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Alfred M. Bruckstein

Publications and source records attributed to Alfred M. Bruckstein.

At least 19 recordsLinked to original sources

Sensor to Pixels: Decentralized Swarm Gathering via Image-Based Reinforcement Learning

This study highlights the potential of image-based reinforcement learning methods for addressing swarm-related tasks. In multi-agent reinforcement learning, effective policy learning depends on how agents sense, interpret, and process inputs. Traditional approaches often rely on handcrafted feature extraction or raw vector-based representations, which limit the scalability and efficiency of learned policies concerning input order and size. In this work we propose an image-based reinforcement learning method for decentralized control of a multi-agent system, where observations are encoded as structured visual inputs that can be processed by Neural Networks, extracting its spatial features and producing novel decentralized motion control rules. We evaluate our approach on a multi-agent convergence task of agents with limited-range and bearing-only sensing that aim to keep the swarm cohesive during the aggregation. The algorithm's performance is evaluated against two benchmarks: an analytical solution proposed by Bellaiche and Bruckstein, which ensures convergence but progresses slowly, and VariAntNet, a neural network-based framework that converges much faster but shows medium success rates in hard constellations. Our method achieves high convergence, with a pace nearly matching that of VariAntNet. In some scenarios, it serves as the only practical alternative.

cs.LG

VariAntNet: Learning Decentralized Control of Multi-Agent Systems

A simple multi-agent system can be effectively utilized in disaster response applications, such as firefighting. Such a swarm is required to operate in complex environments with limited local sensing and no reliable inter-agent communication or centralized control. These simple robotic agents, also known as Ant Robots, are defined as anonymous agents that possess limited sensing capabilities, lack a shared coordinate system, and do not communicate explicitly with one another. A key challenge for simple swarms lies in maintaining cohesion and avoiding fragmentation despite limited-range sensing. Recent advances in machine learning offer effective solutions to some of the classical decentralized control challenges. We propose VariAntNet, a deep learning-based decentralized control model designed to facilitate agent swarming and collaborative task execution. VariAntNet includes geometric features extraction from unordered, variable-sized local observations. It incorporates a neural network architecture trained with a novel, differentiable, multi-objective, mathematically justified loss function that promotes swarm cohesiveness by utilizing the properties of the visibility graph Laplacian matrix. VariAntNet is demonstrated on the fundamental multi-agent gathering task, where agents with bearing-only and limited-range sensing must gather at some location. VariAntNet significantly outperforms an existing analytical solution, achieving more than double the convergence rate while maintaining high swarm connectivity across varying swarm sizes. While the analytical solution guarantees cohesion, it is often too slow in practice. In time-critical scenarios, such as emergency response operations where lives are at risk, slower analytical methods are impractical and justify the loss of some agents within the swarm. This paper presents and analyzes this trade-off in detail.

cs.LG

Metric Convolutions: A Unifying Theory to Adaptive Image Convolutions

Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical framework. By returning to a metric perspective for images, now seen as two-dimensional manifolds equipped with notions of local and geodesic distances, either symmetric (Riemannian) or not (Finsler), we provide a unifying principle: the kernel positions are samples of unit balls of implicit metrics. With this new perspective, we also propose metric convolutions, a novel approach that samples unit balls from explicit signal-dependent metrics, providing interpretable operators with geometric regularisation. This framework, compatible with gradient-based optimisation, can directly replace existing convolutions applied to either input images or deep features of neural networks. Metric convolutions typically require fewer parameters and provide better generalisation. Our approach shows competitive performance in standard denoising and classification tasks.

cs.CV

Time, Travel, and Energy in the Uniform Dispersion Problem

We investigate the algorithmic problem of uniformly dispersing a swarm of robots in an unknown, gridlike environment. In this setting, our goal is to study the relationships between performance metrics and robot capabilities. We introduce a formal model comparing dispersion algorithms based on makespan, traveled distance, energy consumption, sensing, communication, and memory. Using this framework, we classify uniform dispersion algorithms according to their capability requirements and performance. We prove that while makespan and travel can be minimized in all environments, energy cannot, if the swarm's sensing range is bounded. In contrast, we show that energy can be minimized by ``ant-like'' robots in synchronous settings and asymptotically minimized in asynchronous settings, provided the environment is topologically simply connected, by using our ``Find-Corner Depth-First Search'' (FCDFS) algorithm. Our theoretical and experimental results show that FCDFS significantly outperforms known algorithms. Our findings reveal key limitations in designing swarm robotics systems for unknown environments, emphasizing the role of topology in energy-efficient dispersion.

