arXiv subjects

Alfred M. Bruckstein

Publications and source records attributed to Alfred M. Bruckstein.

At least 37 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↗

arXiv2022

Pincer-Based vs. Same-Direction Strategies of Search for Smart Evaders by Swarms of Agents

Suppose in a given planar region, there are smart mobile evaders and we want to detect them using sweeping agents. We assume that the agents have line sensors of equal length. We propose procedures for designing cooperative sweeping processes that ensure successful completion of the task, thereby deriving conditions on the sweeping speed of the agents and their paths. Successful completion of the task means that evaders with a known limit on their speed cannot escape the sweeping agents. A simpler task for the sweeping swarm is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the speed the sweeping agent must have. This critical speed is derived to ensure the satisfaction of the confinement task. Increasing the speed above the lower bound enables the agents to complete the search task as well. We present a quantitative and qualitative comparison analysis between the total search time of same-direction sweep processes and pincer-movement search strategies. We evaluate the different strategies by using two metrics, total search time and the minimal critical speed required for a successful search. We compare two types of pincer-movement search processes, circular and spiral, with their same-direction counterparts, for any even number of sweeping agents. We prove that pincer based strategies provide superior results in all practical scenarios and that the spiral pincer sweep process allows detection of all evaders while sweeping at nearly theoretically optimal speeds.

cs.MA↗

arXiv2021

A Bound on the Edge-Flipping Distance between Triangulations (Revisiting the Proof)

We revisit here a fundamental result on planar triangulations, namely that the flip distance between two triangulations is upper-bounded by the number of proper intersections between their straight-segment edges. We provide a complete and detailed proof of this result in a slightly generalised setting using a case-based analysis that fills several gaps left by previous proofs of the result.

cs.CC↗

arXiv2021

Doubly Stochastic Pairwise Interactions for Agreement and Alignment

Random pairwise encounters often occur in large populations, or groups of mobile agents, and various types of local interactions that happen at encounters account for emergent global phenomena. In particular, in the fields of swarm robotics, sociobiology, and social dynamics, several types of local pairwise interactions were proposed and analysed leading to spatial gathering or clustering and agreement in teams of robotic agents coordinated motion, in animal herds, or in human societies. We here propose a very simple stochastic interaction at encounters that leads to agreement or geometric alignment in swarms of simple agents, and analyse the process of converging to consensus. Consider a group of agents whose "states" evolve in time by pairwise interactions: the state of an agent is either a real value (a randomly initialised position within an interval) or a vector that is either unconstrained (e.g. the location of the agent in the plane) or constrained to have unit length (e.g. the direction of the agent's motion). The interactions are doubly stochastic, in the sense that, at discrete time steps, pairs of agents are randomly selected and their new states are independently and uniformly set at random in (local) domains or intervals defined by the states of the interacting pair. We show that such processes lead, in finite expected time (measured by the number of interactions that occurred) to agreement in case of unconstrained states and alignment when the states are unit vectors.

cs.MA↗

arXiv2020

Broadcast Guidance of Agents in Deviated Linear Cyclic Pursuit

In this report we show the emergent behavior of a group of agents, ordered from 1 to n, performing deviated, linear, cyclic pursuit, in the presence of a broadcast guidance control. Each agent senses the relative position of its target, i.e. agent i senses the relative position of agent i+1. The broadcast control, a velocity signal, is detected by a random set of agents in the group. We assume the agents to be modeled as single integrators. We show that the emergent behavior of the group is determined by the deviation angle and by the set of agents detecting the guidance control.

cs.RO↗

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↗

arXiv2020

Search for Smart Evaders with Swarms of Sweeping Agents

Suppose that in a given planar circular region, there are some smart mobile evaders and we would like to find them using sweeping agents. We assume that each agent has a line sensor of length 2r. We propose procedures for designing cooperative sweeping processes that ensure the successful completion of the task, thereby deriving conditions on the sweeping velocity of the agents and their paths. Successful completion of the task means that evaders with a given limit on their velocity cannot escape the sweeping agents. A simpler task for the sweeping swarm is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the velocity that the sweeper swarm must have. This critical velocity is derived to ensure the satisfaction of the confinement task. Increasing the velocity above the lower bound enables the agents to complete the search task as well. We present results on the total search time as a function of the sweeping velocity of the swarm's agents given the initial conditions on the size of the search region and the maximal velocity of the evaders.

