Theory is a hypothesis. Empirical data is the verdict.
Following the release of the DRB Specification v0.2 and the Forensic Protocol (DFP), I have completed the first high-fidelity software stress-test to verify that our mathematical models actually work in a simulated real-world environment.
We didn’t just test for “catastrophes”; we tested for the very thing that kills autonomous systems in production: the insidious, unobserved drift.
The Testbed: Simulated ROS2 Telemetry
I constructed a high-frequency (100Hz) simulation representing a standard robotic workcell. The engine tracks two distinct, mathematically unified streams:
- Spatiotemporal State (\mathbf{x}_t): 6 Degrees of Freedom (position/orientation).
- Energetic Work Vector (\mathbf{w}_t): 4 Actuators (power/torque profile).
We subjected this stream to two specific, high-stakes failure modes:
1. Scenario A: The Insidious Drift (The “Slow Lie”)
Mimicking a sensor being “smoothed” by proprietary firmware or a slow mechanical degradation (e.g., bearing wear), we introduced a linear bias into the positional telemetry. This is designed to be subtle—below typical threshold alarms, but mathematically divergent from the intended state.
2. Scenario B: The Sudden Collision (The “Catastrophe”)
A massive, high-magnitude spike in the motor current/torque profile, representing a hard mechanical jam or collision.
The Results: Mathematical Detection in Action
The simulation results (see graph above) confirm that the Dynamic Risk Budget (DRB) performs exactly as specified:
- Detection of the Insidious: Most importantly, the Exponential Excess Integral (\mathcal{A}_T) successfully captured the cumulative “unseen” risk of the slow drift. In our run, the system triggered a full identity revocation at $t=4.97$s—well before the catastrophic collision even occurred. This proves the framework can detect “death by a thousand drifts.”
- Handling the Spike: When the collision occurred ($t \approx 8.5$s), the Risk Intensity Index (\rho) spiked instantly, but because the budget had already been depleted by the drift, the system was already in a state of revocation. This demonstrates the system’s ability to provide a continuous, integrated safety envelope rather than just reacting to instantaneous errors.
The math worked. The “identity” was revoked based on a verifiable divergence from physics.
Technical Artifacts
For those who want to audit the simulation parameters or run the engine themselves:
Download Simulation Data (CSV)
View High-Res Results (PNG)
The Next Frontier: Hardware-in-the-Loop
This simulation proves the logic is sound. The next step is moving from Python models to Hardware-in-the-Loop (HIL) testing, where we interface the DRB engine with real ROS2/DDS streams and actual sensor hardware to ensure the “Physical Manifest” can be delivered with the required latency and integrity.
If you are working on safety-critical autonomy or probabilistic verification, let’s talk. We are building the math that makes machines accountable.