cs.RO

Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embedding

Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the underlying data structure, multi-dimensional scaling (MDS) methods focus on preserving pairwise dissimilarities, such as distances. They optimise the embedding to have pairwise distances as close as possible to the data dissimilarities. However, the current standard is limited to embedding data in Riemannian manifolds. Motivated by the lack of asymmetry in the Riemannian metric of the embedding space, this paper extends the MDS problem to a natural asymmetric generalisation of Riemannian manifolds called Finsler manifolds. Inspired by Euclidean space, we define a canonical Finsler space for embedding asymmetric data. Due to its simplicity with respect to geodesics, data representation in this space is both intuitive and simple to analyse. We demonstrate that our generalisation benefits from the same theoretical convergence guarantees. We reveal the effectiveness of our Finsler embedding across various types of non-symmetric data, highlighting its value in applications such as data visualisation, dimensionality reduction, directed graph embedding, and link prediction.

cs.CV

Distributed and Decentralized Control and Task Allocation for Flexible Swarms

This paper introduces a novel bio-mimetic approach for distributed control of robotic swarms, inspired by the collective behaviors of swarms in nature such as schools of fish and flocks of birds. The agents are assumed to have limited sensory perception, lack memory, be Identical, anonymous, and operate without interagent explicit communication. Despite these limitations, we demonstrate that collaborative exploration and task allocation can be executed by applying simple local rules of interactions between the agents. A comprehensive model comprised of agent, formation, and swarm layers is proposed in this paper, where each layer performs a specific function in shaping the swarm's collective behavior, thereby contributing to the emergence of the anticipated behaviors. We consider four principles combined in the design of the distributed control process: Cohesiveness, Flexibility, Attraction-Repulsion, and Peristaltic Motion. We design the control algorithms as reactive behaviour that enables the swarm to maintain connectivity, adapt to dynamic environments, spread out and cover a region with a size determined by the number of agents, and respond to various local task requirements. We explore some simple broadcast control-based steering methods, that result in inducing "anonymous ad-hoc leaders" among the agents, capable of guiding the swarm towards yet unexplored regions with further tasks. Our analysis is complemented by simulations, validating the efficacy of our algorithms. The experiments with various scenarios showcase the swarm`s capability to self-organize and perform tasks effectively under the proposed framework. The possible implementations include domains that necessitate emergent coordination and control in multi-agent systems, without the need for advanced individual abilities or direct communication.

cs.MA

Patrolling Grids with a Bit of Memory

This work addresses the challenge of patrolling regular grid graphs of any dimension using a single mobile agent with minimal memory and limited sensing range. We show that it is impossible to patrol some grid graphs with $0$ bits of memory, regardless of sensing range, and give an exact characterization of those grid graphs that can be patrolled with $0$ bits of memory and sensing range $V$. On the other hand, we show that an algorithm exists using $1$ bit of memory and $V=1$ that patrols any $d$-dimensional grid graph. This result is surprising given that the agent must be able to move in $2d$ distinct directions to patrol, while $1$ bit of memory allows specifying only two directions per sensory input. Our $1$-bit patrolling algorithm handles this by carefully exploiting a small state-space to access all the needed directions while avoiding getting stuck. Overall, our results give concrete evidence that extremely little memory is needed for patrolling highly regular environments like grid graphs compared to arbitrary graphs. The techniques we use, such as partitioning the environment into sensing regions and exploiting distinct coordinates resulting from higher-dimensionality, may be applicable to analyzing the space complexity of patrolling in other types of regular environments as well.

cs.RO

Defense Against Smart Invaders with Swarms of Sweeping Agents

The goal of this research is to devise guaranteed defense policies that allow to protect a given region from the entrance of smart mobile invaders by detecting them using a team of defending agents equipped with identical line sensors. By designing cooperative defense strategies that ensure all invaders are detected, conditions on the defenders' speed are derived. Successful accomplishment of the defense task implies invaders with a known limit on their speed cannot slip past the defenders and enter the guarded region undetected. The desired outcome of the defense protocols is to defend the area and additionally to expand it as much as possible. Expansion becomes possible if the defenders' speed exceeds a critical speed that is necessary to only defend the initial region. We present results on the total search time, critical speeds and maximal expansion possible for two types of novel pincer-movement defense processes, circular and spiral, for any even number of defenders. The proposed spiral process allows to detect invaders at nearly the lowest theoretically optimal speed, and if this speed is exceeded, it also allows to expand the protected region almost to the maximal area.

