe extends the five robot evaluation universes with additional capital universes:

$ \mathbf{U}_{\text{PC}} = (\underbrace{U_S, U_R, U_E, U_{Eth}, U_{HC}}_{\text{Physical}}, \underbrace{U_{\text{Cost}}, U_{\text{Revenue}}, U_{\text{Risk\_Fin}}}_{\text{Capital}}) $

An action candidate — say, dispatching 20 additional robots to the packing area during a demand surge — is evaluated across all eight universes simultaneously. The Safety Universe checks that the increased robot density does not create collision risks. The Human Comfort Universe evaluates whether the human workers in the packing area will be overwhelmed by robot proximity. The Cost Universe evaluates the energy and wear costs of the additional robot dispatches. The Revenue Universe evaluates the expected revenue increase from faster order fulfillment.

The gate function extends naturally:

$ G_{\text{PC}}(\mathbf{s}) = G(s_S, s_R, s_E, s_{Eth}, s_{HC}) \wedge G_{\text{capital}}(s_{\text{Cost}}, s_{\text{Revenue}}, s_{\text{Risk\_Fin}}) $

where the physical gate and the capital gate must both PERMIT for the action to proceed. If the physical gate returns HALT (too many robots create a safety hazard), the action is halted regardless of its financial benefit. If the capital gate returns HALT (the cost exceeds the budget), the action is halted regardless of its efficiency improvement. Fail-closed is maintained across both physical and capital dimensions.

8.3 Autonomous Industrial Holding

At the enterprise level, an Autonomous Industrial Holding operates multiple facilities, each with its own robot fleet and local governance system. The MARIA OS Galaxy-level coordinate G provides the organizational boundary. Each facility is a Universe U_k with its own set of Planets (functional domains), Zones (operational units), and Agents (individual robots).

The key governance challenge at the holding level is cross-facility responsibility attribution. When a robot at Facility A causes a delay that cascades to Facility B's delivery schedule, the Responsibility Matrix must span both facilities. We extend the responsibility vector to include cross-facility responsibility:

$ \mathbf{\rho}_{\text{cross}}^i = (\rho_H^i, \rho_R^i, \rho_S^i, \rho_E^i, \rho_{\text{upstream}}^i, \rho_{\text{downstream}}^i) \in [0,1]^6 $

where rho_upstream^i quantifies the responsibility of upstream facilities and rho_downstream^i quantifies the responsibility of downstream facilities, subject to the extended conservation constraint sum_k rho_k^i = 1.

The Conflict Heatmap at the holding level aggregates facility-level heatmaps into a facility interaction graph where edges represent inter-facility dependencies and edge weights represent cross-facility conflict intensity. A high conflict intensity between Facility A and Facility B indicates that their robot operations are interfering with each other's objectives, requiring coordination at the Galaxy level.

8.4 Hierarchical Gate Propagation

Gate decisions propagate hierarchically through the MARIA OS coordinate system:

$ G_{\text{Galaxy}} \to G_{\text{Universe}} \to G_{\text{Planet}} \to G_{\text{Zone}} \to G_{\text{Agent}} $

A HALT at the Galaxy level (e.g., a facility-wide safety lockdown) propagates down to all Agents. A HALT at the Agent level (e.g., a single robot encountering an obstacle) affects only that Agent. The propagation direction is always top-down for HALT and bottom-up for ESCALATE.

$ G_C(\mathbf{s}) = \min\left(G_G(\mathbf{s}_G), G_U(\mathbf{s}_U), G_P(\mathbf{s}_P), G_Z(\mathbf{s}_Z), G_A(\mathbf{s}_A)\right) $

where the min operation maps {PERMIT=2, ESCALATE=1, HALT=0} to integers and returns the most restrictive gate decision in the hierarchy. Any ancestor's HALT overrides any descendant's PERMIT.

9. Experimental Design

9.1 Simulation Environments

We design experiments across three robot deployment scenarios that collectively cover the key challenges of physical-world governance: spatial navigation with human coexistence, precision manipulation with irreversibility, and urban operation with regulatory complexity.

Scenario 1: Warehouse Logistics (WL). A simulated warehouse environment with 200 mobile robots, 50 human workers, 10,000 shelf units arranged in a grid layout, and continuous pick-pack-ship operations. The simulation runs in Gazebo with ROS2 Humble, using Nav2 for robot navigation and custom task allocation. Key metrics: throughput (orders per hour), safety incidents (collision count), human comfort violations (personal space invasions), and governance overhead (latency added by gate evaluation).

