Related papers: Min-Max Gathering on Infinite Grid
We deal with a set of autonomous robots moving on an infinite grid. Those robots are opaque, have limited visibility capabilities, and run using synchronous Look-Compute-Move cycles. They all agree on a common chirality, but have no global…
We consider the classical problem of making mobile processes gather or converge at a same position (as performed by swarms of animals in Nature). Existing works assume that each process can see all other processes, or all processes within a…
Robot swarms offer significant potential for inspecting diverse infrastructure, ranging from bridges to space stations. However, effective inspection requires accurate robot localization, which demands substantial computational resources…
In this chapter, we propose a novel approach for solving the coordination of a fleet of mobile robots, which consists of finding a set of collision-free trajectories for individual robots in the fleet. This problem is studied for several…
In the general pattern formation (GPF) problem, a swarm of simple autonomous, disoriented robots must form a given pattern. The robots' simplicity imply a strong limitation: When the initial configuration is rotationally symmetric, only…
We develop and analyze algorithms for dispersing a swarm of primitive robots in an unknown environment, R. The primary objective is to minimize the makespan, that is, the time to fill the entire region. An environment is composed of pixels…
Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…
In densely-packed robot swarms operating in confined regions, spatial interference -- which manifests itself as a competition for physical space -- forces robots to spend more time navigating around each other rather than performing the…
In this paper we introduce the notion of optimization under control and communication constraint in a robotic network. Starting from a general setup, we focus our attention on the problem of achieving rendezvous in minimum time for a…
We study the algorithmic problem of optimally covering a tree with $k$ mobile robots. The tree is known to all robots, and our goal is to assign a walk to each robot in such a way that the union of these walks covers the whole tree. We…
We consider the problem of maximizing the algebraic connectivity of the communication graph in a network of mobile robots by moving them into appropriate positions. We define the Laplacian of the graph as dependent on the pairwise distance…
Swarm robots, inspired by the emergence of animal herds, are robots that assemble a large number of modules and self-organize themselves to form specific morphologies and exhibit specific functions. These modular robots perform relatively…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
We study the Symmetric Rendezvous Search Problem for a multi-robot system. There are $n>2$ robots arbitrarily located on a line. Their goal is to meet somewhere on the line as quickly as possible. The robots do not know the initial location…
We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims…
The \textsc{Mutual Visibility} is a well-known problem in the context of mobile robots. For a set of $n$ robots disposed in the Euclidean plane, it asks for moving the robots without collisions so as to achieve a placement ensuring that no…
In the dispersion problem, a set of $k$ co-located mobile robots must relocate themselves in distinct nodes of an unknown network. The network is modeled as an anonymous graph $G=(V,E)$, where the nodes of the graph are not labeled. The…
This paper introduces collaborating robots which provide the possibility of enhanced task performance, high reliability and decreased. Collaborating-bots are a collection of mobile robots able to self-assemble and to self-organize in order…
A standard belief on emerging collective behavior is that it emerges from simple individual rules. Most of the mathematical research on such collective behavior starts from imperative individual rules, like always go to the center. But how…
Path planning for multiple tethered robots is a challenging problem due to the complex interactions among the cables and the possibility of severe entanglements. Previous works on this problem either consider idealistic cable models or…