Related papers: Computing braid groups of graphs with applications…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

Batch planning is increasingly necessary to quickly produce diverse and quality motion plans for downstream learning applications, such as distillation and imitation learning. This paper presents Global Tensor Motion Planning (GTMP) -- a…

With the recent influx in demand for multi-robot systems throughout industry and academia, there is an increasing need for faster, robust, and generalizable path planning algorithms. Similarly, given the inherent connection between control…

In this article, we propose the approach to procedural optimization of a neural network, based on the combination of information theory and braid theory. The network studied in the article implemented with the intersections between the…

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…

We use machine learning to classify examples of braids (or flat braids) as trivial or non-trivial. Our ML takes form of supervised learning using neural networks (multilayer perceptrons). When they achieve good results in classification, we…

In this paper, all finite groups whose commuting (non-commuting) graphs can be embed on the plane, torus or projective plane are classified.

A topological theory initiated recently by the author uses methods of algebraic topology to estimate numerically the character of instabilities arising in motion planning algorithms. The present paper studies random motion planning…

We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition…

To safely operate, an autonomous vehicle must know the future behavior of a potentially high number of interacting agents around it, a task often posed as multi-agent trajectory prediction. Many previous attempts to model social…

We present a number of breakthroughs for coordinated motion planning, in which the objective is to reconfigure a swarm of labeled convex objects by a combination of parallel, continuous, collision-free translations into a given target…

Constrained motion planning is a challenging field of research, aiming for computationally efficient methods that can find a collision-free path on the constraint manifolds between a given start and goal configuration. These planning…

Nowadays robot is supposed to demonstrate human-like perception, reasoning and behavior pattern in social or service application. However, most of the existing motion planning methods are incompatible with above requirement. A potential…

Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…

This paper considers the motion planning problem for multiple tethered planar mobile robots. Each robot is attached to a fixed base by a flexible cable. Since the robots share a common workspace, the interactions amongst the robots, cables,…

The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting…

We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…

Coordinating the motion of multiple agents in constrained environments is a fundamental challenge in robotics, motion planning, and scheduling. A motivating example involves $n$ robotic arms, each represented as a line segment. The…

In the field of swarm robotics, one of the most studied problem is Gathering. It asks for a distributed algorithm that brings the robots to a common location, not known in advance. We consider the case of robots constrained to move along…

Objects rarely sit in isolation in human environments. As such, we'd like our robots to reason about how multiple objects relate to one another and how those relations may change as the robot interacts with the world. To this end, we…