Real-Time Hamilton-Jacobi Reachability Analysis of Autonomous System With An FPGA

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.