Related papers: Reachability Analysis for Black-Box Dynamical Syst…
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…
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…
Contact-rich robotic systems, such as legged robots and manipulators, are often represented as hybrid systems. However, the stability analysis and region-of-attraction computation for these systems are often challenging because of the…
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…
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…
Real-world autonomous systems often employ probabilistic predictive models of human behavior during planning to reason about their future motion. Since accurately modeling human behavior a priori is challenging, such models are often…
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…
The Hopf formula for Hamilton-Jacobi reachability (HJR) analysis has been proposed to solve high-dimensional differential games, producing the set of initial states and corresponding controller required to reach (or avoid) a target despite…
Safety is a central requirement for autonomous system operation across domains. Hamilton-Jacobi (HJ) reachability analysis can be used to construct "least-restrictive" safety filters that result in infrequent, but often extreme, control…
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…
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…
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…
Ensuring the safety of autonomous systems under uncertainty is a critical challenge. Hamilton-Jacobi reachability (HJR) analysis is a widely used method for guaranteeing safety under worst-case disturbances. In this work, we propose HJRNO,…
Hamilton-Jacobi-Isaacs (HJI) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. This analysis is computationally intensive and typically performed offline. Online, however, the autonomous system may…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
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…
A new framework for formulating reachability problems with competing inputs, nonlinear dynamics and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems…
As perception-based controllers for autonomous systems become increasingly popular in the real world, it is important that we can formally verify their safety and performance despite perceptual uncertainty. Unfortunately, the verification…
In continuous-time optimal control, evaluating the Hamiltonian requires solving a constrained optimization problem using the system's dynamics model. Hamilton-Jacobi reachability analysis for safety verification has demonstrated practical…
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…