Hamilton-Jacobi reachability: A brief overview and recent advances
By Somil Bansal, Mo Chen, Sylvia L. Herbert, Claire Jennifer Tomlin. IEEE Conference on Decision and Control, 2017
762 citations recorded by the source corpus.
Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical systems; it has been applied to many small-scale systems in the past decade. Its advantages include compatibility with general nonlinear system dynamics, formal treatment of bounded disturbances, and the availability of well-developed numerical tools. The main challenge is addressing its exponential computational complexity with respect to the number of state variables. In this tutorial, we present an overview of basic HJ reachability theory and provide instructions for using the most recent numerical tools, including an efficient GPU-parallelized implementation of a Level Set Toolbox for computing reachable sets. In addition, we review some of the current work in high-dimensional HJ reachability to show how the dimensionality challenge can be alleviated via various general theoretical and application-specific insights.
Subfields: Artificial Intelligence, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/2d0fc3b6c8bca95f290c05ff5c64235e4c06fad4
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In Computational Theory and Mathematics
Citations in the corpus
- Safe Control With Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction Methods for Robotics and Control (2022, methodology): “In particular, safe RL [25] and HJ reachability [24] have received a large amount of research interest in recent years.”
- Recovery RL: Safe Reinforcement Learning With Learned Recovery Zones (2020, methodology): “First, inspired by recent work in robust control [4, 11, 13, 21], we represent the RL agent with two policies: the first policy focuses on optimizing the unconstrained task objective (task policy) and the second policy takes control when the task policy is in danger of constraint violations in the…”