Related papers: Grouped Stirling complexes
An algorithm for robot formation path planning is presented in this paper. Given a map of the working environment, the algorithm finds a path for a formation taking into account possible split of the formation and its consecutive merge. The…
We study the motion of a robotic arm inside a rectangular tunnel. We prove that the configuration space of all possible positions of the robot is a CAT(0) cubical complex. This allows us to use techniques from geometric group theory to find…
The concept of graph compositions is related to several number theoretic concepts, including partitions of positive integers and the cardinality of the power set of finite sets. This paper examines graph compositions where the total number…
We consider a variant of the crash-fault gathering problem called stand-up indulgent gathering (SUIG). In this problem, a group of mobile robots must eventually gather at a single location, which is not known in advance. If no robots crash,…
In this paper we present algorithms for collective construction systems in which a large number of autonomous mobile robots trans- port modular building elements to construct a desired structure. We focus on building block structures…
Consider a set of $n$ simple autonomous mobile robots (asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, non-rigid, deterministic) initially in distinct…
We consider a collection of $k \geq 2$ robots that evolve in a ring-shaped network without common orientation, and address a variant of the crash-tolerant gathering problem called the \emph{Stand-Up Indulgent Gathering} (SUIG): given a…
We consider the problem of realizing a group as the fundamental group of a graph of groups where the vertex groups are restricted to certain classes (for example, coming from a certain finite list of groups, or having bounded geometric…
Let $G$ be a group and $X$ be a $G$-space. A subset $F$ of $X$ is called a kaleidoscopical configuration if there exists a surjective coloring $\chi:X\to Y$ such that the restriction of $\chi$ on each subset $gF$, $g\in G$ is a bijection.…
Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is the fixed point subspace of an element of G. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then…
We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the…
A discrete subset $S$ of a topologically gyrogroup $G$ is called a {\it suitable set} for $G$ if $S\cup \{1\}$ is closed and the subgyrogroup generated by $S$ is dense in $G$, where $1$ is the identity element of $G$. In this paper, we…
A dominating set $S$ of graph $G$ is called an $r$-grouped dominating set if $S$ can be partitioned into $S_1,S_2,\ldots,S_k$ such that the size of each unit $S_i$ is $r$ and the subgraph of $G$ induced by $S_i$ is connected. The concept of…
This paper investigates how a novel paradigm called group-control can be effectively used for motion planning for microrobot swarms in a global field. We prove that Small-Time Local Controllability (STLC) in robot positions is achievable…
Configuration spaces of distinct labeled points on the plane are of practical relevance in designing safe control schemes for Automated Guided Vehicles (robots) in industrial settings. In this announcement, we consider the problem of the…
Let $G=(V,E)$ be a bipartite graph embedded in a plane (or $n$-holed torus). Two subgraphs of $G$ differ by a {\it $Z$-transformation} if their symmetric difference consists of the boundary edges of a single face---and if each subgraph…
Let $G$ be a connected undirected graph on $n$ vertices with no loops but possibly multiedges. Given an arithmetical structure $(\textbf{r}, \textbf{d})$ on $G$, we describe a construction which associates to it a graph $G'$ on $n-1$…
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…
The configuration space of the mechanism of a planar robot is studied. We consider a robot which has $n$ arms such that each arm is of length 1+1 and has a rotational joint in the middle, and that the endpoint of the $k$-th arm is fixed to…
Using results on the topology of moduli space of polygons [Jaggi, 92; Kapovich and Millson, 94], it can be shown that for a planar robot arm with $n$ segments there are some values of the base-length, $z$, at which the configuration space…