Real-Time Hamilton-Jacobi Reachability Analysis of Autonomous System With An FPGA
Bibliographic record
Abstract
Hamilton-Jacobi (HJ) reachability analysis is a powerful technique used to verify the safety of autonomous systems. HJ reachability is ideal for analysing nonlinear systems with disturbances and flexible set representations. A drawback to this approach is that it suffers from the curse of dimensionality, which prevents real-time deployment on safety-critical systems. In this paper, we show that a customized hardware design on an Field Programmable Gate Array (FPGA) could accelerate 4D grid-based HJ reachability analysis up to 14 times compared to an optimized implementation and 103 times compared to state-of-the-art MATLAB toolboxes on a 16-thread CPU. Because of this, we are able to achieve guaranteed real- time collision avoidance in dynamic environments that abruptly change with a 4D car model by re-solving the HJ partial differential equation (PDE) at a frequency of 4Hz on an FPGA. Our design can overcome the complex data access pattern while taking advantage of the parallel nature of the computations for solving the HJ PDE. The low latency of our computation is consistent, which is crucial for safety-critical systems. The methodology presented here is without loss of generality: it can potentially be applied to different systems dynamics, and more- over, leveraged for higher dimensional systems. We validate our approach in real world collision avoidance experiments with a robot car in a changing environment. We also provide the code of our hardware design and an AWS AFI image.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".