reachability analysis
USC CURVE fellowship
Faculty: Professor Somil Bansal
PhD mentor : Hao Wang
Collaborator: Peter Wang
This project focuses on Hamilton-Jacobi Reachability analysis. If you are unfamiliar with the topic, below are some good resources to get started.
Because this project is quite theoretical, it took me (as a sophomore) almost a whole semester to just understand the mathematical formulation and background knowledge of Reachability. Then familiarized with two toolboxes DeepReach and HelperOC to solve Reachability problems.
To fully comprehend DeepReach, I first implemented a simple 2D system. This pdf includes the problem description and the analytical solution of hamiltonian. Below are results obtained from DeepReach.
Understanding DeepReach code and its implementation, I worked on a project that aims to improve the performance of DeepReach on high-dimensional Reachability problems by exploiting different activation functions in the DNN.
Abstract:
With the continuous advancement in autonomous systems, it becomes crucial to provide robust safety guarantees for safety-critical systems. Hamilton-Jacobi Reachability Analysis is a formal verification method that guarantees performance and safety for dynamical systems and is widely applicable to various tasks and challenges. Traditionally, reachability problems are solved by using grid-based methods, whose computational and memory cost scales exponentially with the dimensionality of the system. To overcome this challenge, DeepReach, a deep learning-based approach that approximately solves high-dimensional reachability problems, is proposed and has shown lots of promise. In this paper, we aim to improve the performance of DeepReach on high-dimensional systems by exploring different choices of activation functions. We first run experiments on a 3D system as a proof of concept. Then we demonstrate the effectiveness of our approach on a 9D multi-vehicle collision problem.
The whole project is too much for this webpage. For more details, please check out the following:
Here again, I want to express my deep appreciation for Professor Bansal and PhD candidate Hao Wang for their huge support throughout this research project. Without them, this piece of work would be impossible. Also, thanks everyone in the SIA lab for helping and supporting each other, making this research experience so wonderful!
