Real-Time GPU-Accelerated Monte Carlo Evaluation of Safety-Critical AEB Systems Under Uncertainty

The gist The framework demonstrates that GPU-accelerated Monte Carlo simulation can provide a deployable runtime component for uncertainty-aware Automatic Emergency Braking (AEB) evaluation, establishing a scalable computational foundation for risk-aware AEB threshold selection under NHTSA regulations.

Problem Formulation and Model Fidelity

The work evaluates the stopping-distance distribution of a passenger vehicle undergoing emergency braking under uncertainty through Monte Carlo simulation The point-mass longitudinal model employed in this work provides an appropriate abstraction for braking-distance evaluation This model captures dominant stopping-distance variability sources: aerodynamic drag, road grade, actuator lag, and weight transfer The system state is defined as x(t) = [x(t), v(t), abrake,actual(t)] The longitudinal acceleration during braking is governed by aerodynamic drag, gravitational effects due to road grade, and the realized braking deceleration The complete system evolves according to dx/dt = v, dv/dt = atotal(v, θ), dabrake,actual = 1/τ(abrake,cmd - abrake,actual)

Monte Carlo Framework and Uncertainty Representation

The Monte Carlo framework is used to propagate parameter uncertainty through the nonlinear braking dynamics Several model parameters are treated as random variables, including initial speed, road grade, aerodynamic drag coefficient, vehicle mass, tire-road friction coefficient, and actuator time constant For each realization ξ(i), the system dynamics are integrated from the initial state until the vehicle stops to produce an independent stopping-distance sample D(i)stop The simulation parameters include a fixed integration time step ∆t = 0.001 s, maximum simulation horizon Tmax = 10 s, and commanded braking deceleration abrake,cmd = −6.0 m/s2 Uncertainty is modeled using independent normal random variables for parameters such as v0 ∼ N (30.0, 2.0 2) m/s

GPU Implementation and Parallelization Strategy

The GPU implementation is suited for parallel execution because each rollout is independent The parallelization strategy employs a one-thread-per-sample strategy, where each Monte Carlo rollout is assigned to a single GPU thread The GPU kernel proceeds through the sequence of loading the sampled parameter vector ξ(i) from global memory, initializing the state vector x(0), integrating the nonlinear dynamics using a fixed-step fourth-order Runge-Kutta (RK4) integrator until zero speed is reached, and writing the resulting stopping distance to an output array indexed by the thread identifier This design ensures that the GPU implementation uses: the same parameter samples generated deterministically on the CPU, achieving bit-exact numerical correspondence

Performance and Real-Time Feasibility Analysis

The computational complexity for both CPU and GPU implementations is O(N), where N is the number of Monte Carlo samples The speedup factor S = TCPU/TGPU depends on parallelism, overhead amortization, memory bandwidth, and occupancy Performance scaling exhibits three characteristic regimes: kernel-overhead dominance at N ≤ 10,000, linear scaling between 10,000 155k The framework's real-time feasibility analysis uses a timing budget where the Monte Carlo budget is set to 530 ms after accounting for perception processing (120 ms) and decision logic (50 ms) overhead With this budget, the Jetson AGX Orin can execute up to N ≈ 25,000 samples within the 530 ms Monte Carlo budget

Risk-Aware Decision Making and Conclusion

The collision probability is defined as P(collision H0) = P(Dstop > H0), representing the fraction of uncertain scenarios in which the ego vehicle cannot stop before reaching the lead vehicle Evaluating this over a range of headway distances yields a collision-risk curve that informs AEB threshold selection For the simulated braking scenario, minimum safe headways are determined, such as 5% risk requiring H0 = 100.6 m The demonstrated acceleration and cross-platform consistency establish a computational foundation for NHTSA-compliant AEB evaluation This capability simplifies regression testing, certification documentation, and compliance verification under the NHTSA AEB final rule The framework separates the dynamics model from the simulation backend and enforces deterministic CPU-GPU consistency This enables uncertainty-aware AEB threshold calibration and probabilistic braking risk estimation under parameter uncertainty. The results establish Monte Carlo–based uncertainty evaluation as a deployable runtime component rather than an offline validation tool.

Future Work

A next step is incorporation of dynamic leadvehicle motion and time-varying headway within the Monte Carlo simulation loop to enable closed-loop evaluation Incorporating perception effects such as sensing latency, measurement noise, dropout, and occlusion would enhance realism Kernel-level optimizations may reduce execution time without compromising numerical fidelity The framework can be extended to broader probabilistic safety-evaluation tasks including closed-loop AEB controller assessment and rare-event simulation.

References

[1] National Highway Traffic Safety Administration, “Federal motor vehicle safety standards; automatic emergency braking systems for light vehicles: Final rule,” Federal Register, 89 FR 40118, 2024, fMVSS No. 127, published May 9, 2024

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[4] International Organization for Standardization, “Iso 22737: Intelligent transport systems — pedestrian automatic emergency braking systems — performance requirements and test procedures,” 2021, standard

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[6] C. Stockle, W. Utschick, S. Herrmann, and T. Dirndorfer, “Robust design ¨ of an automatic emergency braking system considering sensor measurement errors,” in 2018 21st International Conference on Intelligent Transportation Systems (ITSC)

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1. Bold header: Develop a risk-aware AEB threshold selection mechanism based on collision probability curves. This allows for quantitative risk-aware AEB threshold selection for multiple safety margins by deriving P(Dstop > H0) from stopping-distance distributions, enabling engineers to set headways based on desired risk tolerance (e.g., 5% risk (aggressive)).

2. Bold header: Implement a unified, bit-exact validation workflow across development and deployment environments. The framework ensures this by achieving exact numerical agreement between CPU and GPU outputs across all hardware platforms, simplifying regression testing for NHTSA compliance.

3. Bold header: Enable real-time probabilistic AEB evaluation within the embedded pipeline. The system can execute approximately 25,000 Monte Carlo samples within a 530 ms budget on automotive-grade platforms like the Jetson AGX Orin, making uncertainty quantification a deployable runtime component.

4. Bold header: Enhance perception robustness by incorporating stochastic sensing uncertainties. By including sensing latency, measurement noise, dropout, and occlusion, the system can evaluate AEB behavior under these conditions to improve performance beyond deterministic TTC thresholds.

5. Bold header: Provide closed-loop uncertainty evaluation for lead-vehicle dynamics. Extending the framework to incorporate dynamic leadvehicle motion and time-varying headway would allow for closedloop evaluation where uncertainty in lead-vehicle behavior propagates through the braking trajectory.