Scenario 2: Surgical Assistance (SA). A simulated surgical environment with a 7-DOF robotic arm assisting in laparoscopic procedures. The simulation uses MoveIt2 for motion planning with force-torque feedback. The robot hands instruments, retracts tissue, and positions camera viewpoints. Key metrics: task completion accuracy (position error mm), force limit violations (N), ethical compliance (patient consent boundary maintenance), and governance overhead.

Scenario 3: Autonomous Delivery (AD). A simulated urban delivery scenario with 50 delivery robots navigating sidewalks, crosswalks, and building entrances. The simulation uses a custom urban environment in Gazebo with pedestrian models, traffic signals, and regulatory zones (school zones, hospital zones, construction zones). Key metrics: delivery time (minutes), pedestrian interactions (yielding compliance), regulatory violations (speed in restricted zones), noise complaints, and governance overhead.

9.2 Baseline Comparisons

We compare the MARIA OS Robot Judgment Architecture against four baselines:

• No Governance (NG): Raw ROS2 planning with no additional evaluation. Actions are executed as soon as the planner produces them, subject only to kinematic/dynamic feasibility.
• Threshold Safety (TS): Standard safety-only evaluation where actions are halted only if they violate a single safety threshold (e.g., minimum distance to human < 0.5m). No multi-universe evaluation, no conflict detection, no responsibility attribution.
• Multi-Objective Planner (MO): A Pareto-optimal planner that considers safety, efficiency, and comfort as objectives in the planning cost function. No gates, no fail-closed behavior — the planner produces the best compromise but cannot halt if no good compromise exists.
• Rule-Based Governance (RB): A rule engine with 200+ hand-crafted rules covering common scenarios (e.g., 'IF human_distance < 1m AND speed > 0.5m/s THEN halt'). No mathematical scoring, no continuous evaluation, no responsibility attribution.

9.3 Metrics

| Metric | Symbol | Unit | Goal |

| --- | --- | --- | --- |

| Gate evaluation latency | T_gate | ms | < 8ms |

| Conflict detection rate | CDR | % | > 99% |

| Safety incident rate | SIR | per 1000 hrs | < 0.1 |

| Ethical drift (KL-divergence) | D_ethical | nats | < 0.03 |

| Responsibility attribution completeness | RAC | % | 100% |

| Throughput overhead | TO | % | < 5% |

| False HALT rate | FHR | % | < 1% |

| Escalation rate | ER | per 1000 decisions | < 10 |

9.4 Experimental Protocol

Each scenario runs for 1000 simulated hours (approximately 41.7 days) with the following data collection:

• Decision logs recorded at every decision node (expected: ~10^7 decision nodes per scenario)
• Universe scores recorded for all five universes at every decision node
• Gate decisions (PERMIT/HALT/ESCALATE) recorded with timestamps
• Conflict heatmaps recorded at 1Hz for visualization and analysis
• Responsibility vectors recorded at every decision node
• Ethical drift statistics computed with a sliding window of W = 1000 decisions

Statistical significance is assessed using the Mann-Whitney U test for non-parametric comparisons between MARIA and baselines, with Bonferroni correction for multiple comparisons. We report 95% confidence intervals for all primary metrics.

10. Results

10.1 Gate Evaluation Latency

The gate evaluation latency was measured across all three scenarios with the following results:

| Scenario | Mean T_gate (ms) | P95 T_gate (ms) | P99 T_gate (ms) | Max T_gate (ms) |

| --- | --- | --- | --- | --- |

| Warehouse Logistics | 2.34 | 3.12 | 4.87 | 6.91 |

| Surgical Assistance | 2.78 | 3.89 | 5.23 | 7.44 |

| Autonomous Delivery | 2.51 | 3.45 | 5.01 | 7.12 |

All scenarios maintained worst-case gate evaluation latency below 8ms. The Surgical Assistance scenario exhibited higher latency due to the more complex Ethics Universe evaluation (patient consent boundary checking requires spatial reasoning in the surgical workspace). The maximum observed latency of 7.44ms occurred during a high-complexity surgical procedure with three simultaneous ethical constraints active.

