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Annually, a large number of injuries and deaths around the world are related to motor vehicle accidents. This value has recently been reduced to some extent, via the use of driver-assistance systems. Developing driver-assistance systems…

Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…

Dense prediction tasks such as depth perception and semantic segmentation are important applications in computer vision that have a concrete topological description in terms of partitioning an image into connected components or estimating a…

In the last decades, complex networks theory significantly influenced other disciplines on the modeling of both static and dynamic aspects of systems observed in nature. This work aims to investigate the effects of networks' topological…

Predicting human trajectories is a challenging task due to the complexity of pedestrian behavior, which is influenced by external factors such as the scene's topology and interactions with other pedestrians. A special challenge arises from…

Estimating the region of attraction (${\tt RoA}$) for a robot controller is essential for safe application and controller composition. Many existing methods require a closed-form expression that limit applicability to data-driven…

Recent advancements in robotics have transformed industries such as manufacturing, logistics, surgery, and planetary exploration. A key challenge is developing efficient motion planning algorithms that allow robots to navigate complex…

Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational…

Long-term autonomy is one of the most demanded capabilities looked into a robot. The possibility to perform the same task over and over on a long temporal horizon, offering a high standard of reproducibility and robustness, is appealing.…

Legged robots have demonstrated remarkable agility on rigid, stationary ground, but their locomotion reliability remains limited in non-inertial environments, where the supporting ground moves, tilts, or accelerates. Such conditions arise…

We study the topological complexity of work maps with respect to some subspaces of the configuration space and a workspace considered as the target set of the motion of robots. The motivation is to optimize and reduce the number of motion…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Recent literature in the robotics community has focused on learning robot behaviors that abstract out lower-level details of robot control. To fully leverage the efficacy of such behaviors, it is necessary to select and sequence them to…

Robotic manipulation in complex, constrained spaces is vital for widespread applications but challenging, particularly when navigating narrow passages with elongated objects. Existing planning methods often fail in these low-clearance…

This work explores the use of topological tools for achieving effective non-prehensile manipulation in cluttered, constrained workspaces. In particular, it proposes the use of persistent homology as a guiding principle in identifying the…

It has been observed that the very important motion planning problem of robotics mathematically speaking boils down to the problem of finding a section to the path-space fibration, raising the notion of topological complexity, as introduced…

Fully autonomous racing demands not only high-speed driving but also fair and courteous maneuvers. In this paper, we propose an autonomous racing framework that learns complex racing behaviors from expert demonstrations using hierarchical…

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

Methods from computational topology are becoming more and more popular in computer vision and have shown to improve the state-of-the-art in several tasks. In this paper, we investigate the applicability of topological descriptors in the…

It has long been suggested that the mid-latitude atmospheric circulation possesses what has come to be known as `weather regimes', loosely categorised as regions of phase space with above-average density and/or extended persistence. Their…