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 does not evolve. Online, however, an autonomous system might experience changes in system dynamics, control authority, external disturbances, and/or the surrounding environment, requiring updated safety assurances. Rather than restarting the safety analysis from scratch, which can be timeconsuming and often intractable to perform online, we propose to compute parameter-conditioned reachable sets. Assuming expected system and environment changes can be parameterized, we treat these parameters as virtual states in the system and leverage recent advances in high-dimensional reachability analysis to solve the corresponding reachability problem offline. This results in a family of reachable sets that is parameterized by the environment and system factors. Online, as these factors change, the system can simply query the corresponding safety function from this family to ensure system safety, enabling a real-time update of the safety assurances. Through various simulation studies, we demonstrate the capability of our approach in maintaining system safety despite the system and environment evolution.

Robots such as autonomous vehicles and assistive manipulators are increasingly operating in dynamic environ-ments and close physical proximity to people. In such scenarios, the robot can leverage a human motion predictor to predict their future states and plan safe and efficient trajectories. However, no model is ever perfect - when the observed human behavior deviates from the model predictions, the robot might plan unsafe maneuvers. Recent works have explored maintaining a confidence parameter in the human model to overcome this challenge, wherein the predicted human actions are tempered online based on the likelihood of the observed human action under the prediction model. This has opened up a new research challenge, i.e., how to compute the future human states online as the confidence parameter changes? In this work, we propose a Hamilton-Jacobi (HJ) reachability-based approach to overcome this challenge. Treating the confidence parameter as a virtual state in the system, we compute a parameter-conditioned forward reachable tube (FRT) that provides the future human states as a function of the confidence parameter. Online, as the confidence parameter changes, we can simply query the corresponding FRT, and use it to update the robot plan. Computing parameter-conditioned FRT corre-sponds to an (offline) high-dimensional reachability problem, which we solve by leveraging recent advances in data-driven reachability analysis. Overall, our framework enables online maintenance and updates of safety assurances in human-robot interaction scenarios, even when the human prediction model is incorrect. We demonstrate our approach in several safety-critical autonomous driving scenarios, involving a state-of-the-art deep learning-based prediction model.

This paper presents an algorithm for a team of mobile robots to simultaneously learn a spatial field over a domain and spatially distribute themselves to optimally cover it. Drawing from previous approaches that estimate the spatial field through a centralized Gaussian process, this work leverages the spatial structure of the coverage problem and presents a decentralized strategy where samples are aggregated locally by establishing communications through the boundaries of a Voronoi partition. We present an algorithm whereby each robot runs a local Gaussian process calculated from its own measurements and those provided by its Voronoi neighbors, which are incorporated into the individual robot's Gaussian process only if they provide sufficiently novel information. The performance of the algorithm is evaluated in simulation and compared with centralized approaches.