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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…
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. Hamilton-Jacobi (HJ) reachability is an ideal tool for analyzing…
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…
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…
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…
We consider the problem of planning trajectories for a group of $N$ vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically,…
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…
We present a fast planning architecture called Hamilton-Jacobi-based bidirectional A* (HJBA*) to solve general tight parking scenarios. The algorithm is a two-layer composed of a high-level HJ-based reachability analysis and a lower-level…
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)…
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…
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…
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…
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…
Autonomous robots commonly aim to complete a nominal behavior while minimizing a cost; this leaves them vulnerable to failure or unplanned scenarios, where a backup or contingency plan to a safe set is needed to avoid a total mission…
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…
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 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…
Hamilton-Jacobi (HJ) reachability provides formal safety guarantees for dynamical systems, but solving high-dimensional HJ partial differential equations limits its use in real-time planning. This paper presents a contingency-aware…
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…
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…