Related papers: Exact and Efficient Hamilton-Jacobi-based Guarante…
Reachability analysis evaluates system safety, by identifying the set of states a system may evolve within over a finite time horizon. In contrast to model-based reachability analysis, data-driven reachability analysis estimates reachable…
We propose a novel, mesh-free, and gradient-free fixed-point approach for computing viscosity solutions of high-dimensional Hamilton-Jacobi (HJ) equations. By leveraging the Hopf-Lax formula, our approach iteratively solves the associated…
We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…
Collision detection and collision avoidance are essential components in these systems for safe human-robot interactions. Robotics systems that can work "out-of-the-box" without excessive amount of installation and calibration from the…
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…
Designing provably safe control is a core problem in trustworthy autonomy. However, most prior work in this regard assumes either that the system dynamics are known or deterministic, or that the state and action space are finite,…
Safety filters based on Control Barrier Functions (CBFs) have emerged as a practical tool for the safety-critical control of autonomous systems. These approaches encode safety through a value function and enforce safety by imposing a…
Control barrier functions (CBFs) have been demonstrated as an effective method for safety-critical control of autonomous systems. Although CBFs are simple to deploy, their design remains challenging, motivating the development of…
We give a full characterization of the range of the operator which associates, to any initial condition, the viscosity solution at time $T$ of a Hamilton-Jacobi equation with convex Hamiltonian. Our main motivation is to be able to treat…
We propose a scalable reachability-based framework for probabilistic, data-driven safety verification of unknown nonlinear dynamics. We use Koopman theory with a neural network (NN) lifting function to learn an approximate linear…
In this paper, we propose a novel image restoration framework that integrates optimal control techniques with the Hamilton-Jacobi-Bellman (HJB) equation. Motivated by models from production planning, our method restores degraded images by…
In this paper, we first give the regular point reduction and the two types of Hamilton-Jacobi equation for a regular controlled Hamiltonian (RCH) system with symmetry and momentum map on the generalization of a semidirect product Lie group.…
Intercepting dynamic objects in uncertain environments involves a significant unresolved challenge in modern robotic systems. Current control approaches rely solely on estimated information, and results lack guarantees of robustness and…
In this paper, we present an approach for guaranteeing the completion of complex tasks with cyber-physical systems (CPS). Specifically, we leverage temporal logic trees constructed using Hamilton-Jacobi reachability analysis to (1) check…
An open question in autonomous driving is how best to use simulation to validate the safety of autonomous vehicles. Existing techniques rely on simulated rollouts, which can be inefficient for finding rare failure events, while other…
The decision logic for the ACAS X family of aircraft collision avoidance systems is represented as a large numeric table. Due to storage constraints of certified avionics hardware, neural networks have been suggested as a way to…
Formal verification of robotic tasks requires a simple yet conformant model of the used robot. We present the first work on generating reachset conformant models for robotic contact tasks considering hybrid (mixed continuous and discrete)…
This paper introduces a novel methodology that leverages the Hamilton-Jacobi solution to enhance non-linear model predictive control (MPC) in scenarios affected by navigational uncertainty. Using Hamilton-Jacobi-Theoretic approach, a…
Hybrid zonotopes generalize constrained zonotopes by introducing additional binary variables and possess some unique properties that make them convenient to represent nonconvex sets. This paper presents novel hybrid zonotope-based methods…
In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the…