Related papers: Exact and Efficient Hamilton-Jacobi Reachability f…
We consider the problem of robotic planning under uncertainty. This problem may be posed as a stochastic optimal control problem, complete solution to which is fundamentally intractable owing to the infamous curse of dimensionality. We…
We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing…
We consider the problem of robotic planning under uncertainty in this paper. This problem may be posed as a stochastic optimal control problem, a solution to which is fundamentally intractable owing to the infamous "curse of…
Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…
The reachable sets of nonlinear control systems can in general only be numerically approximated, and are often very expensive to calculate. In this paper, we propose an algorithm that tracks only the boundaries of the reachable sets and…
We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…
In this paper we propose a convex programming based method to address a long-standing problem of inner-approximating backward reachable sets of state-constrained polynomial systems subject to time-varying uncertainties. The backward…
In this paper a decentralized control algorithm for systems composed of $N$ dynamically decoupled agents, coupled by feasibility constraints, is presented. The control problem is divided into $N$ optimal control sub-problems and a…
To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for…
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…
Designing controllers that are both safe and performant is inherently challenging. This co-optimization can be formulated as a constrained optimal control problem, where the cost function represents the performance criterion and safety is…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…
Reach-avoid differential games play an important role in collision avoidance, motion planning and control of aircrafts, and related applications. The central problem is the computation of the set of initial states from which the ego player…
With the recent surge of interest in UAVs for civilian services, the importance of developing tractable multi-agent analysis techniques that provide safety and performance guarantees have drastically increased. Hamilton-Jacobi (HJ)…
In this paper, we present a framework for enabling autonomous vehicles to interact with cyclists in a manner that balances safety and optimality. The approach integrates Hamilton-Jacobi reachability analysis with deep Q-learning to jointly…
This work extends reachability analyses based on ellipsoidal techniques to Linear Time Invariant (LTI) systems subject to an integral quadratic constraint (IQC) between the past state and disturbance signals , interpreted as an input-output…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when the…
This paper presents an enhanced direct-method-based approach for the real-time solution of optimal control problems to handle path constraints, such as obstacles. The principal contributions of this work are twofold: first, the existing…