10.2 Conflict Detection and Resolution

| Scenario | Total Conflicts | Detected | CDR | Resolution Breakdown |

| --- | --- | --- | --- | --- |

| WL | 45,230 | 44,868 | 99.2% | Pareto: 72%, Override: 18%, Defer: 8%, Escalate: 2% |

| SA | 12,450 | 12,398 | 99.6% | Pareto: 45%, Override: 40%, Defer: 5%, Escalate: 10% |

| AD | 89,120 | 88,347 | 99.1% | Pareto: 65%, Override: 20%, Defer: 10%, Escalate: 5% |

The conflict detection rate exceeded 99% in all scenarios. The undetected conflicts (0.4-0.9%) were analyzed and found to be cases where the ConflictScore was just below the detection threshold tau_CS — none of the undetected conflicts resulted in safety incidents, indicating that the threshold is slightly conservative but safe.

The Surgical Assistance scenario showed the highest escalation rate (10%) due to the severity of surgical decision consequences. The Warehouse Logistics scenario showed the highest total conflict count due to the dense robot-human interaction environment.

10.3 Safety Comparison Against Baselines

| System | WL SIR | SA SIR | AD SIR |

| --- | --- | --- | --- |

| No Governance | 4.82 | 8.21 | 6.34 |

| Threshold Safety | 0.94 | 2.13 | 1.67 |

| Multi-Objective Planner | 0.52 | 1.44 | 0.89 |

| Rule-Based Governance | 0.31 | 0.87 | 0.45 |

| MARIA Robot Judgment | 0.04 | 0.08 | 0.06 |

MARIA Robot Judgment achieved Safety Incident Rates (per 1000 hours) that were 7.75x lower than the Rule-Based Governance baseline (the next best system) in the Warehouse Logistics scenario, 10.9x lower in Surgical Assistance, and 7.5x lower in Autonomous Delivery. The improvement over No Governance was 120x, 102x, and 105x respectively.

The key differentiator was the Multi-Universe evaluation: incidents that occurred with Rule-Based Governance were typically situations where safety was preserved but human comfort was violated (leading to human behavioral changes that indirectly caused safety incidents). The Human Comfort Universe in MARIA detected these indirect risk factors and prevented the root cause.

10.4 Ethical Drift Monitoring

The ethical drift D_ethical was monitored continuously across all scenarios. With the Embodied Ethics Calibration Model active:

| Scenario | Mean D_ethical | Max D_ethical | Corrections Triggered | Time to Correction |

| --- | --- | --- | --- | --- |

| WL | 0.012 | 0.028 | 7 | 4.2 min avg |

| SA | 0.008 | 0.019 | 3 | 2.1 min avg |

| AD | 0.015 | 0.029 | 12 | 5.8 min avg |

All scenarios maintained D_ethical below the 0.03 threshold. The Autonomous Delivery scenario triggered the most corrections (12) due to the highest environmental non-stationarity (changing pedestrian densities, weather conditions, time-of-day effects). Each correction was logged through the MARIA OS Decision Pipeline with full traceability.

Without the calibration model (ablation study), D_ethical grew monotonically as predicted by Theorem 4, reaching 0.15 in WL, 0.09 in SA, and 0.22 in AD after 1000 hours. This confirms that ethical drift is a real phenomenon in deployed robots and that active correction is necessary.

10.5 Responsibility Attribution

Responsibility attribution completeness was 100% across all scenarios — every decision node had a fully computed responsibility vector summing to 1.0. The aggregate responsibility distributions were:

| Scenario | bar_rho_H | bar_rho_R | bar_rho_S | bar_rho_E |

| --- | --- | --- | --- | --- |

| WL | 0.12 | 0.61 | 0.08 | 0.19 |

| SA | 0.34 | 0.42 | 0.11 | 0.13 |

| AD | 0.08 | 0.55 | 0.12 | 0.25 |

The Surgical Assistance scenario showed the highest human responsibility share (0.34) due to the high frequency of ESCALATE decisions requiring surgeon approval. The Autonomous Delivery scenario showed the highest environmental responsibility share (0.25) due to the unpredictability of urban environments. These distributions align with intuitive expectations and provide quantitative evidence for governance calibration.

10.6 Throughput Overhead

| Scenario | Baseline Throughput | MARIA Throughput | Overhead |

| --- | --- | --- | --- |

| WL | 847 orders/hr | 812 orders/hr | -4.1% |

| SA | 12.4 procedures/hr | 11.9 procedures/hr | -4.0% |

| AD | 340 deliveries/hr | 328 deliveries/hr | -3.5% |

The throughput overhead was below 5% in all scenarios. The overhead comes from two sources: gate evaluation latency (which delays individual actions by 2-3ms, cumulating over thousands of decisions) and conflict resolution rerouting (which increases path lengths for some actions). The overhead is the price of responsibility-bounded judgment, and it is a modest price compared to the 100x+ safety improvement.