cs.MA

Exploration of unknown indoor regions by a swarm of energy-constrained drones

Several distributed algorithms are presented for the exploration of unknown indoor regions by a swarm of flying, energy constrained agents. The agents, which are identical, autonomous, anonymous and oblivious, uniformly cover the region and thus explore it using predefined action rules based on locally sensed information and the energy level of the agents. While flying drones have many advantages in search and rescue scenarios, their main drawback is a high power consumption during flight combined with limited, on-board energy. Furthermore, in these scenarios agent size is severely limited and consequently so are the total weight and capabilities of the agents. The region is modeled as a connected sub-set of a regular grid composed of square cells that the agents enter, over time, via entry points. Some of the agents may settle in unoccupied cells as the exploration progresses. Settled agents conserve energy and become virtual pheromones for the exploration and coverage process, beacons that subsequently aid the remaining, and still exploring, mobile agents. The termination of the coverage process is based on a backward propagating information diffusion scheme. Various algorithmical alternatives are discussed and upper bounds derived and compared to experimental results. Finally, an optimal entry rate that minimizes the total energy consumption is derived for the case of a linear regions.

cs.MA

Spiral Sweeping Search for Smart Evaders

Consider a given planar circular region, in which there is an unknown number of smart mobile evaders. We wish to detect evaders using a line formation of sweeping agents whose total sensing length is predetermined. We propose procedures for designing spiral sweeping protocols that ensure the successful completion of the task, thus deriving conditions on the sweeping speed of the linear formation and its path. Successful completion of the task implies that evaders with a given limit on their speed cannot escape the sweeping agents. A simpler task for the sweeping formation is the confinement of evaders to a desired region, such as their original domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the speed that the sweeping agents must have. This critical speed is derived to ensure the satisfaction of the confinement task. Increasing the speed above the lower bound enables the sweepers to complete the search task as well. We develop two spiral line formation search processes for smart evaders, that address current limitations in search against smart evaders. Additionally, we present a quantitative and qualitative comparison analysis between the total search time of circular line formation sweep processes and spiral line formation processes. We evaluate the different strategies by using two metrics, total search time and the minimal critical speed required for a successful search.

cs.MA

Guaranteed Evader Detection in Multi-Agent Search Tasks using Pincer Trajectories

Assume that inside an initial planar area there are smart mobile evaders attempting to avoid detection by a team of sweeping searching agents. All sweepers detect evaders with fan-shaped sensors, modeling the field of view of real cameras. Detection of all evaders is guaranteed with cooperative sweeping strategies, by setting requirements on sweepers' speed, and by carefully designing their trajectories. Assume the smart evaders have an upper limit on their speed which is a-priori known to the sweeping team. An easier task for the team of sweepers is to confine evaders to the domain in which they are initially located. The sweepers accomplish the confinement task if they move sufficiently fast and detect evaders by applying an appropriate search strategy. Any given search strategy results in a minimal sweeper's speed in order to be able to detect all evaders. The minimal speed guarantees the ability of the sweeping team to confine evaders to their original domain, and if the sweepers move faster they are able to detect all evaders that are present in the region. We present results on the total search time for a novel pincer-movement based search protocol that utilizes complementary trajectories along with adaptive sensor geometries for any even number of pursuers.

cs.MA

A model is worth tens of thousands of examples

Traditional signal processing methods relying on mathematical data generation models have been cast aside in favour of deep neural networks, which require vast amounts of data. Since the theoretical sample complexity is nearly impossible to evaluate, these amounts of examples are usually estimated with crude rules of thumb. However, these rules only suggest when the networks should work, but do not relate to the traditional methods. In particular, an interesting question is: how much data is required for neural networks to be on par or outperform, if possible, the traditional model-based methods? In this work, we empirically investigate this question in two simple examples, where the data is generated according to precisely defined mathematical models, and where well-understood optimal or state-of-the-art mathematical data-agnostic solutions are known. A first problem is deconvolving one-dimensional Gaussian signals and a second one is estimating a circle's radius and location in random grayscale images of disks. By training various networks, either naive custom designed or well-established ones, with various amounts of training data, we find that networks require tens of thousands of examples in comparison to the traditional methods, whether the networks are trained from scratch or even with transfer-learning or finetuning.

