Randomized smoothing is a recently proposed defense against adversarial attacks that has achieved state-of-the-art provable robustness against $\ell_2$ perturbations. A number of works have extended the guarantees to other metrics, such as $\ell_1$ or $\ell_\infty$, by using different smoothing measures. Although the current framework has been shown to yield near-optimal $\ell_p$ radii, the total safety region certified by the current framework can be arbitrarily small compared to the optimal. In this work, we propose a framework to improve the certified safety region for these smoothed classifiers without changing the underlying smoothing scheme. The theoretical contributions are as follows: 1) We generalize the certification for randomized smoothing by reformulating certified radius calculation as a nested optimization problem over a class of functions.

Soft robotics has advanced rapidly, yet its control methods remain fragmented: different morphologies and actuation schemes still require task-specific controllers, hindering theoretical integration and large-scale deployment. A generic control framework is therefore essential, and a key obstacle lies in the persistent use of rigid-body control logic, which relies on precise models and strict low-level execution. Such a paradigm is effective for rigid robots but fails for soft robots, where the ability to tolerate and exploit approximate action representations, i.e., control compliance, is the basis of robustness and adaptability rather than a disturbance to be eliminated. Control should thus shift from suppressing compliance to explicitly exploiting it. Human motor control exemplifies this principle: instead of computing exact dynamics or issuing detailed muscle-level commands, it expresses intention through high-level movement tendencies, while reflexes and biomechanical mechanisms autonomously resolve local details. This architecture enables robustness, flexibility, and cross-task generalization. Motivated by this insight, we propose a generic soft-robot control framework grounded in control compliance and validate it across robots with diverse morphologies and actuation mechanisms. The results demonstrate stable, safe, and cross-platform transferable behavior, indicating that embracing control compliance, rather than resisting it, may provide a widely applicable foundation for unified soft-robot control.

If f,g are both log-concave functions then the convolution f null g is also log-concave.

Effective, reliable, and efficient evaluation of autonomous driving safety is essential to demonstrate its trustworthiness. Criticality metrics provide an objective means of assessing safety. However, as existing metrics primarily target longitudinal conflicts, accurately quantifying the risks of lateral conflicts - prevalent in urban settings - remains challenging. This paper proposes the Modified-Emergency Index (MEI), a metric designed to quantify evasive effort in lateral conflicts. Compared to the original Emergency Index (EI), MEI refines the estimation of the time available for evasive maneuvers, enabling more precise risk quantification. We validate MEI on a public lateral conflict dataset based on Argoverse-2, from which we extract over 1,500 high-quality AV conflict cases, including more than 500 critical events. MEI is then compared with the well-established ACT and the widely used PET metrics. Results show that MEI consistently outperforms them in accurately quantifying criticality and capturing risk evolution. Overall, these findings highlight MEI as a promising metric for evaluating urban conflicts and enhancing the safety assessment framework for autonomous driving. The open-source implementation is available at https://github.com/AutoChengh/MEI.

In this work, we propose a framework to improve the certified safety region for these smoothed classifiers without changing the underlying smoothing scheme.

The recent adoption of artificial intelligence (AI) in robotics has driven the development of algorithms that enable autonomous systems to adapt to complex social environments. In particular, safe and efficient social navigation is a key challenge, requiring AI not only to avoid collisions and deadlocks but also to interact intuitively and predictably with its surroundings. To date, methods based on probabilistic models and the generation of conformal safety regions have shown promising results in defining safety regions with a controlled margin of error, primarily relying on classification approaches and explicit rules to describe collision-free navigation conditions. This work explores how topological features contribute to explainable safety regions in social navigation. Instead of using behavioral parameters, we leverage topological data analysis to classify and characterize different simulation behaviors. First, we apply global rule-based classification to distinguish between safe (collision-free) and unsafe scenarios based on topological properties. Then, we define safety regions, $S_\varepsilon$, in the topological feature space, ensuring a maximum classification error of $\varepsilon$. These regions are built with adjustable SVM classifiers and order statistics, providing robust decision boundaries. Local rules extracted from these regions enhance interpretability, keeping the decision-making process transparent. Our approach initially separates simulations with and without collisions, outperforming methods that not incorporate topological features. It offers a deeper understanding of robot interactions within a navigable space. We further refine safety regions to ensure deadlock-free simulations and integrate both aspects to define a compliant simulation space that guarantees safe and efficient navigation.

Randomized smoothing is a recently proposed defense against adversarial attacks that has achieved state-of-the-art provable robustness against \ell_2 perturbations. A number of works have extended the guarantees to other metrics, such as \ell_1 or \ell_\infty, by using different smoothing measures. Although the current framework has been shown to yield near-optimal \ell_p radii, the total safety region certified by the current framework can be arbitrarily small compared to the optimal. In this work, we propose a framework to improve the certified safety region for these smoothed classifiers without changing the underlying smoothing scheme. The theoretical contributions are as follows: 1) We generalize the certification for randomized smoothing by reformulating certified radius calculation as a nested optimization problem over a class of functions.

Safety is a fundamental requirement of many robotic systems. Control barrier function (CBF)-based approaches have been proposed to guarantee the safety of robotic systems. However, the effectiveness of these approaches highly relies on the choice of CBFs. Inspired by the universal approximation power of neural networks, there is a growing trend toward representing CBFs using neural networks, leading to the notion of neural CBFs (NCBFs). Current NCBFs, however, are trained and deployed in benign environments, making them ineffective for scenarios where robotic systems experience sensor faults and attacks. In this paper, we study safety-critical control synthesis for robotic systems under sensor faults and attacks. Our main contribution is the development and synthesis of a new class of CBFs that we term fault tolerant neural control barrier function (FT-NCBF). We derive the necessary and sufficient conditions for FT-NCBFs to guarantee safety, and develop a data-driven method to learn FT-NCBFs by minimizing a loss function constructed using the derived conditions. Using the learned FT-NCBF, we synthesize a control input and formally prove the safety guarantee provided by our approach. We demonstrate our proposed approach using two case studies: obstacle avoidance problem for an autonomous mobile robot and spacecraft rendezvous problem, with code available via https://github.com/HongchaoZhang-HZ/FTNCBF.