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 that form a connected subset of the integer grid. There is at most one robot per pixel and robots move horizontally or vertically at unit speed. Robots enter R by means of k>=1 door pixels Robots are primitive finite automata, only having local communication, local sensors, and a constant-sized memory. We first give algorithms for the single-door case (i.e., k=1), analyzing the algorithms both theoretically and experimentally. We prove that our algorithms have optimal makespan 2A-1, where A is the area of R. We next give an algorithm for the multi-door case (k>1), based on a wall-following version of the leader-follower strategy. We prove that our strategy is O(log(k+1))-competitive, and that this bound is tight for our strategy and other related strategies.
There has been considerable study recently of distributed control and coordination of a set of autonomous robots. Gage @cite_0 @cite_1 has proposed the development of command and control tools for arbitrarily large swarms of microrobots and has proposed coverage paradigms in the context of robot dispersal in an environment. @cite_18 @cite_15 propose the notion of pheromone robotics'' for world-embedded computation. @cite_22 @cite_25 @cite_23 @cite_21 developed multi-robot algorithms, directly inspired by ant behaviors, for searching and covering. @cite_26 @cite_29 and @cite_24 @cite_3 @cite_13 have studied algorithmic aspects of pattern formation in distributed autonomous robotics under various models of robots with minimal capabilities. The related flocking problem, which requires that a set of robots follow a leader while maintaining a formation, has been studied in several recent papers; see, e.g., @cite_12 @cite_2 @cite_16 . Balch @cite_20 has developed Teambots'', a Java-based general-purpose multi-robot simulator.
@cite_18 @cite_26 @cite_22 @cite_29 @cite_21 @cite_1 @cite_20 @cite_3 @cite_0 @cite_24 @cite_23 @cite_2 @cite_15 @cite_16 @cite_13 @cite_25 @cite_12
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We present a novel end-to-end solution for distributed multirobot coordination that translates multitouch gestures into low-level control inputs for teams of robots. Highlighting the need for a holistic solution to the problem of scalable human control of multirobot teams, we present a novel control algorithm with provable guarantees on the robots’ motion that lends itself well to input from modern tablet and smartphone interfaces. Concretely, we develop an iOS application in which the user is presented with a team of robots and a bounding box (prism). The user carefully translates and scales the prism in a virtual environment; these prism coordinates are wirelessly transferred to our server and then received as input to distributed onboard robot controllers. We develop a novel distributed multirobot control policy which provides guarantees on convergence to a goal with distance bounded linearly in the number of robots, and avoids interrobot collisions. This approach allows the human user to solve the cognitive tasks such as path planning, while leaving precise motion to the robots. Our system was tested in simulation and experiments, demonstrating its utility and effectiveness. Distributed algorithms for multi-robot systems rely on network communications to share information. However, the motion of the robots changes the network topology, which affects the information presented to the algorithm. For an algorithm to produce accurate output, robots need to communicate rapidly enough to keep the network topology correlated to their physical configuration. Infrequent communications will cause most multi-robot distributed algorithms to produce less accurate results, and cause some algorithms to stop working altogether. The central theme of this work is that algorithm accuracy, communications bandwidth, and physical robot speed are related. This thesis has three main contributions: First, I develop a prototypical multi-robot application and computational model, propose a set of complexity metrics to evaluate distributed algorithm performance on multi-robot systems, and introduce the idea of the robot speed ratio, a dimensionless measure of robot speed relative to message speed in networks that rely on multi-hop communication. The robot speed ratio captures key relationships between communications bandwidth, mobility, and algorithm accuracy, and can be used at design time to trade off between them. I use this speed ratio to evaluate the performance of existing distributed algorithms for multi-hop communication and navigation. Second, I present a definition of boundaries in multi-robot systems, and develop new distributed algorithms to detect and characterize them. Finally, I define the problem of dynamic task assignment, and present four distributed algorithms that solve this problem, each representing a different trade-off between accuracy, running time, and communication resources. All the algorithms presented in this work are provably correct under ideal conditions and produce verifiable real-world performance. They are self-stabilizing and robust to communications failures, population changes, and other errors. All the algorithms were tested on a swarm of 112 robots. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.) Swarms of mobile robots recently attracted the focus of the Distributed Computing community. One of the fundamental problems in this context is that of exploration: the robots must coordinate to visit all locations that are reachable from their initial positions. Despite its apparent simplicity, this problem proved quite hard to characterise fully, due to many model variants, leading to informal error-prone reasoning. Over the past few years, a significant effort permitted to set up a formal framework, relying on the Coq proof assistant, which was used to provide certified results when robots evolve in a continuous bi-dimensional Euclidean space. However, the most challenging issues with exploration arise in the discrete setting (a.k.a. graph), where locations are modeled as vertices and where edges between vertices denote the ability for a robot to move from one location to the next. We present a formal model to tackle problems and reason about robot algorithms arising in the discrete setting. Our approach extends and generalises previous research efforts focusing on the continuous model. As case studies, we consider fundamental impossibility results for exploration with stop in the discrete model. To our knowledge, those are the first certified results in this context. This framework paves the way for a general certification workflow dedicated to mobile robots on graphs. Consider a setting where robots must visit sites represented as nodes in a graph, but each robot may fail when traversing an edge. The goal is to find a set of paths for a team of robots which maximizes the expected number of nodes collectively visited, while guaranteeing that the paths satisfy a notion of “independence” formalized by a matroid (e.g. limits on team size, number of visits to regions), and that the probabilities that each robot survives to its destination are above a given threshold. We call this problem the Matroid Team Surviving Orienteers (MTSO) problem, which has broad applications such as environmental monitoring in risky regions and search and rescue in dangerous conditions. We present the MTSO formally and detail numerous examples of matroids in a path planning context. We then propose an approximate greedy algorithm for selecting a feasible set of paths and prove that the value of the output is within a factor p s p s + λ of the optimum, where p s is the per-robot survival probability threshold and 1 λ ≤ 1 is the approximation factor of an oracle routine for the well known orienteering problem. We demonstrate the efficiency of our approach by applying it to a scenario where a team of robots must gather information while avoiding pirates in the Coral Triangle. The deployment of multiple robots for achieving a common goal helps to improve the performance, efficiency, and or robustness in a variety of tasks. In particular, the observation of moving targets is an important multirobot application that still exhibits numerous open challenges, including the effective coordination of the robots. This paper reviews control techniques for cooperative mobile robots monitoring multiple targets. The simultaneous movement of robots and targets makes this problem particularly interesting, and our review systematically addresses this cooperative multirobot problem for the first time. We classify and critically discuss the control techniques: cooperative multirobot observation of multiple moving targets, cooperative search, acquisition, and track, cooperative tracking, and multirobot pursuit evasion. We also identify the five major elements that characterize this problem, namely, the coordination method, the environment, the target, the robot and its sensor(s). These elements are used to systematically analyze the control techniques. The majority of the studied work is based on simulation and laboratory studies, which may not accurately reflect real-world operational conditions. Importantly, while our systematic analysis is focused on multitarget observation, our proposed classification is useful also for related multirobot applications. This paper presents the optimal path of nonholonomic multi robots with coherent formation in a leader-follower structure in the presence of obstacles using Asexual Reproduction Optimization (ARO). The robots path planning based on potential field method are accomplished and a novel formation controller for mobile robots based on potential field method is proposed. The efficiency of the proposed method is verified through simulation and experimental studies by applying them to control the formation of four e-Pucks robots (low-cost mobile robot platform). Also the proposed method is compared with Simulated Annealing, Improved Harmony Search and Cuckoo Optimization Algorithm methods and the experimental results, higher performance and fast convergence time to the best solution of the ARO demonstrated that this optimization method is appropriate for real time control application. Consider a set of n finite set of simple autonomous mobile robots (asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, non-rigid, deterministic) initially in distinct locations, moving freely in the plane and able to sense the positions of the other robots. We study the primitive task of the robots arranging themselves on the vertices of a regular n-gon not fixed in advance (Uniform Circle Formation). In the literature, the existing algorithmic contributions are limited to conveniently restricted sets of initial configurations of the robots and to more powerful robots. The question of whether such simple robots could deterministically form a uniform circle has remained open. In this paper, we constructively prove that indeed the Uniform Circle Formation problem is solvable for any initial configuration in which the robots are in distinct locations, without any additional assumption (if two robots are in the same location, the problem is easily seen to be unsolvable). In addition to closing a long-standing problem, the result of this paper also implies that, for pattern formation, asynchrony is not a computational handicap, and that additional powers such as chirality and rigidity are computationally irrelevant. A number of recent studies concern algorithms for distributed control and coordination in systems of autonomous mobile robots. The common theoretical model adopted in these studies assumes that the positional input of the robots is obtained by perfectly accurate visual sensors, that robot movements are accurate, and