cs.LG

From Compass and Ruler to Convolution and Nonlinearity: On the Surprising Difficulty of Understanding a Simple CNN Solving a Simple Geometric Estimation Task

Neural networks are omnipresent, but remain poorly understood. Their increasing complexity and use in critical systems raises the important challenge to full interpretability. We propose to address a simple well-posed learning problem: estimating the radius of a centred pulse in a one-dimensional signal or of a centred disk in two-dimensional images using a simple convolutional neural network. Surprisingly, understanding what trained networks have learned is difficult and, to some extent, counter-intuitive. However, an in-depth theoretical analysis in the one-dimensional case allows us to comprehend constraints due to the chosen architecture, the role of each filter and of the nonlinear activation function, and every single value taken by the weights of the model. Two fundamental concepts of neural networks arise: the importance of invariance and of the shape of the nonlinear activation functions.

cs.LG

Stigmergy-based, Dual-Layer Coverage of Unknown Indoor Regions

We present algorithms for uniformly covering an unknown indoor region with a swarm of simple, anonymous and autonomous mobile agents. The exploration of such regions is made difficult by the lack of a common global reference frame, severe degradation of radio-frequency communication, and numerous ground obstacles. We propose addressing these challenges by using airborne agents, such as Micro Air Vehicles, in dual capacity, both as mobile explorers and (once they land) as beacons that help other agents navigate the region. The algorithms we propose are designed for a swarm of simple, identical, ant-like agents with local sensing capabilities. The agents enter the region, which is discretized as a graph, over time from one or more entry points and are tasked with occupying all of its vertices. Unlike many works in this area, we consider the requirement of informing an outside operator with limited information that the coverage mission is complete. Even with this additional requirement we show, both through simulations and mathematical proofs, that the dual role concept results in linear-time termination, while also besting many well-known algorithms in the literature in terms of energy use.

cs.MA

Multi-Agent Distributed and Decentralized Geometric Task Allocation

We consider the general problem of geometric task allocation, wherein a large, decentralised swarm of simple mobile agents must detect the locations of tasks in the plane and position themselves nearby. The tasks are represented by an a priori unknown demand profile $Φ(x,y)$ that determines how many agents are needed in each location. The agents are autonomous, oblivious and indistinguishable, and have finite sensing range. They must configure themselves according to $Φ$ using only local information about $Φ$ and about the positions of nearby agents. All agents act according to the same local sensing-based rule of motion, and cannot explicitly communicate nor share information. We propose an optimization-based approach to the problem which results in attraction-repulsion dynamics. Repulsion encourages agents to spread out and explore the region so as to find the tasks, and attraction causes them to accumulate at task locations. We derive this approach via gradient descent over an appropriate ``error'' functional, and test it extensively through numerical simulations. The figures in this work are snapshots of simulations that can be viewed online at https://youtu.be/kyUiGYSaaoQ.

cs.MA

Optimal Physical Sorting of Mobile Agents

Given a collection of red and blue mobile agents located on two grid rows, we seek to move all the blue agents to the far left side and all the red agents to the far right side, thus \textit{physically sorting} them according to color. The agents all start on the bottom row. They move simultaneously at discrete time steps and must not collide. Our goal is to design a centralized algorithm that controls the agents so as to sort them in the least number of time steps. We derive an \textbf{exact} lower bound on the amount of time any algorithm requires to sort a given initial configuration of agents. We find an instance optimal algorithm that provably matches this lower bound, attaining the best possible sorting time for any initial configuration. Surprisingly, we find that whenever the leftmost agent is red and the rightmost agent is blue, a straightforward decentralized and local sensing-based algorithm is at most $1$ time step slower than the centralized instance-optimal algorithm.

cs.DM

Emerging cooperation on the road by myopic local interactions

We study a combinatorial problem inspired by the following scenario: fully autonomous vehicles drive on a multi-lane ($m \geq 2$) road. Each vehicle heads to its own destination and is allowed to exit the road only through a single designated off-ramp lane. However, an individual vehicle has a severely limited memory and sensing capabilities, and, moreover, does not communicate with its peers. In this work we present a distributed algorithm that, nonetheless, allows vehicles to get to the desired lane without collisions and in timely manner.

cs.MA

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