cs.MA↗

arXiv2020

Probabilistic Gathering Of Agents With Simple Sensors

Gathering is a fundamental task for multi-agent systems and the problem has been studied under various assumptions on the sensing capabilities of mobile agents. This paper addresses the problem for a group of agents that are identical and indistinguishable, oblivious, and lack the capacity of direct communication. At the beginning of unit-time intervals, the agents select random headings in the plane and then detect the presence of other agents behind them. Then they move forward only if no agents are detected in their sensing "back half-plane". Two types of motion are considered: when no peers are detected behind them, either the agents perform unit jumps forward, or they start to move with unit speed while continuously sensing their back half-plane, and stop whenever another agent appears there. For the first type of motion extensive empirical evidence suggests that with high probability clustering occurs in finite expected time to a small region with diameter of about the size of the unit jump, while for continuous sensing and motion we can prove gathering in finite expected time if a "blind-zone" is assumed in their sensing half-plane. Relationships between the number of agents or the size of the blind-zone and convergence time are empirically studied and compared to a theoretical upper-bound dependent on these factors.

cs.MA↗

arXiv2020

Search for Smart Evaders with Sweeping Agents

Suppose that in a given planar circular region, there are some smart mobile evaders and we would like to find them using sweeping agents. We assume that the sweeping agents are in a line formation whose total length is 2r. We propose procedures for designing a sweeping process that ensures the successful completion of the task, thereby deriving conditions on the sweeping velocity of the linear formation and its path. Successful completion of the task means that evaders with a given limit on their velocity cannot escape the sweeping agents. A simpler task for the sweeping formation is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the velocity that the sweeper line formation must have. This critical velocity is derived to ensure the satisfaction of the confinement task. Increasing the velocity above the lower bound enables the agents to complete the search task as well. We present results on the total search time as a function of the sweeping velocity of the formation given the initial conditions on the size of the search region and the maximal velocity of the evaders.

cs.MA↗

arXiv2020

Seeing Things in Random-Dot Videos

Humans possess an intricate and powerful visual system in order to perceive and understand the environing world. Human perception can effortlessly detect and correctly group features in visual data and can even interpret random-dot videos induced by imaging natural dynamic scenes with highly noisy sensors such as ultrasound imaging. Remarkably, this happens even if perception completely fails when the same information is presented frame by frame rather than in a video sequence. We study this property of surprising dynamic perception with the first goal of proposing a new detection and spatio-temporal grouping algorithm for such signals when, per frame, the information on objects is both random and sparse and embedded in random noise. The algorithm is based on the succession of temporal integration and spatial statistical tests of unlikeliness, the a contrario framework. The algorithm not only manages to handle such signals but the striking similarity in its performance to the perception by human observers, as witnessed by a series of psychophysical experiments on image and video data, leads us to see in it a simple computational Gestalt model of human perception with only two parameters: the time integration and the visual angle for candidate shapes to be detected.

cs.CV↗

arXiv2019

Erratic Extremism causes Dynamic Consensus (a new model for one-dimensional opinion dynamics)

A society of agents, with ideological positions, or "opinions" measured by real values ranging from $-\infty$ (the "far left") to $+\infty$ (the "far right"), is considered. At fixed (unit) time intervals agents repeatedly reconsider and change their opinions if and only if they find themselves at the extremes of the range of ideological positions held by members of the society. Extremist agents are erratic: they become either more radical, and move away from the positions of other agents, with probability $\varepsilon$, or more moderate, and move towards the positions held by peers, with probability $(1 - \varepsilon)$. The change in the opinion of the extremists is one unit on the real line. We prove that the agent positions cluster in time, with all non-extremist agents located within a unit interval. However, the consensus opinion is dynamic. Due to the extremists' erratic behavior the clustered opinion set performs a "sluggish" random walk on the entire range of possible ideological positions (the real line). The inertia of the group, the reluctance of the society's agents to change their consensus opinion, increases with the size of the group. The extremists perform biased random walk excursions to the right and left and, in time, their actions succeed to move the society of agents in random directions. The "far left" agent effectively pushes the group consensus toward the right, while the "far right" agent counter-balances the push and causes the consensus to move toward the left. We believe that this model, and some of its variations, has the potential to explain the real world swings in societal ideologies that we see around us.