11. Discussion

11.1 Fail-Closed in the Physical World: Feasibility Confirmed

The central research question of this paper — can fail-closed gate evaluation be maintained within physical-world real-time constraints? — is answered affirmatively by the experimental results. The Robot Gate Engine completes evaluation within 8ms in all tested scenarios, including worst-case conditions with multiple simultaneous constraint evaluations. The key insight is that fail-closed does not require slow evaluation; it requires correct evaluation. The parallel universe architecture ensures that evaluation time scales with the slowest universe (not the sum of all universes), and pre-computed feature extraction ensures that each universe operates on O(1) or O(log n) data structures rather than raw sensor data.

11.2 The Multi-Universe Advantage

The 7.5-10.9x safety improvement over Rule-Based Governance (the strongest non-MARIA baseline) demonstrates the value of multi-dimensional evaluation. Rule-based systems can enumerate known-dangerous scenarios but cannot detect novel combinations of individually-safe conditions that create emergent danger. The Multi-Universe architecture detects these emergent dangers because the tension between universes (captured by the ConflictScore) is a continuous signal that responds to any combination of conditions, not just pre-enumerated ones.

The Ethics and Human Comfort universes, which have no analog in traditional robot safety systems, proved critical for preventing indirect safety incidents. In the Warehouse Logistics scenario, 23% of incidents in the Rule-Based baseline were caused by human workers making unexpected movements in response to robot behavior that was physically safe but psychologically distressing (e.g., a robot accelerating rapidly toward a human, then stopping at the minimum safe distance). The Human Comfort Universe detected these situations and reduced robot speed before the human became distressed, eliminating the cascade from discomfort to unpredictable human behavior to safety incident.

11.3 Embodied Ethics: From Theory to Measurement

The Embodied Ethics Calibration Model transforms ethical compliance from a design-time property ('the robot was programmed to be ethical') to a runtime observable ('the robot's behavior currently deviates from its ethical policy by D_ethical = 0.012 nats'). This shift has profound implications for robot certification and liability. A robot manufacturer can demonstrate not just that the robot was designed with ethical constraints but that those constraints are continuously monitored and corrected in deployment.

The drift monotonicity result (Theorem 4) is particularly important: it proves that ethical drift is not a possible failure mode but an inevitable one in non-stationary environments. Any deployed robot without active drift correction will eventually deviate from its ethical constraints, no matter how carefully those constraints were encoded at design time. This argues strongly for regulatory mandates requiring active ethical monitoring in deployed robot systems.

11.4 Responsibility Attribution: Legal and Regulatory Implications

The Robotic Responsibility Protocol provides a quantitative framework that could transform robot accident investigation. Currently, accident attribution in robotics follows the same ad-hoc process used for traditional industrial accidents, with expert witnesses providing qualitative opinions about causation. The Responsibility Matrix provides a quantitative, pre-computed, and continuously monitored alternative.

The legal implications are significant. If the Responsibility Matrix shows that rho_H = 0.05 at the critical decision node (the human had almost no oversight capability), a product liability claim against the manufacturer becomes stronger because the system was designed to operate with minimal human oversight for that class of decisions. Conversely, if rho_H = 0.85 (the human had full information, intervention capability, and chose to approve the action), the human operator bears the primary responsibility. These quantitative attributions do not replace legal judgment, but they provide the evidentiary foundation that legal judgment can operate on.

11.5 Scalability Considerations

The Layered Robot Judgment Architecture adds one ROS2 lifecycle node per robot (the MARIA Bridge Node), five parallel evaluation threads per robot, and approximately 2KB/s of additional message traffic per robot. For a 200-robot warehouse, this is 200 nodes, 1000 evaluation threads, and 400KB/s of additional traffic — well within the capacity of a modern DDS network and a standard server rack.

The Conflict Heatmap computation scales with workspace area, not robot count. A 10,000 m^2 warehouse at 1m resolution requires a 100x100 heatmap — the same computation regardless of whether there are 10 or 1000 robots in the space. Robot count affects only the sensor input to the heatmap (more robots mean more dynamic obstacles), not the heatmap computation itself.

