Related papers: Computing braid groups of graphs with applications…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…
We show that a group admits a planar, finitely generated Cayley graph if and only if it admits a special kind of group presentation we introduce, called a planar presentation. Planar presentations can be recognised algorithmically. As a…
Search-based planning with motion primitives is a powerful motion planning technique that can provide dynamic feasibility, optimality, and real-time computation times on size, weight, and power-constrained platforms in unstructured…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
In this work we establish a simple yet effective strategy, based on optimal transport theory, for enabling a group of robots to accomplish complex tasks, such as shape formation and assembly. We demonstrate the feasibility of this approach…
In this contribution, we demonstrate that Graph Neural Networks and Transformers can learn to reason about geometric constraints. We train them to predict spatial position of points in a discrete 2D grid from a set of constraints that…
This paper proposes a novel online motion planning approach to robot navigation based on nonlinear model predictive control. Common approaches rely on pure Euclidean optimization parameters. In robot navigation, however, state spaces often…
In this paper, we introduce a novel framework that can learn to make visual predictions about the motion of a robotic agent from raw video frames. Our proposed motion prediction network (PROM-Net) can learn in a completely unsupervised…
Multi-robot path planning is difficult due to the combinatorial explosion of the search space with every new robot added. Complete search of the combined state-space soon becomes intractable. In this paper we present a novel form of…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
The performance of optimization-based robot motion planning algorithms is highly dependent on the initial solutions, commonly obtained by running a sampling-based planner to obtain a collision-free path. However, these methods can be slow…
A planar orthogonal drawing {\Gamma} of a connected planar graph G is a geometric representation of G such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and…
In this paper, we present a learning approach to goal assignment and trajectory planning for unlabeled robots operating in 2D, obstacle-filled workspaces. More specifically, we tackle the unlabeled multi-robot motion planning problem with…
In the field of complex networks and graph theory, new results are typically tested on graphs generated by a variety of algorithms such as the Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model. Unfortunately, most graph generating…
In trying to build humanoid robots that perform useful tasks in a world built for humans, we address the problem of autonomous locomotion. Humanoid robot planning and control algorithms for walking over rough terrain are becoming…
Forecasting human trajectories is critical for tasks such as robot crowd navigation and autonomous driving. Modeling social interactions is of great importance for accurate group-wise motion prediction. However, most existing methods do not…
Knowing the symmetries of a polyhedron can be very useful for the analysis of its structure as well as for practical polyhedral computations. In this note, we study symmetry groups preserving the linear, projective and combinatorial…
Motion is an important signal for agents in dynamic environments, but learning to represent motion from unlabeled video is a difficult and underconstrained problem. We propose a model of motion based on elementary group properties of…
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as parameters and form part of the input of the underlying…