cs.MA↗

arXiv2019

Local Interactions for Cohesive Flexible Swarms

Distributed gathering algorithms aim to achieve complete visibility graphs via a "never lose a neighbour" policy. We suggest a method to maintain connected graph topologies, while reducing the number of effective edges in the graph to order n. This allows to achieve different goals and swarming behaviours: the system remains connected but flexible, hence can maneuver in environments that are replete with obstacles and narrow passages, etc.

cs.MA↗

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

Benefiting from Duplicates of Compressed Data: Shift-Based Holographic Compression of Images

Storage systems often rely on multiple copies of the same compressed data, enabling recovery in case of binary data errors, of course, at the expense of a higher storage cost. In this paper we show that a wiser method of duplication entails great potential benefits for data types tolerating approximate representations, like images and videos. We propose a method to produce a set of distinct compressed representations for a given signal, such that any subset of them allows reconstruction of the signal at a quality depending only on the number of compressed representations utilized. Essentially, we implement the holographic representation idea, where all the representations are equally important in refining the reconstruction. Here we propose to exploit the shift sensitivity of common compression processes and generate holographic representations via compression of various shifts of the signal. Two implementations for the idea, based on standard compression methods, are presented: the first is a simple, optimization-free design. The second approach originates in a challenging rate-distortion optimization, mitigated by the alternating direction method of multipliers (ADMM), leading to a process of repeatedly applying standard compression techniques. Evaluation of the approach, in conjunction with the JPEG2000 image compression standard, shows the effectiveness of the optimization in providing compressed holographic representations that, by means of an elementary reconstruction process, enable impressive gains of several dBs in PSNR over exact duplications.

cs.MM↗

arXiv2019

COME TOGETHER: Multi-Agent Geometric Consensus (Gathering, Rendezvous, Clustering, Aggregation)

This report surveys results on distributed systems comprising mobile agents that are identical and anonymous, oblivious and interact solely by adjusting their motion according to the relative location of their neighbours. The agents are assumed capable of sensing the presence of other agents within a given sensing range and able to implement rules of motion based on full or partial information on the geometric constellation of their neighbouring agents. Eight different problems that cover assumptions of finite vs infinite sensing range, direction and distance vs direction only sensing and discrete vs continuous motion, are analyzed in the context of geometric consensus, clustering or gathering tasks.

cs.MA↗

arXiv2019

On Steering Swarms

The main contribution of this paper is a novel method allowing an external observer/controller to steer and guide swarms of identical and indistinguishable agents, in spite of the agents' lack of information on absolute location and orientation. Importantly, this is done via simple global broadcast signals, based on the observed average swarm location, with no need to send control signals to any specific agent in the swarm.

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↗

arXiv2018

Restoration by Compression

In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods were suggested only for the Gaussian denoising task, leaving more complicated restoration problems without a generally constructive approach. Here we present practical methods for complexity-regularized restoration of signals, accommodating degradations caused by a known linear operator of an arbitrary form. Our iterative procedure, obtained using the alternating direction method of multipliers (ADMM) approach, addresses the restoration task as a sequence of simpler problems involving L2-regularized estimations and rate-distortion optimizations (considering the squared-error criterion). Further, we replace the rate-distortion optimizations with an arbitrary standardized compression technique and thereby restore the signal by leveraging underlying models designed for compression. Additionally, we propose a shift-invariant complexity regularizer, measuring the bit-cost of all the shifted forms of the estimate, extending our method to use averaging of decompressed outputs gathered from compression of shifted signals. On the theoretical side, we present an analysis of complexity-regularized restoration of a cyclo-stationary Gaussian signal from deterioration by a linear shift-invariant operator and an additive white Gaussian noise. The theory shows that optimal complexity-regularized restoration relies on an elementary restoration filter and compression spreading reconstruction quality unevenly based on the energy distribution of the degradation filter. Nicely, these ideas are realized also in the proposed practical methods. The presented experiments show good results for image deblurring and inpainting using the JPEG2000 and HEVC compression standards.

cs.IT↗