Related papers: Fast Reachable Set Approximations via State Decoup…
Hamilton-Jacobi (HJ) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. However, the provided safety assurances are often predicated on the assumption that once deployed, the system or its environment…
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…
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…
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…
Hamilton-Jacobi (HJ) reachability analysis is a widely used method for ensuring the safety of robotic systems. Traditional approaches compute reachable sets by numerically solving an HJ Partial Differential Equation (PDE) over a grid, which…
Hamilton-Jacobi reachability analysis is a powerful technique used to verify the safety of autonomous systems. This method is very good at handling non-linear system dynamics with disturbances and flexible set representations. A drawback to…
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,…
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…
With the continuous advancement in autonomous systems, it becomes crucial to provide robust safety guarantees for safety-critical systems. Hamilton-Jacobi Reachability Analysis is a formal verification method that guarantees performance and…
A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage…
This study focuses on reachability problems in differential games. An improved level set method for computing reachable tubes is proposed in this paper. The reachable tube is described as a sublevel set of a value function, which is the…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
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 provides a formal method for guaranteeing safety in constrained control problems. It synthesizes a value function to represent a long-term safe set called feasible region. Early synthesis methods…
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…
Safe value functions, such as control barrier functions, characterize a safe set and synthesize a safety filter, overriding unsafe actions, for a dynamic system. While function approximators like neural networks can synthesize approximately…
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…
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 is a formal verification tool widely used in robotic safety analysis. Given a target set as unsafe states, a dynamical system is guaranteed not to enter the target under the worst-case disturbance if it…
Objective: In a companion paper, we propose a parametric hybrid automaton model and an algorithm for the online synthesis of robustly correct and near-optimal controllers for cyber-physical system with reach-avoid guarantees. A key part of…