Shantanu Das

Map construction of unknown graphs by multiple agents

We consider a distributed version of the graph exploration and mapping problem where a mobile agent has to traverse the edges of an unlabelled (i.e., anonymous) graph and return to its starting point, building a map of the graph in the process. In our case, instead of a single agent, there are k identical (i.e., mutually indistinguishable) agents initially dispersed among the n nodes of the graph. The agents can communicate by writing to the small public bulletin boards available at each node. The objective is for each agent to build an identically labelled map of the graph; we call this the Labelled Map Construction problem. This problem is much more difficult than exploration by a single agent, because it involves achieving cooperation among multiple agents. In fact, this problem is deterministically unsolvable in some cases. We present deterministic algorithms that successfully and efficiently solve the problem under the condition that the values of n and k are co-prime with each other. We also show how the problem of Labelled Map Construction is related to other problems like leader election and rendezvous of agents.

Localized Movement Control for Fault Tolerance of Mobile Robot Networks

In this paper, we present a novel localized movement control algorithm to form a fault-tolerant bi-connected robotic network topology from a connected network, such that total distance of movement of robots is minimized. The proposed distributed algorithm uses p-hop neighbor information to identify critical head robots that can direct two neighbors to move toward each other and bi-connect their neighborhood. Simulation results show that the total distance of movement of robots decreases significantly with our localized algorithm when compared to the globalized one, and our localized algorithm achieved 100% success on considered non-bi-connected networks. To the best of our knowledge, it is the first work on localized movement control for the fault tolerance of mobile robot networks.

On the computational power of oblivious robots: forming a series of geometric patterns

We study the computational power of a distributed system consisting of simple autonomous robots moving on the plane. The robots are endowed with visual perception but do not have any means of explicit communication with each other, and have no memory of the past. In the extensive literature it has been shown how such simple robots can form a single geometric pattern (e.g., a line, a circle, etc), however arbitrary, in spite of their obliviousness. This brings to the front the natural research question: what are the real computational limits imposed by the robots being oblivious? In particular, since obliviousness limits what can be remembered, under what conditions can oblivious robots form a series of geometric patterns? Notice that a series of patterns would create some form of memory in an otherwise memory-less system. In this paper we examine and answer this question showing that, under particular conditions, oblivious robot systems can indeed form series of geometric patterns starting from any arbitrary configuration. More precisely, we study the series of patterns that can be formed by robot systems under various restrictions such as anonymity, asynchrony and lack of common orientation. These results are the first strong indication that oblivious solutions may be obtained also for tasks that intuitively seem to require memory.

Gathering of Mobile Robots Tolerating Multiple Crash Faults

We study distributed coordination among autonomous mobile robots, focussing on the problem of gathering the robots at a single location. The gathering problem has been solved previously using deterministic algorithms even for robots that are anonymous, oblivious, disoriented, and operate in the semi-synchronous ATOM model. However these solutions require all robots to be fault-free. The recent results of Agmon and Peleg [1] show how to gather all correct robots when one of the robots may crash permanently. We study gathering in n-robot systems with f crashes for any f <; n. In such a scenario, no robot can wait for another robot, i.e., the algorithm must be wait-free. We provide such a wait-free algorithm to gather all correct robots assuming the capabilities of strong multiplicity detection and chirality. Unlike previous solutions, our algorithm does not impose the requirement of initially distinct locations, and works for any arbitrary initial configuration of robots (except the bivalent configuration where deterministic gathering is not possible).

Constructing a map of an anonymous graph: applications of universal sequences

We study the problem of mapping an unknown environment represented as an unlabelled undirected graph. A robot (or automaton) starting at a single vertex of the graph G has to traverse the graph and return to its starting point building a map of the graph in the process. We are interested in the cost of achieving this task (whenever possible) in terms of the number of edge traversal made by the robot. Another optimization criteria is to minimize the amount of information that the robot has to carry when moving from node to node in the graph. We present efficient algorithms for solving map construction using a robot that is not allowed to mark any vertex of the graph, assuming the knowledge of only an upper bound on the size of the graph. We also give universal algorithms (independent of the size of the graph) for map construction when only the starting location of the robot is marked. Our solutions apply the technique of universal exploration sequences to solve the map construction problem under various constraints. We also show how the solution can be adapted to solve other problems such as the gathering of two identical robots dispersed in an unknown graph.

A localized algorithm for bi-connectivity of connected mobile robots

Teams of multiple mobile robots may communicate with each-other using a wireless ad-hoc network. Fault-tolerance in communication can be achieved by making the communication network bi-connected. We present the first localized protocol for constructing a fault-tolerant bi-connected robotic network topology from a connected network, in such a way that the total movement of robots is minimized. The proposed distributed algorithm uses p-hop neighbor information to identify critical head robots that can direct two neighbors to move toward each other and bi-connect their neighborhood. Simulation results show that the total distance of movement of robots decreases significantly (e.g. about 2.5 times for networks with density 10) with our localized algorithm when compared to the existing globalized one. Proposed localized algorithm does not guarantee bi-connectivity, may partition the network, and may even stop at connected but not bi-connected stage. However, our algorithm achieved 100% success on all networks with average degrees ≥10, and over 70% success on sparse networks with average degrees ≥5.

