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Multi-objective search (MOS) has become essential in robotics, as real-world robotic systems need to simultaneously balance multiple, often conflicting objectives. Recent works explore complex interactions between objectives, leading to…
A property $\Pi$ on a finite set $U$ is \emph{monotone} if for every $X \subseteq U$ satisfying $\Pi$, every superset $Y \subseteq U$ of $X$ also satisfies $\Pi$. Many combinatorial properties can be seen as monotone properties. The problem…
A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, possibly at different times, have to meet at the same node. Agents are anonymous (identical), execute the same deterministic…
We consider the machine covering problem for selfish related machines. For a constant number of machines, m, we show a monotone polynomial time approximation scheme (PTAS) with running time that is linear in the number of jobs. It uses a…
Collective decision-making is an essential capability of large-scale multi-robot systems to establish autonomy on the swarm level. A large portion of literature on collective decision-making in swarm robotics focuses on discrete decisions…
Swarm robotics utilises decentralised self-organising systems to form complex collective behaviours built from the bottom-up using individuals that have limited capabilities. Previous work has shown that simple occlusion-based strategies…
Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify…
In the gathering problem, n autonomous robots have to meet on a single point. We consider the gathering of a closed chain of point-shaped, anonymous robots on a grid. The robots only have local knowledge about a constant number of…
We study the problem of multi-robot target assignment to minimize the total distance traveled by the robots until they all reach an equal number of static targets. In the first half of the paper, we present a necessary and sufficient…
In this paper, we study the $r$-gather problem, a natural formulation of minimum-size clustering in metric spaces. The goal of $r$-gather is to partition $n$ points into clusters such that each cluster has size at least $r$, and the maximum…
We study the problem of minimizing the resource capacity of autonomous agents cooperating to achieve a shared task. More specifically, we consider high-level planning for a team of homogeneous agents that operate under resource constraints…
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…
This paper investigates efficient techniques to collect and concentrate an under-actuated particle swarm despite obstacles. Concentrating a swarm of particles is of critical importance in health-care for targeted drug delivery, where…
The subject is the localization problem of an underwater swarm of autonomous underwater robots (AUV), in the frame of the HARNESS project; by localization, we mean the relative swarm configuration, i.e., the geometrical shape of the group.…
This paper deals with the classical problem of exploring a ring by a cohort of synchronous robots. We focus on the perpetual version of this problem in which it is required that each node of the ring is visited by a robot infinitely often.…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
Recent advances in Distributed Computing highlight models and algorithms for autonomous swarms of mobile robots that self-organise and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade…
We consider a set of k autonomous robots that are endowed with visibility sensors (but that are otherwise unable to communicate) and motion actuators. Those robots must collaborate to reach a sin- gle vertex that is unknown beforehand, and…
Robots with very limited capabilities are placed on the vertices of a graph and are required to move toward a single, common vertex, where they remain stationary once they arrive. This task is referred to as the GATHERING problem. Most of…
Research in multi-robot and swarm systems has seen significant interest in cooperation of agents in complex and dynamic environments. To effectively adapt to unknown environments and maximize the utility of the group, robots need to…