Arrvindh Shriraman | Searcharxiv

arXiv2025

OptimizedDP: An Efficient, User-friendly Library For Optimal Control and Dynamic Programming

This paper introduces OptimizedDP, a high-performance software library for several common grid-based dynamic programming (DP) algorithms used in control theory and robotics. Specifically, OptimizedDP provides functions to numerically solve a class of time-dependent (dynamic) Hamilton-Jacobi (HJ) partial differential equations (PDEs), time-independent (static) HJ PDEs, and additionally value iteration for continuous action-state space Markov Decision Processes (MDP). The computational complexity of grid-based DP is exponential with respect to the number of grid or state space dimensions, and thus can have bad execution runtimes and memory usage whenapplied to large state spaces. We leverage the user-friendliness of Python for different problem specifications without sacrificing the efficiency of the core computation. This is achieved by implementing the core part of the code which the user does not see in heterocl, a framework we use to abstract away details of how computation is parallelized. Compared to similar toolboxes for level set methods that are used to solve the HJ PDE, our toolbox makes solving the PDE at higher dimensions possible as well as achieving an order of magnitude improvements in execution times, while keeping the interface easy for specifying different problem descriptions. Because of that, the toolbox has been adopted to solve control and optimization problems that were considered intractable before. Our toolbox is available publicly at https://github.com/SFU-MARS/optimized_dp.

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arXiv2020

Real-Time Formal Verification of Autonomous Systems With An FPGA

Hamilton-Jacobi reachability analysis is a powerful technique used to verify the safety of autonomous systems. This method is very good at handling non-linear system dynamics 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 a Field Programmable Gate Array (FPGA) could accelerate 4D grid-based Hamilton-Jacobi (HJ) reachability analysis up to 16 times compared to an optimized implementation and 142 times compared to MATLAB ToolboxLS on a 16-thread CPU. Our design can overcome the complex data access pattern while taking advantage of the parallel nature of the HJ PDE computation. Because of this, we are able to achieve real-time formal verification with a 4D car model by re-solving the HJ PDE at a frequency of 5Hz on the FPGA as the environment changes. The latency of our computation is deterministic, which is crucial for safetycritical systems. Our approach presented here can be applied to different systems dynamics, and moreover, potentially leveraged for higher dimensions systems. We also demonstrate obstacle avoidance with a robot car in a changing environment.

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