Distributed exploration of an unknown graph

We consider a group of identical asynchronous agents, initially located at different nodes of an undirected simple graph. The nodes of the graph are unlabeled, and each contains a whiteboard where the visiting agents can write to and read from. The agents, initially, do not know the graph nor its topology. The only a-priori knowledge the agents may have is either the number n of nodes, or the total number k of agents. The goal is for the agents to construct a labelled map of the unknown graph, the same for all agents, so to be in complete agreement with each-other about their environment. This problem, called Labelled Map Construction, is closely related to a variety of other basic problems, including election and rendezvous. We are interested in efficient and generic protocols that can solve the problem, irrespective of the graph topology, where the cost of the algorithm is measured in terms of the total number of moves (or, edge traversals) made by the agents. We present a novel deterministic algorithm that, provided that n and k are co-prime (a necessary condition), constructs a map of the graph, elects a leader among the agents, and provides a unique labelling on the nodes of the graph. Our algorithm uses no more than O(km) edge traversals where m is the number of edges in the graph. Our result improves on the finding by Barriere et al. [4] for graphs with sense of direction, extending it to graphs with arbitrary labelling, provided that one of n or k is known.

Autonomous mobile robots with lights

We consider the well known distributed setting of computational mobile entities, called robots, operating in the Euclidean plane in Look-Compute-Move (LCM) cycles. We investigate the computational impact of expanding the capabilities of the robots by endowing them with an externally visible memory register, called light, whose values, called colors, are persistent, that is they are not automatically reset at the end of each cycle. We refer to so endowed entities as luminous robots.We study the computational power of luminous robots with respect to the three main settings of activation and synchronization: fully-synchronous, semi-synchronous, and asynchronous. We establish several results. A main contribution is the constructive proof that asynchronous robots, illuminated with a constant number of colors, are strictly more powerful than traditional semi-synchronous robots.We also constructively prove that, for luminous robots, the difference between asynchrony and semi-synchrony disappears. This result must be contrasted with the strict dominance between the models without lights (even if the robots are enhanced with an unbounded amount of persistent internal memory).Additionally we show that there are problems that robots cannot solve without lights, even if they are fully-synchronous, but can be solved by asynchronous luminous robots with O ( 1 ) colors. It is still open whether or not asynchronous luminous robots with O ( 1 ) colors are more powerful than fully-synchronous robots without lights.We prove that this is indeed the case if the robots have the additional capability of remembering a single snapshot. This in turn shows that, for asynchronous robots, to have O ( 1 ) colors and a single snapshot renders them more powerful than to have an unlimited amount of persistent memory (including snapshots) but no lights.

Rendezvous of Mobile Agents When Tokens Fail Anytime

We consider the problem of Rendezvous or gathering of multiple autonomous entities (called mobile agents) moving in an unlabelled environment (modelled as a graph). The problem is usually solved using randomization or assuming distinct identities for the agents, such that they can execute different protocols. When the agents are all identical and deterministic, and the environment itself is symmetrical (e.g. a ring) it is difficult to break the symmetry between them unless, for example, the agents are provided with a token to mark the nodes. We consider fault-tolerant protocols for the problem where the tokens used by the agents may disappear unexpectedly. If all tokens fail, then it becomes impossible, in general, to solve the problem. However, we show that with any number of failures (less than a total collapse), we can always solve the problem if the original instance of the problem was solvable. Unlike previous solutions, we can tolerate failures occurring at arbitrary times during the execution of the algorithm. Our solution can be applied to any arbitrary network even when the topology is unknown.

Effective elections for anonymous mobile agents

We present distributed protocols for electing a leader among k mobile agents that are dispersed among the n nodes of a graph. While previous solutions for the agent election problem were restricted to specific topologies or under specific conditions, the protocols presented in this paper face the problem in the most general case, i.e. for an arbitrary topology where the nodes of the graph may not be distinctly labelled and the agents might be all identical (and thus indistinguishable from each other). In such cases, the agent election problem is often difficult, and sometimes impossible to solve using deterministic means. We have designed protocols for solving the problem that—unlike previous solutions—are effective, meaning that they always succeed in electing a leader under any given setting if at all it is possible, and otherwise detect the fact that election is impossible in that setting. We present several election protocols, all effective. Starting with the straightforward solution, that requires an exponential amount of edge-traversals by the agents, we describe significantly more efficient algorithms; in the latter the total number of edge-traversals made by the agents is always polynomial, their difference is in the amount of bits of storage they required at the nodes.