Related papers: Generating Formal Safety Assurances for High-Dimen…
We present a method for optimal coordination of multiple vehicle teams when multiple endpoint configurations are equally desirable, such as seen in the autonomous assembly of formation flight. The individual vehicles' positions in the…
We present a semi-real-time algorithm for minimal-time optimal path planning based on optimal control theory, dynamic programming, and Hamilton-Jacobi (HJ) equations. Partial differential equation (PDE) based optimal path planning methods…
In this paper, we propose a hybrid MPC local planner that uses a learning-based approximation of a time-varying safe set, derived from local observations and applied as the MPC terminal constraint. This set can be represented as a…
When autonomous vehicles encounter untrained scenarios, ensuring safety hinges on effective safety verification to prevent accidents stemming from unexpected model decisions. Reachability analysis, a method of safety verification, offers…
Reach-avoid problems involve driving a system to a set of desirable configurations while keeping it away from undesirable ones. Providing mathematical guarantees for such scenarios is challenging but have numerous potential practical…
We address the problem of safety verification for nonlinear stochastic systems, specifically the task of certifying that system trajectories remain within a safe set with high probability. To tackle this challenge, we adopt a set-erosion…
This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…
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…
Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment…
This paper investigates the problem of maintaining the safe operation of Waste-to-Energy (WtE) systems under operational constraints and uncertain waste inflows. We model this as a robust viability problem, formulated as a zero-sum…
In this paper, we develop algorithms to overcome the curse of dimensionality in possibly non-convex state-dependent Hamilton-Jacobi equations (HJ PDEs) arising from optimal control and differential game problems. The subproblems are…
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…
Ensuring safety is important for the practical deployment of reinforcement learning (RL). Various challenges must be addressed, such as handling stochasticity in the environments, providing rigorous guarantees of persistent state-wise…
In this paper we examine how Lagrangian techniques can be used to compute underapproximations and overapproximation of the finite-time horizon, stochastic reach-avoid level sets for discrete-time, nonlinear systems. This approach is…
A procedure for the numerical approximation of high-dimensional Hamilton-Jacobi-Bellman (HJB) equations associated to optimal feedback control problems for semilinear parabolic equations is proposed. Its main ingredients are 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, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…
Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations such as package delivery, firefighting, and fast disaster response. As a result, UAV traffic management systems are needed to support…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…