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Recent literature has proposed approaches that learn control policies with high performance while maintaining safety guarantees. Synthesizing Hamilton-Jacobi (HJ) reachable sets has become an effective tool for verifying safety and…
Hamilton-Jacobi (HJ) reachability analysis has been developed over the past decades into a widely-applicable tool for determining goal satisfaction and safety verification in nonlinear systems. While HJ reachability can be formulated very…
Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical control systems. Its advantages include compatibility with general nonlinear system…
Hybrid dynamical systems with nonlinear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of nonlinear…
Hamilton-Jacobi (HJ) reachability analysis is a widely adopted verification tool to provide safety and performance guarantees for autonomous systems. However, it involves solving a partial differential equation (PDE) to compute a safety…
With the recent surge of interest in introducing autonomous vehicles to the everyday lives of people, developing accurate and generalizable algorithms for predicting human behavior becomes highly crucial. Moreover, many of these emerging…
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…
Safety is an important topic in autonomous driving since any collision may cause serious injury to people and damage to property. Hamilton-Jacobi (HJ) Reachability is a formal method that verifies safety in multi-agent interaction and…
Autonomous spacecraft docking requires control policies that simultaneously ensure collision avoidance and target reachability under coupled, high-dimensional translational-rotational dynamics. Hamilton-Jacobi (HJ) reachability provides…
Hamilton-Jacobi (HJ) reachability analysis is a powerful framework for ensuring safety and performance in autonomous systems. However, existing methods typically rely on a white-box dynamics model of the system, limiting their applicability…
While we have made significant algorithmic developments to enable autonomous systems to perform sophisticated tasks, it remains difficult for them to perform tasks effective and safely. Most existing approaches either fail to provide any…
Road safety continues to be a pressing global issue, with vehicle collisions imposing significant human, societal, and economic burdens. Human-machine shared collision avoidance in critical collision scenarios aims to aid drivers' accident…
Learning-based approaches for controlling safety-critical systems are rapidly growing in popularity; thus, it is important to assure their performance and safety. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification…
Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…
Hamilton-Jacobi (HJ) reachability is a method that provides rigorous analyses of the safety properties of dynamical systems. This method has been successfully applied to many low-dimensional dynamical system models such as coarse models of…
Multi-agent differential games are important and useful tools for analyzing many practical problems. With the recent surge of interest in using UAVs for civil purposes, the importance and urgency of developing tractable multi-agent analysis…
Providing formal safety and performance guarantees for autonomous systems is becoming increasingly important. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for providing these guarantees, since it can…
Autonomous systems like aircraft and assistive robots often operate in scenarios where guaranteeing safety is critical. Methods like Hamilton-Jacobi reachability can provide guaranteed safe sets and controllers for such systems. However,…
Safety assurance is a fundamental requirement for deploying learning-enabled autonomous systems. Hamilton-Jacobi (HJ) reachability analysis is a fundamental method for formally verifying safety and generating safe controllers. However,…
Hamilton-Jacobi (HJ) reachability is a rigorous mathematical framework that enables robots to simultaneously detect unsafe states and generate actions that prevent future failures. While in theory, HJ reachability can synthesize safe…