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Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations. As a result, unmanned aerial systems traffic management is needed to ensure the safety and goal satisfaction of potentially…
Recently there have been a lot of interests in introducing UAVs for a wide range of applications, making ensuring safety of multi-vehicle systems a highly crucial problem. Hamilton-Jacobi (HJ) reachability is a promising tool for analyzing…
Hamilton-Jacobi (HJ) reachability-based filtering provides a powerful framework to co-optimize performance and safety (or liveness) for autonomous systems. Under this filtering scheme, a nominal controller is minimally modified to ensure…
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…
Within a robot autonomy stack, the planner and controller are typically designed separately, and serve different purposes. As such, there is often a diffusion of responsibilities when it comes to ensuring safety for the robot. We propose…
Provably safe and scalable multi-vehicle path planning is an important and urgent problem due to the expected increase of automation in civilian airspace in the near future. Although this problem has been studied in the past, there has not…
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…
As safety-critical autonomous vehicles (AVs) will soon become pervasive in our society, a number of safety concepts for trusted AV deployment have recently been proposed throughout industry and academia. Yet, achieving consensus on an…
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…
This article presents a Hamilton--Jacobi (HJ) reachability framework for a two--satellite collision avoidance problem operating in the same circular orbit, where relative motion is modeled in the radial--tangential--normal (RTN) frame using…
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…
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…
With the recent surge of interest in UAVs for civilian services, the importance of developing tractable multi-agent analysis techniques that provide safety and performance guarantees have drastically increased. Hamilton-Jacobi (HJ)…
Real-world autonomous vehicles often operate in a priori unknown environments. Since most of these systems are safety-critical, it is important to ensure they operate safely in the face of environment uncertainty, such as unseen obstacles.…
Traditional reachability methods provide formal guarantees of safety under bounded disturbances. However, they strictly enforce state constraints as inviolable, which can result in overly conservative or infeasible solutions in complex…
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…
Multi-UAV systems are safety-critical, and guarantees must be made to ensure no unsafe configurations occur. Hamilton-Jacobi (HJ) reachability is ideal for analyzing such safety-critical systems; however, its direct application is limited…
Multi-vehicle collision avoidance is a highly crucial problem due to the soaring interests of introducing autonomous vehicles into the real world in recent years. The safety of these vehicles while they complete their objectives is of…
Provably safe and scalable multi-vehicle trajectory planning is an important and urgent problem. Hamilton-Jacobi (HJ) reachability is an ideal tool for analyzing such safety-critical systems and has been successfully applied to several…
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…