11.6 Limitations

Several limitations must be acknowledged:

• Simulation gap: All experiments were conducted in simulation (Gazebo). Physical-world deployment may reveal latency sources not captured in simulation, such as hardware interrupt jitter, network congestion, and thermal throttling of embedded GPUs.
• Universe completeness: The five evaluation universes cover the primary dimensions of physical-world robot judgment, but additional universes may be needed for specific domains (e.g., a Sterility Universe for surgical robots, a Traffic Law Universe for delivery robots in specific jurisdictions).
• Ethical policy specification: The Embodied Ethics Calibration Model assumes that pi_stated is a well-defined probability distribution over actions. In practice, ethical constraints are often specified as natural-language rules that must be formalized into distributions — this formalization step is a potential source of error.
• Adversarial robustness: The noise-robust threshold (Theorem 3) assumes Gaussian sensor noise. Adversarial attacks that inject non-Gaussian perturbations could potentially fool the gate evaluation. Adversarial robustness of the Robot Gate Engine is a topic for future work.
• Computational requirements: The parallel universe evaluation requires a multi-core embedded processor (at minimum 6 cores: 5 for universe evaluation + 1 for gate aggregation). Single-core embedded platforms cannot support the architecture as designed.

11.7 Future Directions

Several promising extensions emerge from this work:

• Adaptive universe thresholds: Learning optimal threshold configurations from deployment data, rather than setting them manually. This connects to the dynamic gate adaptation work in [25].
• Cross-robot conflict heatmaps: Extending the conflict heatmap to capture conflicts between robots (not just between a single robot's objectives), enabling fleet-level conflict avoidance.
• Federated ethical learning: Training the Embodied Ethics Calibration Model across a fleet of robots in different facilities, sharing ethical corrections without sharing raw sensor data.
• Hardware safety certification: Pursuing IEC 61508 SIL-3 certification for the Robot Gate Engine hardware implementation, enabling deployment in safety-critical industrial applications.
• Natural-language responsibility reports: Generating human-readable explanations of the Responsibility Matrix for non-technical stakeholders (insurers, regulators, juries).

12. Conclusion

This paper has presented a comprehensive framework for bringing responsibility-bounded judgment to physical-world robotic systems. The five contributions — Robot Gate Engine, Real-Time Conflict Heatmap, Embodied Ethics Calibration Model, Robotic Responsibility Protocol, and Layered Robot Judgment Architecture — collectively demonstrate that the MARIA OS governance principles of Multi-Universe evaluation, fail-closed gates, and max_i scoring can be maintained under the extreme constraints of physical-world robotics: sub-10ms control loops, noisy sensor data, irreversible actuator commands, and embodied ethical drift.

The experimental results confirm three central claims:

1. Fail-closed is feasible in real-time: The Robot Gate Engine achieves worst-case evaluation latency below 8ms, within the control loop budget of industrial and service robots. The parallel universe architecture and pre-computed feature extraction are the key enablers. 2. Multi-Universe evaluation prevents emergent danger: The 7.5-10.9x safety improvement over rule-based governance demonstrates that multi-dimensional evaluation detects hazards that single-criterion and rule-based systems cannot, particularly indirect hazards mediated through human comfort and ethical compliance. 3. Responsibility is quantifiable and conserved: The Robotic Responsibility Protocol achieves 100% responsibility attribution completeness, with the conservation property (Theorem 6) ensuring that no portion of responsibility goes unassigned. This provides the evidentiary foundation for robot accident investigation and liability determination.

The Embodied Ethics Calibration Model addresses what we believe is the most underappreciated challenge in robot deployment: the inevitable drift of practiced behavior from stated ethical constraints in non-stationary environments (Theorem 4). Active ethical monitoring and correction is not an optional feature — it is a mathematical necessity for any robot that claims sustained ethical compliance.

The Layered Robot Judgment Architecture bridges MARIA OS and ROS2 without modifying either system, demonstrating that governance can be added to existing robot middleware stacks as a composable layer. This lowers the adoption barrier: organizations already using ROS2 can add MARIA OS governance without refactoring their existing robot software.

We close with the thesis that motivated this work: responsibility-bounded judgment is not only possible in the physical world — it is the prerequisite for any robot deployment that claims to be autonomous. A robot that can move but cannot explain why it moved, that can act but cannot attribute responsibility for its actions, that can learn but cannot detect when its learning has drifted from its ethical constraints — such a robot is not autonomous. It is unaccountable. And unaccountable automation is not a technology problem waiting for better algorithms. It is a governance problem waiting for better architecture. This paper provides that architecture.

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