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.