Related papers: Computing Sound Lower and Upper Bounds on Hamilton…
Racing demands each vehicle to drive at its physical limits, when any safety infraction could lead to catastrophic failure. In this work, we study the problem of safe reinforcement learning (RL) for autonomous racing, using the vehicle's…
Recent approaches to leveraging deep learning for computing reachable sets of continuous-time dynamical systems have gained popularity over traditional level-set methods, as they overcome the curse of dimensionality. However, as with…
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…
H-infinity filter has been widely applied in engineering field, but copping with bounded noise is still an open problem and difficult to solve. This paper considers the H-infinity filtering problem for linear system with bounded process and…
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…
We provide a novel uniform convergence guarantee for DeepReach, a deep learning-based method for solving Hamilton-Jacobi-Isaacs (HJI) equations associated with reachability analysis. Specifically, we show that the DeepReach algorithm, as…
Recent developments in autonomous driving and robotics underscore the necessity of safety-critical controllers. Control barrier functions (CBFs) are a popular method for appending safety guarantees to a general control framework, but they…
Latent safety filters extend Hamilton-Jacobi (HJ) reachability to operate on latent state representations and dynamics learned directly from high-dimensional observations, enabling safe visuomotor control under hard-to-model constraints.…
This paper investigates a Hamilton-Jacobi (HJ) analysis to solve finite-horizon optimal control problems for high-dimensional systems. Although grid-based methods, such as the level-set method [1], numerically solve a general class of 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 consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A new formulation…
This paper presents a two-stage framework for constrained near-optimal feedback control of input-affine nonlinear systems. An approximate value function for the unconstrained control problem is computed offline by solving the…
Learning-enabled planning and control algorithms are increasingly popular, but they often lack rigorous guarantees of performance or safety. We introduce an algorithm for computing underapproximate backward reachable sets of nonlinear…
Hard constraints in reinforcement learning (RL) often degrade policy performance. Lagrangian methods offer a way to blend objectives with constraints, but require intricate reward engineering and parameter tuning. In this work, we extend…
Optimal feedback controllers for nonlinear systems can be derived by solving the Hamilton-Jacobi-Bellman (HJB) equation. However, because the HJB is a nonlinear partial differential equation, numerical methods typically provide only…
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…
Forward reachability analysis is a dominant approach for verifying reach-avoid specifications in neural feedback systems, i.e., dynamical systems controlled by neural networks, and a number of directions have been proposed and studied. In…
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…
We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by…
First-order optimization algorithms are widely used today. Two standard building blocks in these algorithms are proximal operators (proximals) and gradients. Although gradients can be computed for a wide array of functions, explicit…