Related papers: Reach-Avoid Differential game with Reachability An…
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…
Reach-avoid problems involve driving a system to a set of desirable configurations while keeping it away from undesirable ones. Providing mathematical guarantees for such scenarios is challenging but have numerous potential practical…
Traditional reachability methods provide formal guarantees of safety under bounded disturbances. However, they strictly enforce state constraints as inviolable, which can result in overly conservative or infeasible solutions in complex…
This paper investigates a reach-avoid game between two players with damped double integrator dynamics. An optimal state-feedback strategy is derived using a differential game framework combined with geometric analysis. To facilitate the…
Safe multi-agent motion planning (MAMP) under task-induced constraints is a critical challenge in robotics. Many real-world scenarios require robots to navigate dynamic environments while adhering to manifold constraints imposed by tasks.…
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…
Safety is an important topic in autonomous driving since any collision may cause serious injury to people and damage to property. Hamilton-Jacobi (HJ) Reachability is a formal method that verifies safety in multi-agent interaction and…
This paper studies a 3D multiplayer reach-avoid differential game with a goal region and a play region. Multiple pursuers defend the goal region by consecutively capturing multiple evaders in the play region. The players have heterogeneous…
We present a numeric method to compute the safe operating flight conditions for a helicopter such that we can ensure a safe landing in the event of a partial or total engine failure. The unsafe operating region is the complement of the…
Provably safe and scalable multi-vehicle path planning is an important and urgent problem due to the expected increase of automation in civilian airspace in the near future. Although this problem has been studied in the past, there has not…
Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations. As a result, unmanned aerial systems traffic management is needed to ensure the safety and goal satisfaction of potentially…
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…
Hamilton-Jacobi reachability analysis is a powerful technique used to verify the safety of autonomous systems. This method is very good at handling non-linear system dynamics with disturbances and flexible set representations. A drawback to…
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…
Multi-vehicle collision avoidance is a highly crucial problem due to the soaring interests of introducing autonomous vehicles into the real world in recent years. The safety of these vehicles while they complete their objectives is of…
We present a fast planning architecture called Hamilton-Jacobi-based bidirectional A* (HJBA*) to solve general tight parking scenarios. The algorithm is a two-layer composed of a high-level HJ-based reachability analysis and a lower-level…
Hamilton-Jacobi (HJ) reachability provides formal safety guarantees for dynamical systems, but solving high-dimensional HJ partial differential equations limits its use in real-time planning. This paper presents a contingency-aware…
Hamilton-Jacobi (HJ) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. However, the provided safety assurances are often predicated on the assumption that once deployed, the system or its environment…
The paper presents a robust control technique that combines the Control Lyapunov function and Hamilton-Jacobi Reachability to compute a controller and its Region of Attraction (ROA). The Control Lyapunov function uses a linear system model…
Reachability analysis provides formal guarantees for performance and safety properties of nonlinear control systems. Here, one aims to compute the backward reachable set (BRS) or tube (BRT) -- the set of states from which the system can be…