Related papers: Exact and Efficient Hamilton-Jacobi-based Guarante…
Fast and Safe Tracking (FaSTrack) is a modular framework that provides safety guarantees while planning and executing trajectories in real time via value functions of Hamilton-Jacobi (HJ) reachability. These value functions are computed…
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…
This work in progress considers reachability-based safety analysis in the domain of autonomous driving in multi-agent systems. We formulate the safety problem for a car following scenario as a differential game and study how different…
Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle…
Autonomous systems operating in close proximity with each other to cover a specified area has many potential applications, but to achieve effective coordination, two key challenges need to be addressed: coordination and safety. For…
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of…
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…
Recent advances in machine learning technologies and sensing have paved the way for the belief that safe, accessible, and convenient autonomous vehicles may be realized in the near future. Despite tremendous advances within this context,…
The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these…
This report aims to compare two safety methods: control barrier function and Hamilton-Jacobi reachability analysis. We will consider the difference with a focus on the following aspects: generality of system dynamics, difficulty of…
We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…
Deploying autonomous systems in safety critical settings necessitates methods to verify their safety properties. This is challenging because real-world systems may be subject to disturbances that affect their performance, but are unknown a…
We present an overview of recently developed data-driven tools for safety analysis of autonomous vehicles and advanced driver assist systems. The core algorithms combine model-based, hybrid system reachability analysis with sensitivity…
Recent learning-based safety filters have outperformed conventional methods, such as hand-crafted Control Barrier Functions (CBFs), by effectively adapting to complex constraints. However, these learning-based approaches lack formal safety…
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous…
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…
A novel method for computing reachable sets is proposed in this paper. In the proposed method, a Hamilton-Jacobi-Bellman equation with running cost functionis numerically solved and the reachable sets of different time horizons are…
A discrete-time linear dynamical system (LDS) is given by an update matrix $M \in \mathbb{R}^{d\times d}$, and has the trajectories $\langle s, Ms, M^2s, \ldots \rangle$ for $s \in \mathbb{R}^d$. Reachability-type decision problems of…
Reinforcement Learning (RL) algorithms have achieved remarkable performance in decision making and control tasks due to their ability to reason about long-term, cumulative reward using trial and error. However, during RL training, applying…
Data-driven safety verification of robotic systems often relies on zonotopic reachability analysis due to its scalability and computational efficiency. However, for nonlinear systems, these methods can become overly conservative, especially…