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Real-world autonomous vehicles often operate in a priori unknown environments. Since most of these systems are safety-critical, it is important to ensure they operate safely in the face of environment uncertainty, such as unseen obstacles.…
Provably safe and scalable multi-vehicle trajectory planning is an important and urgent problem. Hamilton-Jacobi (HJ) reachability is an ideal tool for analyzing such safety-critical systems and has been successfully applied to several…
Within a robot autonomy stack, the planner and controller are typically designed separately, and serve different purposes. As such, there is often a diffusion of responsibilities when it comes to ensuring safety for the robot. We propose…
Providing formal safety and performance guarantees for autonomous systems is becoming increasingly important. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for providing these guarantees, since it can…
We propose a hybrid approach that combines Hamilton-Jacobi (HJ) reachability and mixed-integer optimization for solving a reach-avoid game with multiple attackers and defenders. The reach-avoid game is an important problem with potential…
Motivated by the scalability limitations of Eulerian methods for variational Hamilton-Jacobi-Isaacs (HJI) formulations that provide a least restrictive controller in problems that involve state or input constraints under a worst-possible…
We consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A new formulation…
Autonomous navigation requires planning to reach a goal safely and efficiently in complex and potentially dynamic environments. Graph search-based algorithms are widely adopted due to their generality and theoretical guarantees when…
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…
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…
Safety is a central requirement for autonomous system operation across domains. Hamilton-Jacobi (HJ) reachability analysis can be used to construct "least-restrictive" safety filters that result in infrequent, but often extreme, control…
Autonomous ground vehicles (AGVs) must navigate safely in cluttered environments while accounting for complex dynamics and environmental uncertainty. Hamilton-Jacobi Reachability (HJR) offers formal safety guarantees through the computation…
Hamilton-Jacobi (HJ) reachability analysis provides a formal method for guaranteeing safety in constrained control problems. It synthesizes a value function to represent a long-term safe set called feasible region. Early synthesis methods…
Autonomous systems like aircraft and assistive robots often operate in scenarios where guaranteeing safety is critical. Methods like Hamilton-Jacobi reachability can provide guaranteed safe sets and controllers for such systems. However,…
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…
Hamilton-Jacobi-Isaacs (HJI) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. This analysis is computationally intensive and typically performed offline. Online, however, the autonomous system may…
As perception-based controllers for autonomous systems become increasingly popular in the real world, it is important that we can formally verify their safety and performance despite perceptual uncertainty. Unfortunately, the verification…
Hamilton-Jacobi (HJ) reachability analysis is a fundamental tool for the safety verification and control synthesis of nonlinear control systems. Classical HJ reachability analysis methods compute value functions over grids which discretize…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
Hamilton-Jacobi (HJ) Reachability is widely used to compute value functions for states satisfying specific control objectives. However, it becomes intractable for high-dimensional problems due to the curse of dimensionality. Dimensionality…