In this paper, we present controllers that enable mobile robots to persistently monitor or sweep a changing environment. The environment is modeled as a field that is defined over a finite set of locations. The field grows linearly at locations that are not within the range of a robot and decreases linearly at locations that are within range of a robot. We assume that the robots travel on given closed paths. The speed of each robot along its path is controlled to prevent the field from growing unbounded at any location. We consider the space of speed controllers that are parametrized by a finite set of basis functions. For a single robot, we develop a linear program that computes a speed controller in this space to keep the field bounded, if such a controller exists. Another linear program is derived to compute the speed controller that minimizes the maximum field value over the environment. We extend our linear program formulation to develop a multirobot controller that keeps the field bounded. We characterize, both theoretically and in simulation, the robustness of the controllers to modeling errors and to stochasticity in the environment.
A problem more closely related to ours is that of patrolling @cite_21 @cite_25 , where an environment must be continually surveyed by a group of robots such that each point is visited with equal frequency. Similarly, in @cite_34 vehicles must repeatedly visit the cells of a gridded environment. Also, continual perimeter patrolling is addressed in @cite_19 . In another related work, a region is persistently covered in @cite_37 by controlling robots to move at constant speed along predefined paths. Our work is different from these, however, in that we treat the situation in which different parts of the environment may require different levels of attention. This is a significant difference as it induces a difficult resource trade-off problem as one typically finds in queuing theory @cite_31 , or dynamic vehicle routing @cite_33 @cite_6 . @cite_32 , the authors consider unequal frequency of visits in a gridded environment, but they control the robots using a greedy method that does not have performance guarantees.
@cite_37 @cite_33 @cite_21 @cite_32 @cite_6 @cite_19 @cite_31 @cite_34 @cite_25
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Patrolling involves generating patrol paths for mobile robots such that every point on the paths is repeatedly covered. This paper focuses on patrolling in closed areas, where every point in the area is to be visited repeatedly by one or more robots. Previous work has often examined paths that allow for repeated coverage, but ignored the frequency in which points in the area are visited. In contrast, we first present formal frequency-based optimization criteria used for evaluation of patrol algorithms. Then, we present a patrol algorithm that guarantees maximal uniform frequency, i.e., each point in the target area is covered at the same optimal frequency. This solution is based on finding a circular path that visits all points in the area, while taking into account terrain directionality and velocity constraints. Robots are positioned uniformly along this path in minimal time, using a second algorithm. Moreover, the solution is guaranteed to be robust in the sense that uniform frequency of the patrol is achieved as long as at least one robot works properly. We then present a set of algorithms for handling events along the patrol path. The algorithms differ in the way they handle the event, as a function of the time constraints for handling them. However, all the algorithms handle events while maintaining the patrol path, and minimizing the disturbance to the system. This paper discusses the problem of generating patrol paths for a team of mobile robots inside a designated target area. Patrolling requires an area to be visited repeatedly by the robot(s) in order to monitor its current state. First, we present frequency optimization criteria used for evaluation of patrol algorithms. We then present a patrol algorithm that guarantees maximal uniform frequency, i.e., each point in the target area is covered at the same optimal frequency. This solution is based on finding a circular path that visits all points in the area, while taking into account terrain directionality and velocity constraints. Robots are positioned uniformly along this path, using a second algorithm. Moreover, the solution is guaranteed to be robust in the sense that uniform frequency of the patrol is achieved as long as at least one robot works properly. Consider a set of mobile robots placed on distinct nodes of a discrete, anonymous, and bidirectional ring. Asynchronously, each robot takes a snapshot of the ring, determining the size of the ring and which nodes are either occupied by robots or empty. Based on the observed configuration, it decides whether to move to one of its adjacent nodes or not. In the first case, it performs the computed move, eventually. This model of computation is known as Look-Compute-Move. The computation depends on the required task. In this paper, we solve both the well-known Gathering and Exclusive Searching tasks. In the former problem, all robots must simultaneously occupy the same node, eventually. In the latter problem, the aim is to clear all edges of the graph. An edge is cleared if it is traversed by a robot or if both its endpoints are occupied. We consider the exclusive searching where it must be ensured that two robots never occupy the same node. Moreover, since the robots are oblivious, the clearing is perpetual, i.e., the ring is cleared infinitely often. In the literature, most contributions are restricted to a subset of initial configurations. Here, we design two different algorithms and provide a characterization of the initial configurations that permit the resolution of the problems under very weak assumptions. More precisely, we provide a full characterization (except for few pathological cases) of the initial configurations for which gathering can be solved. The algorithm relies on the necessary assumption of the local-weak multiplicity detection. This means that during the Look phase a robot detects also whether the node it occupies is occupied by other robots, without acquiring the exact number. For the exclusive searching, we characterize all (except for few pathological cases) aperiodic configurations from which the problem is feasible. We also provide some impossibility results for the case of periodic configurations. A set of k mobile agents are placed on the boundary of a simply connected planar object represented by a cycle of unit length. Each agent has its own predefined maximal speed, and is capable of moving around this boundary without exceeding its maximal speed. The agents are required to protect the boundary from an intruder which attempts to penetrate to the interior of the object through a point of the boundary, unknown to the agents. The intruder needs some time interval of length τ to accomplish the intrusion. Will the intruder be able to penetrate into the object, or is there an algorithm allowing the agents to move perpetually along the boundary, so that no point of the boundary remains unprotected for a time period τ? Such a problem may be solved by designing an algorithm which defines the motion of agents so as to minimize the idle time I, i.e., the longest time interval during which any fixed boundary point remains unvisited by some agent, with the obvious goal of achieving I < τ. Depending on the type of the environment, this problem is known as either boundary patrolling or fence patrolling in the robotics literature. The most common heuristics adopted in the past include the cyclic strategy, where agents move in one direction around the cycle covering the environment, and the partition strategy, in which the environment is partitioned into sections patrolled separately by individual agents. This paper is, to our knowledge, the first study of the fundamental problem of boundary patrolling by agents with distinct maximal speeds. In this scenario, we give special attention to the performance of the cyclic strategy and the partition strategy. We propose general bounds and methods for analyzing these strategies, obtaining exact results for cases with 2, 3, and 4 agents. We show that there are cases when the cyclic strategy is optimal, cases when the partition strategy is optimal and, perhaps more surprisingly, novel, alternative methods have to be used to achieve optimality.