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Goal-conditioned policies, such as those learned via imitation learning, provide an easy way for humans to influence what tasks robots accomplish. However, these robot policies are not guaranteed to execute safely or to succeed when faced with out-of-distribution goal requests. In this work, we enable robots to know when they can confidently execute a user’s desired goal, and automatically suggest safe alternatives when they cannot. Our approach is inspired by control-theoretic safety filtering, wherein a safety filter minimally adjusts a robot’s candidate action to be safe. Our key idea is to pose alternative suggestion as a safe control problem in goal space, rather than in action space. Offline, we use reachability analysis to compute a goal-parameterized reach-avoid value network which quantifies the safety and liveness of the robot’s pre- trained policy. Online, our robot uses the reach-avoid value network as a safety filter, monitoring the human’s given goal and actively suggesting alternatives that are similar but meet the safety specification. We demonstrate our Safe ALTernatives (SALT) framework in simulation experiments with indoor navigation and Franka Panda tabletop manipulation, and with both discrete and continuous goal representations. We find that SALT is able to learn to predict successful and failed closed-loop executions, is a less pessimistic monitor than open- loop uncertainty quantification, and proposes alternatives that consistently align with those that people find acceptable. 

Abstract Graphene's emergence enables creating chiral metamaterials in helical shapes for terahertz (THz) applications, overcoming material limitations. However, practical implementation remains theoretical due to fabrication challenges. This paper introduces a dual‐component self‐assembly technique that enables creating vertically‐aligned continuous monolayer graphene helices at microscale with great flexibility and high controllability. This assembly process not only facilitates the creation of 3D microstructures, but also positions the 3D structures from a horizontal to a vertical orientation, achieving an aspect ratio (height/width) of ≈2700. As a result, an array of vertically‐aligned graphene helices is formed, reaching up to 4 mm in height, which is equivalent to 4 million times the height of monolayer graphene. The benefit of these 3D chiral structures made from graphene is their capability to infinitely extend in height, interacting with light in ways that are not possible with traditional 2D layering methods. Such an impressive height elevates a level of interaction with light that far surpasses what is achievable with traditional 2D layering methods, resulting in a notable enhancement of optical chirality properties. This approach is applicable to various 2D materials, promising advancements in innovative research and diverse applications across fields. 

Abstract Current graphene‐based plasmonic devices are restricted to 2D patterns defined on planar substrates; thus, they suffer from spatially limited 2D plasmon fields. Here, 3D graphene forming freestanding nanocylinders realized by a plasma‐triggered self‐assembly process are introduced. The graphene‐based nanocylinders induce hybridized edge (in‐plane) and radial (out‐of‐plane) coupled 3D plasmon modes stemming from their curvature, resulting in a four orders of magnitude stronger field at the openings of the cylinders than in rectangular 2D graphene ribbons. For the characterization of the 3D plasmon modes, synchrotron nanospectroscopy measurements are performed, which provides the evidence of preservation of the hybridized 3D graphene plasmons in the high precision curved nanocylinders. The distinct 3D modes introduced in this paper, provide an insight into geometry‐dependent 3D coupled plasmon modes and their ability to achieve non‐surface‐limited (volumetric) field enhancements.