that internal calculations performed by the robots on (real) coordinates are perfectly accurate as well. The current paper concentrates on the effect of weakening this rather strong set of assumptions and replacing it with the more realistic assumption that the robot sensors, movement, and internal calculations may have slight inaccuracies. Specifically, the paper concentrates on the ability of robot systems with inaccurate sensors, movements, and calculations to carry out the task of convergence. The paper presents several impossibility theorems, limiting the inaccuracy levels that still allow convergence, and prohibiting a general algorithm for gathering, namely, meeting at a point, in a finite number of steps. The main positive result is an algorithm for convergence under bounded measurement, movement, and calculation errors. In this paper, we present an approach to designing decentralized robot control policies that mimic certain microscopic and macroscopic behaviors of ants performing collective transport tasks. In prior work, we used a stochastic hybrid system model to characterize the observed team dynamics of ant group retrieval of a rigid load. We have also used macroscopic population dynamic models to design enzyme-inspired stochastic control policies that allocate a robotic swarm around multiple boundaries in a way that is robust to environmental variations. Here, we build on this prior work to synthesize stochastic robot attachment–detachment policies for tasks in which a robotic swarm must achieve non-uniform spatial distributions around multiple loads and transport them at a constant velocity. Three methods are presented for designing robot control policies that replicate the steady-state distributions, transient dynamics, and fluxes between states that we have observed in ant populations during group retrieval. The equilibrium population matching method can be used to achieve a desired transport team composition as quickly as possible; the transient matching method can control the transient population dynamics of the team while driving it to the desired composition; and the rate matching method regulates the rates at which robots join and leave a load during transport. We validate our model predictions in an agent-based simulation, verify that each controller design method produces successful transport of a load at a regulated velocity, and compare the advantages and disadvantages of each method. 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 algorithms and proofs of correctness. This paper builds upon a previously proposed formal framework to certify the correctness of impossibility results regarding distributed algorithms that are dedicated to autonomous mobile robots evolving in a continuous space. As a case study, we consider the problem of gathering all robots at a particular location, not known beforehand. A fundamental (but not yet formally certified) result, due to Suzuki and Yamashita, states that this simple task is impossible for two robots executing deterministic code and initially located at distinct positions. Not only do we obtain a certified proof of the original impossibility result, we also get the more general impossibility of gathering with an even number of robots, when any two robots are possibly initially at the same exact location. We propose a multi-robot exploration algorithm that uses adaptive coordination to provide heterogeneous behavior. The key idea is to maximize the efficiency of exploring and mapping an unknown environment when a team is faced with unreliable communication and limited battery life (e.g., with aerial rotorcraft). The proposed algorithm utilizes four states: explore, meet, sacrifice, and relay. The explore state uses a frontier-based exploration algorithm, the meet state returns to the last known location of communication to share data, the sacrifice state sends the robot out to explore without consideration of remaining battery, and the relay state lands the robot until a meeting occurs. This approach allows robots to take on the role of a relay to improve communication between team members. In addition, the robots can “sacrifice” themselves by continuing to explore even when they do not have sufficient battery to return to the base station. We compare the performance of the proposed approach to state-of-the-art frontier-based exploration, and results show gains in explored area. The feasibility of components of the proposed approach is also demonstrated on a team of two custom-built quadcopters exploring an office environment. This paper presents a distributed algorithm whereby a group of mobile robots self-organize and position themselves into forming a circle in a loosely synchronized environment. In spite of its apparent simplicity, the difficulty of the problem comes from the weak assumptions made on the system. In particular, robots are anonymous, oblivious (i.e., stateless), unable to communicate directly, and disoriented in the sense that they share no knowledge of a common coordinate system. Furthermore, robots' activations are not synchronized. More specifically, the proposed algorithm ensures that robots deterministically form a non-uniform circle in a finite number of steps and converges to a situation in which all robots are located evenly on the boundary of the circle. This paper presents a machine vision based ap- proach for human operators to select individual and groups of autonomous robots from a swarm of UAVs. The angular distance between the robots and the human is estimated using measures of the detected human face, which aids to determine human and multi-UAV localization and positioning. In turn, this is exploited to effectively and naturally make the human select the spatially situated robots. Spatial gestures for selecting robots are presented by the human operator using tangible input devices (i.e., colored gloves). To select