Safe and Efficient Social Navigation through Explainable Safety Regions Based on Topological Features

The recent adoption of artificial intelligence 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. 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 extends the existing perspective by investigating how topological features can contribute to the creation of explainable safety regions in social navigation scenarios, enabling the classification and characterization of different simulation behaviors. Rather than relying on behaviors parameters to generate safety regions, we leverage topological features through topological data analysis. We first utilize global rule-based classification to provide interpretable characterizations of different simulation behaviors, distinguishing between safe and unsafe scenarios based on topological properties. Next, we define safety regions, S_varepsilon, representing zones in the topological feature space where collisions are avoided with a maximum classification error of varepsilon. These regions are constructed using adjustable SVM classifiers and order statistics, ensuring a robust and scalable decision boundary. Our approach initially separates simulations with and without collisions, outperforming methods that not incorporate topological features. 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.