918 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 15, NO. 5, OCTOBER 1999 Distributed Covering by Ant-Robots Using Evaporating Traces Israel A. Wagner, Michael Lindenbaum, and Alfred M. Bruckstein Abstract—Ants and other insects are known to use chemicals called pheromones for various communication and coordination tasks. In this paper, we investigate the ability of a group of robots, that communicate by leaving traces, to perform the task of cleaning the floor of an un-mapped building, or any task that requires the traversal of an unknown region. More specifically, we consider robots which leave chemical odor traces that evaporate with time, and are able to evaluate the strength of smell at every point they reach, with some measurement error. Our abstract model is a decentralized multiagent adaptive system with a shared memory, moving on a graph whose vertices are the floor-tiles. We describe three methods of covering a graph in a distributed fashion, using smell traces that gradually vanish with time, and show that they all result in eventual task completion, two of them in a time polynomial in the number of tiles. As opposed to existing traversal methods (e.g., depth first search), our algorithms are adaptive: they will complete the traversal of the graph even if some of the a(ge)nts die or the graph changes (edges/vertices added or deleted) during the execution, as long as the graph stays connected. Another advantage of our agent interaction processes is the ability of agents to use noisy information at the cost of longer cover time. Index Terms—Ant-robotics, covering, exploration, multi-agent systems, robotics. I. INTRODUCTION O NE of the basic theoretical (and practical) problems in multiagent systems is how to design adaptive rules of behavior for the individual, that will lead to a desired colony behavior while reducing cost in terms of communication overhead and hardware complexity. We shall consider a task in which the floor of a building has to be cleaned by a group of autonomous robots that do not have a prior knowledge of the building’s floorplan. We model the floorplan of the building as being composed of small rectangular regions (tiles or rooms), all of the same size, and assume that a tile/room can be cleaned in one unit of time. To help their navigation, the robots are allowed to leave traces while they walk, e.g. by means of odor, heat, or color trails. We further assume that the intensity of traces decreases with time, therefore by comparing the trace levels at two neighboring tiles, the robot can deduce which tile was visited more recently. The state Manuscript received April 22, 1996; revised February 7, 1999. This paper was recommended for publication by Associate Editor R. Chatila and Editor S. Salcudean upon evaluation of the reviewers’ comments. I. A. Wagner is with IBM Haifa Research Laboratory, Matam, Haifa 31905, Israel (e-mail: wagner@haifasc3.vnet.ibm.com). M. Lindenbaum and A. M. Bruckstein are with the Department of Com- puter Science, Technion, Haifa 32000, Israel (e-mail: mic@cs.technion.ac.il; freddy@cs.technion.ac.il). Publisher Item Identifier S 1042-296X(99)08505-5. of cleanness of the path can also serve as a trace, if the dust is slowly falling back on the floor, and hence enables a chronological comparison between tiles in terms of agent visits. See Fig. 1 for an example. The topology of the building may change while the robots work; e.g. people or furniture may move and doors may open or close, hence a preliminary phase of floorplan mapping will not be of much help here. Such a problem is critical in case of a damage to a nuclear reactor, where robots are the only creatures that can survive the radiation and move around to clean hazardous waste [33]. Central control is usually not possible since the strong radioactive radiation avoids almost any possibility of wireless communication. Similarly, one might consider a surveillance task in which robotic guards have to visit the rooms and corridors of a dynamic art gallery, and to guarantee that each and every room and corridor is visited frequently enough. In this paper, we present systematic methods for local, cue-based operation of a group of robots that solves the above problems. As a (simplifying) mathematical model, we use graph traversal, inspired by ant foraging, based on the assumption that the world is divided into vertices (tiles) and edges (tile-separating lines), and an ant leaves a constant amount of pheromone at each point it visits. These traces are later used by the ant and its fellows as a memory of the latest time this point has been visited so far. We shall describe three search algorithms, prove their convergence, bound their worst-case time complexity, and test them empirically. As far as we know, this work presents the first performance analysis of a model that considers the cooperative potential of trace-oriented behavior in terms of time-complexity, under noisy circumstances. A. Related Work 1) Robotic Covering: Covering is an important applica- tion of robotics; researchers have investigated various aspects of the topic, and we shall only be able to present a short sample here. In [10], the issue of inter-robot communication was addressed in the context of various missions, among them grazing—i.e., visiting every point of a region for purposes of object-fetching. There, a reactive model of behavior is presented, and simulations show that detailed communication does not contribute much to the performance. In [4], many experimental works are presented for planetary exploration by autonomous robots. Heuristic navigation methods are given in [28] for path planning of an autonomous mobile cleaning robot, and in [37] for a robot exploration and mapping strategy. In [32], an algorithm is presented for exploration of an 1042–296X/99$10.00  1999 IEEE