Related papers: Grouped Stirling complexes
The pattern formation task is commonly seen in a multi-robot system. In this paper, we study the problem of forming complex shapes with functionally limited mobile robots, which have to rely on other robots to precisely locate themselves.…
Micro- and nanorobots are often controlled by global input signals, such as an electromagnetic or gravitational field. These fields move each robot maximally until it hits a stationary obstacle or another stationary robot. This paper…
This paper develops an algorithm that guides a multi-robot system in an unknown environment in search of fixed targets. The area to be scanned contains an unknown number of convex obstacles of unknown size and shape. The algorithm covers…
This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…
Given a semisimple linear algebraic $k$-group $G$, one has a spherical building $\Delta_G$, and one can interpret the geometric realisation $\Delta_G(\mathbb R)$ of $\Delta_G$ in terms of cocharacters of $G$. The aim of this paper is to…
A set $V$ is said to be separated by subsets $V_1,\ldots,V_k$ if, for every pair of distinct elements of $V$, there is a set $V_i$ that contains exactly one of them. Imposing structural constraints on the separating subsets is often…
If $G$ is a graph, then $X\subseteq V(G)$ is a general position set if for every two vertices $v,u\in X$ and every shortest $(u,v)$-path $P$, it holds that no inner vertex of $P$ lies in $X$. In this note we propose three algorithms to…
This paper presents a novel planning method that achieves navigation of multi-robot formations in cluttered environments, while maintaining the formation throughout the robots motion. The method utilises a decentralised approach to find…
A detailed analysis of the Fundamental Plane properties of Globular Cluster is performed. If a sample of ordinary King-model clusters is considered, it is found that, in the "S-space" defined by the parameters (log r_c, log sigma_0,…
Synthetic active collectives, composed of many nonliving individuals capable of cooperative changes in group shape and dynamics, hold promise for practical applications and for the elucidation of guiding principles of natural collectives.…
A novel multi-robot path planning approach is presented in this paper. Based on the standard Dijkstra, the algorithm looks for the optimal paths for a formation of robots, taking into account the possibility of split and merge. The…
We present progress on the problem of reconfiguring a 2D arrangement of building material by a cooperative group of robots. These robots must avoid collisions, deadlocks, and are subjected to the constraint of maintaining connectivity of…
Let G be a connected, loopless multigraph. The sandpile group of G is a finite abelian group associated to G whose order is equal to the number of spanning trees in G. Holroyd et al. used a dynamical process on graphs called rotor-routing…
A consistent path system in a graph $G$ is an collection of paths, with exactly one path between any two vertices in $G$. A path system is said to be consistent if it is intersection-closed. We say that $G$ is strictly metrizable if every…
Assume that $G$ is a finite group. For every $a, b \in\mathbb N,$ we define a graph $\Gamma_{a,b}(G)$ whose vertices correspond to the elements of $G^a\cup G^b$ and in which two tuples $(x_1,\dots,x_a)$ and $(y_1,\dots,y_b)$ are adjacent if…
This paper covers some recent progress in the study of sg-open sets, sg-compact spaces, N-scattered spaces and some related concepts. A subset $A$ of a topological space $(X,\tau)$ is called sg-closed if the semi-closure of $A$ is included…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
In this paper we consider the generalized anchored configuration spaces on $n$ labeled points on a~graph. These are the spaces of all configurations of $n$ points on a~fixed graph $G$, subject to the condition that at least $q$ vertices in…
If $G$ is a finite group, then the spectrum $\omega(G)$ is the set of all element orders of $G$. The prime spectrum $\pi(G)$ is the set of all primes belonging to $\omega(G)$. A simple graph $\Gamma(G)$ whose vertex set is $\pi(G)$ and in…
We consider a swarm of $n$ robots in \mathbb{R}^d. The robots are oblivious, disoriented (no common coordinate system/compass), and have limited visibility (observe other robots up to a constant distance). The basic formation task gathering…