arXiv subjects

Michael Amir

Publications and source records attributed to Michael Amir.

22 records · Page 2Linked to original sources

arXiv2022

A Discrete Model of Collective Marching on Rings

We study the collective motion of autonomous mobile agents on a ringlike environment. The agents' dynamics is inspired by known laboratory experiments on the dynamics of locust swarms. In these experiments, locusts placed at arbitrary locations and initial orientations on a ring-shaped arena are observed to eventually all march in the same direction. In this work we ask whether, and how fast, a similar phenomenon occurs in a stochastic swarm of simple agents whose goal is to maintain the same direction of motion for as long as possible. The agents are randomly initiated as marching either clockwise or counterclockwise on a wide ring-shaped region, which we model as $k$ "narrow" concentric tracks on a cylinder. Collisions cause agents to change their direction of motion. To avoid this, agents may decide to switch tracks so as to merge with platoons of agents marching in their direction. We prove that such agents must eventually converge to a local consensus about their direction of motion, meaning that all agents on each narrow track must eventually march in the same direction. We give asymptotic bounds for the expected amount of time it takes for such convergence or "stabilization" to occur, which depends on the number of agents, the length of the tracks, and the number of tracks. We show that when agents also have a small probability of "erratic", random track-jumping behaviour, a global consensus on the direction of motion across all tracks will eventually be reached. Finally, we verify our theoretical findings in numerical simulations.

cs.MA↗

arXiv2020

Fast Uniform Dispersion of a Crash-prone Swarm

We consider the problem of completely covering an unknown discrete environment with a swarm of asynchronous, frequently-crashing autonomous mobile robots. We represent the environment by a discrete graph, and task the robots with occupying every vertex and with constructing an implicit distributed spanning tree of the graph. The robotic agents activate independently at random exponential waiting times of mean $1$ and enter the graph environment over time from a source location. They grow the environment's coverage by 'settling' at empty locations and aiding other robots' navigation from these locations. The robots are identical and make decisions driven by the same simple and local rule of behaviour. The local rule is based only on the presence of neighbouring robots, and on whether a settled robot points to the current location. Whenever a robot moves, it may crash and disappear from the environment. Each vertex in the environment has limited physical space, so robots frequently obstruct each other. Our goal is to show that even under conditions of asynchronicity, frequent crashing, and limited physical space, the simple mobile robots complete their mission in linear time asymptotically almost surely, and time to completion degrades gracefully with the frequency of the crashes. Our model and analysis are based on the well-studied "totally asymmetric simple exclusion process" in statistical mechanics.

cs.DM↗

arXiv2019

Minimizing Travel in the Uniform Dispersal Problem for Robotic Sensors

The limited energy capacity of individual robotic agents in a swarm often limits the possible cooperative tasks they can perform. In this work, we investigate the problem of covering an unknown connected grid environment (e.g. a maze or connected corridors) with a robotic swarm so as to minimize the maximal number of steps that each member of the swarm makes and their activity time before their work is finished, thereby minimizing the energy requirements. The robots are autonomous, anonymous and identical, with local sensors and finite memory, and possess no communication capabilities. They are assumed to disperse over time from a fixed location, and to move synchronously. The robots are tasked with occupying every cell of the environment, while avoiding collisions. In the literature such topics are known as \textit{uniform dispersal problems}. The goal of minimizing the number of steps traveled by the robots has previously been studied in this context. Our contribution is a local robotic strategy for simply connected grid environments that, by exploiting their topology, achieves optimal makespan (the amount of time it takes to cover the environment) and minimizes the maximal number of steps taken by the individual robots before their deactivation. The robots succeed in discovering optimal paths to their eventual destinations, and finish the covering process in $2V-1$ time steps, where $V$ is the number of cells in the environment.

cs.MA↗

arXiv2019

Probabilistic Pursuits on Graphs

We consider discrete dynamical systems of "ant-like" agents engaged in a sequence of pursuits on a graph environment. The agents emerge one by one at equal time intervals from a source vertex $s$ and pursue each other by greedily attempting to close the distance to their immediate predecessor, the agent that emerged just before them from $s$, until they arrive at the destination point $t$. Such pursuits have been investigated before in the continuous setting and in discrete time when the underlying environment is a regular grid. In both these settings the agents' walks provably converge to a shortest path from $s$ to $t$. Furthermore, assuming a certain natural probability distribution over the move choices of the agents on the grid (in case there are multiple shortest paths between an agent and its predecessor), the walks converge to the uniform distribution over all shortest paths from $s$ to $t$. We study the evolution of agent walks over a general finite graph environment $G$. Our model is a natural generalization of the pursuit rule proposed for the case of the grid. The main results are as follows. We show that "convergence" to the shortest paths in the sense of previous work extends to all pseudo-modular graphs (i.e. graphs in which every three pairwise intersecting disks have a nonempty intersection), and also to environments obtained by taking graph products, generalizing previous results in two different ways. We show that convergence to the shortest paths is also obtained by chordal graphs, and discuss some further positive and negative results for planar graphs. In the most general case, convergence to the shortest paths is not guaranteed, and the agents may get stuck on sets of recurrent, non-optimal walks from $s$ to $t$. However, we show that the limiting distributions of the agents' walks will always be uniform distributions over some set of walks of equal length.

cs.DM↗