Related papers: Conservative Linear Envelopes for Nonlinear, High-…
We propose a novel formulation for approximating reachable sets through a minimum discounted reward optimal control problem. The formulation yields a continuous solution that can be obtained by solving a Hamilton-Jacobi equation.…
Presented is a new method for calculating the time-optimal guidance control for a multiple vehicle pursuit-evasion system. A joint differential game of k pursuing vehicles relative to the evader is constructed, and a Hamilton-Jacobi-Isaacs…
We propose a hybrid approach that combines Hamilton-Jacobi (HJ) reachability and mixed-integer optimization for solving a reach-avoid game with multiple attackers and defenders. The reach-avoid game is an important problem with potential…
Maximum entropy reinforcement learning (RL) methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, most of existing techniques are designed for discrete-time systems. As a…
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…
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…
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…
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…
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…
It is well known that time dependent Hamilton-Jacobi-Isaacs partial differential equations (HJ PDE), play an important role in analyzing continuous dynamic games and control theory problems. An important tool for such problems when they…
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…
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…
Backward reachable tubes (BRTs), computed via viscous Hamilton-Jacobi (HJ) partial differential equations, provide principled safety certificates for learned controllers and planning algorithms in trustworthy machine learning. However,…
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…
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)…
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…
We present a framework to \emph{certify} Hamilton--Jacobi (HJ) reachability learned by reinforcement learning (RL). Building on a discounted initial time \emph{travel-cost} formulation that makes small-step RL value iteration provably…
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…
We consider the problem of overbounding and underbounding both the backward and forward reachable set for a given polynomial vector field, nonlinear in both state and input, with a given semialgebriac set of initial conditions and with…
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,…