Related papers: Online Guaranteed Reachable Set Approximation for …
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,…
Reachability analysis plays a central role in low-thrust spacecraft trajectory optimization by identifying which target states can be achieved under constraints on time, thrust, and propellant. Classical approaches construct reachable sets…
We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…
In this paper, we present a geometric framework for the reachability analysis of attitude control systems. We model the attitude dynamics on the product manifold $\mathrm{SO}(3) \times \mathbb{R}^3$ and introduce a novel parametrized family…
The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
This paper investigates the application of reachability analysis to the re-entry problem faced by vehicles entering Earth's atmosphere. The study delves into the time evolution of reachable sets for the system, particularly when subject to…
Hybrid dynamical systems with nonlinear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of nonlinear…
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…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
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…
For hybrid systems exhibiting periodic behavior, analyzing the invariant set containing the limit cycle is a natural way to study the robustness of the closed-loop system. However, computing these sets can be computationally expensive,…
We investigate the problem of data-driven, on-the-fly control of systems with unknown nonlinear dynamics where data from only a single finite-horizon trajectory and possibly side information on the dynamics are available. Such side…
Hamilton Jacobi (HJ) Reachability is a formal verification tool widely used in robotic safety analysis. Given a target set as unsafe states, a dynamical system is guaranteed not to enter the target under the worst-case disturbance if it…
Autonomous motion planning under unknown nonlinear dynamics presents significant challenges. An agent needs to continuously explore the system dynamics to acquire its properties, such as reachability, in order to guide system navigation…
We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence…
We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…