individuals and groups of robot we formulate a vocabulary of two-handed spatial pointing gestures. With the use of a Support Vector Machine (SVM) trained in a cascaded multi-binary-class configuration, the spatial gestures are effectively learned and recognized by a swarm of UAVs. I. INTRODUCTION Without the use of teleoperated and hand-held interaction devices, human operators generally face difficulties in select- ing and commanding individual and groups of robots from a relatively large group of spatially distributed robots (i.e., a swarm). However, due to the widespread availability of cost effective digital cameras onboard UGVs and UAVs, it is increasing the attention towards developing uninstrumented methods (i.e., methods that do not use sophisticated hardware devices from the human side) for human-swarm interaction (HSI). In previous work, we focused on learning efficient features incrementally (online) from multi-viewpoint images of multiple gestures that were acquired by a swarm of ground robots (1). In this paper, we present a cascaded supervised machine learning approach to deal with the machine vision problem of selecting 3D spatially-situated robots from a networked swarm based on the recognition of spatial hand gestures. These are a natural, easy recognizable, and device- less way to enable human operators to easily interact with external artifacts such as robots. Inspired by natural human behavior, we propose an ap- proach that combines face engagement and pointing gestures to interact with a swarm of robots: standing in front of a population of robots, by looking at them and pointing at them with spatial gestures, a human operator can designate individual or groups of robots of determined size. Robots cooperate to combine their independent observations of the human's face and gestures to cooperatively determine which robots were addressed (i.e., selected). While state of the art computer vision techniques pro- vide excellent face detection, human skeleton, and gesture recognition in ideal conditions, there are often occlusions, This paper presents a methodology for finding optimal control parameters as well as optimal system parameters for robot swarm controllers using probabilistic, population dynamic models. With distributed task allocation as a case study, we show how optimal control parameters leading to a desired steady-state task distribution for two fully-distributed algorithms can be found even if the parameters of the system are unknown. First, a reactive algorithm in which robots change states independently from each other and which leads to a linear macroscopic model describing the dynamics of the system is considered. Second, a threshold-based algorithm where robots change states based on the number of other robots in this state and which leads to a non-linear model is investigated. Whereas analytical results can be obtained for the linear system, the optimization of the non-linear controller is performed numerically. Finally, we show using stochastic simulations that whereas the presented methodology and models work best if the swarm size is large, useful results can already be obtained for team-sizes below a hundred robots. The methodology presented can be applied to scenarios involving the control of large numbers of entities with limited computational and communication abilities as well as a tight energy budget, such as swarms of robots from the centimeter to nanometer range or sensor networks. This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and it analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation. The unifying theme is a formal model for robotic networks that explicitly incorporates their communication, sensing, control, and processing capabilities--a model that in turn leads to a common formal language to describe and analyze coordination algorithms.Written for first- and second-year graduate students in control and robotics, the book will also be useful to researchers in control theory, robotics, distributed algorithms, and automata theory. The book provides explanations of the basic concepts and main results, as well as numerous examples and exercises.Self-contained exposition of graph-theoretic concepts, distributed algorithms, and complexity measures for processor networks with fixed interconnection topology and for robotic networks with position-dependent interconnection topology Detailed treatment of averaging and consensus algorithms interpreted as linear iterations on synchronous networks Introduction of geometric notions such as partitions, proximity graphs, and multicenter functions Detailed treatment of motion coordination algorithms for deployment, rendezvous, connectivity maintenance, and boundary estimation This paper presents a distributed method for navigating a team of robots in formation in 2D and 3D environments with static and dynamic obstacles. The robots are assumed to have a reduced communication and visibility radius and share information with their neighbors. Via distributed consensus the robots compute (a) the convex hull of the robot positions and (b) the largest convex region within free space. The robots then compute, via sequential convex programming, the locally optimal parameters for the formation within this convex neighborhood of the robots. Reconfiguration is allowed, when required, by considering a set of target formations. The robots navigate towards the target collision-free formation with individual local planners that account for their dynamics. The approach is efficient and scalable with the number of robots and performs well in simulations with up to sixteen quadrotors. This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm without pre-assigned terminal positions. The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the swarm assignment and trajectory optimization SATO algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm.