Related papers: Exact and Efficient Hamilton-Jacobi-based Guarante…
A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The method combines a tensor train approximation…
A critical task for developing safe autonomous driving stacks is to determine whether an obstacle is safety-critical, i.e., poses an imminent threat to the autonomous vehicle. Our previous work showed that Hamilton Jacobi reachability…
We address finding the semi-global solutions to optimal feedback control and the Hamilton--Jacobi--Bellman (HJB) equation. Using the solution of an HJB equation, a feedback optimal control law can be implemented in real-time with minimum…
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…
CASL-HJX is a computational framework designed for solving deterministic and stochastic Hamilton-Jacobi equations in two spatial dimensions. It provides a flexible and efficient approach to modeling front propagation problems, optimal…
Maximum entropy reinforcement learning (RL) methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, most of existing techniques are designed for discrete-time systems. As a…
Safety-critical distributed cyber-physical systems (CPSs) have been found in a wide range of applications. Notably, they have displayed a great deal of utility in intelligent transportation, where autonomous vehicles communicate and…
We present a method of computing backward reachable sets for nonlinear discrete-time control systems possessing continuous symmetries. The starting point is a dynamic game formulation of reachability analysis where control inputs aim to…
Path planning for autonomous vehicles in arbitrary environments requires a guarantee of safety, but this can be impractical to ensure in real-time when the vehicle is described with a high-fidelity model. To address this problem, this paper…
Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that…
A method is presented to obtain an inner-approximation of the backward reachable set (BRS) of a given target tube, along with an admissible controller that maintains trajectories inside this tube. The proposed optimization algorithms are…
Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies for high-dimensional…
In multirotor systems, guaranteeing safety while considering unknown disturbances is essential for robust trajectory planning. The Forward reachable set (FRS), the set of feasible states subject to bounded disturbances, can be utilized to…
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
Safe control techniques, such as Hamilton-Jacobi reachability, provide principled methods for synthesizing safety-preserving robot policies but typically assume hand-designed state spaces and full observability. Recent work has relaxed…
This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of…
To operate with limited sensor horizons in unpredictable environments, autonomous robots use a receding-horizon strategy to plan trajectories, wherein they execute a short plan while creating the next plan. However, creating safe,…
This paper considers the problem of reachability analysis of control systems with optimal controllers, as a first step towards verifying the safety and correctness of such systems. Despite their appeal in guaranteeing task satisfaction…
Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for…
We consider the problem of planning trajectories for a group of $N$ vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically,…