Related papers: DeepReach: A Deep Learning Approach to High-Dimens…

Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…

One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…

With the rapid advancements of deep learning in the past decade, it can be foreseen that deep learning will be continuously deployed in more and more safety-critical applications such as autonomous driving and robotics. In this context,…

We introduce a new numerical method to approximate the solutions of a class of stationary Hamilton-Jacobi (HJ) partial differential equations arising from minimum time optimal control problems. We rely on nested grid approximations, and…

A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage…

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…

Planning safe trajectories under uncertain and dynamic conditions makes the autonomous driving problem significantly complex. Current sampling-based methods such as Rapidly Exploring Random Trees (RRTs) are not ideal for this problem…

This paper presents an implicit solution formula for the Hamilton-Jacobi partial differential equation (HJ PDE). The formula is derived using the method of characteristics and is shown to coincide with the Hopf and Lax formulas in the case…

This study aims at characterizing a reachable set of a hybrid dynamical system with a lag constraint in the switch control. The setting does not consider any controllability assumptions and uses a level-set approach. The approach consists…

Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…

This paper proposes an adaptive admittance controller for improving efficiency and safety in physical human-robot interaction (pHRI) tasks in small-batch manufacturing that involve contact with stiff environments, such as drilling,…

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…

Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…

As autonomous systems become more ubiquitous in daily life, ensuring high performance with guaranteed safety is crucial. However, safety and performance could be competing objectives, which makes their co-optimization difficult.…

Physical human-robot interaction has been an area of interest for decades. Collaborative tasks, such as joint compliance, demand high-quality joint torque sensing. While external torque sensors are reliable, they come with the drawbacks of…

We present the framework of delta-complete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving delta-decision problems over the reals. The techniques take into…

Verifying the correct behavior of robots in contact tasks is challenging due to model uncertainties associated with contacts. Standard methods for testing often fall short since all (uncountable many) solutions cannot be obtained. Instead,…

This paper investigates the problem of maintaining the safe operation of Waste-to-Energy (WtE) systems under operational constraints and uncertain waste inflows. We model this as a robust viability problem, formulated as a zero-sum…

Hybrid zonotopes generalize constrained zonotopes by introducing additional binary variables and possess some unique properties that make them convenient to represent nonconvex sets. This paper presents novel hybrid zonotope-based methods…

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…