Related papers: Reachability as a Unifying Framework for Computing…
We proposed an algorithm for solving Hamilton-Jacobi equation associated to an optimal trajectory problem for a vehicle moving inside the pre-specified domain with the speed depending upon the direction of the motion and current position of…
Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…
We propose a novel formulation for approximating reachable sets through a minimum discounted reward optimal control problem. The formulation yields a continuous solution that can be obtained by solving a Hamilton-Jacobi equation.…
We present a framework to \emph{certify} Hamilton--Jacobi (HJ) reachability learned by reinforcement learning (RL). Building on a discounted initial time \emph{travel-cost} formulation that makes small-step RL value iteration provably…
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…
In this article, we consider the infinite-horizon reach-avoid (RA) and stabilize-avoid (SA) zero-sum game problems for general nonlinear continuous-time systems, where the goal is to find the set of states that can be controlled to reach or…
We propose a novel, mesh-free, and gradient-free fixed-point approach for computing viscosity solutions of high-dimensional Hamilton-Jacobi (HJ) equations. By leveraging the Hopf-Lax formula, our approach iteratively solves the associated…
This paper studies the problem of designing a certified vision-based state estimator for autonomous landing systems. In such a system, a neural network (NN) processes images from a camera to estimate the aircraft relative position with…
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…
As robots are being increasingly used in close proximity to humans and objects, it is imperative that robots operate safely and efficiently under real-world conditions. Yet, the environment is seldom known perfectly. Noisy sensors and…
This letter proposes a neural network (NN) aided remote unmanned aerial vehicle (UAV) online control algorithm, coined oHJB. By downloading a UAV's state, a base station (BS) trains an HJB NN that solves the Hamilton-Jacobi-Bellman equation…
This paper presents a numerical optimization algorithm for generating approach and landing trajectories for a six-degree-of-freedom (6-DoF) aircraft. We improve on the existing research on aircraft landing trajectory generation by…
In this paper, we propose a reachable set based collision avoidance algorithm for unmanned aerial vehicles (UAVs). UAVs have been deployed for agriculture research and management, surveillance and sensor coverage for threat detection and…
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…
Safe autonomous navigation is an essential and challenging problem for robots operating in highly unstructured or completely unknown environments. Under these conditions, not only robotic systems must deal with limited localisation…
It is a challenging task for ground robots to autonomously navigate in harsh environments due to the presence of non-trivial obstacles and uneven terrain. This requires trajectory planning that balances safety and efficiency. The primary…
The reachability problem for timed automata asks if there exists a path from an initial state to a target state. The standard solution to this problem involves computing the zone graph of the automaton, which in principle could be infinite.…
This paper presents a robust path-planning framework for safe spacecraft autonomy under uncertainty and develops a computationally tractable formulation based on convex programming. We utilize chance-constrained control to formulate the…
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…
Safe autonomous navigation in unknown environments is an important problem for mobile robots. This paper proposes techniques to learn the dynamics model of a mobile robot from trajectory data and synthesize a tracking controller with safety…