We revisit the linear search problem where a robot, initially placed at the origin on an infinite line, tries to locate a stationary target placed at an unknown position on the line. Unlike previous studies, in which the robot travels along the line at a constant speed, we consider settings where the robot's speed can depend on the direction of travel along the line, or on the profile of the terrain, e.g. when the line is inclined, and the robot can accelerate. Our objective is to design search algorithms that achieve good competitive ratios for the time spent by the robot to complete its search versus the time spent by an omniscient robot that knows the location of the target. We consider several new robot mobility models in which the speed of the robot depends on the terrain.These include 1) different constant speeds for different directions, 2) speed with constant acceleration and or variability depending on whether a certain segment has already been searched, 3) speed dependent on the incline of the terrain. We provide both upper and lower bounds on the competitive ratios of search algorithms for these models, and in many cases, we derive optimal algorithms for the search time.
The search problem has also been studied in environments where search occurs in graphs (see, e.g. @cite_7 ) or along dynamically evolving links of networks @cite_18 @cite_3 . More recently, variants of search using collections of robots have been investigated. The robots can employ either communication (at any distance) or communication, where communication is only possible among co-located robots. For example, the problem of @cite_10 @cite_16 is essentially a search problem where search is completed only when the target is reached by the last robot. Linear group search in the face-to-face communication model has also been studied with robots that either operate at the same speed or with a pair of robots having distinct maximal speeds @cite_5 @cite_8 . Finally, a new direction of research seeks to analyze linear search with multiple robots where some fraction of the robots may exhibit either crash faults @cite_9 or @cite_14 .
@cite_18 @cite_14 @cite_7 @cite_8 @cite_9 @cite_3 @cite_5 @cite_16 @cite_10
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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. 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. We consider the problem of searching on a line using n mobile robots, of which at most f are faulty, and the remaining are reliable. The robots start at the same location and move in parallel along the line with the same speed. There is a target placed on the line at a location unknown to the robots. Reliable robots can find the target when they reach its location, but faulty robots cannot detect the target. Our goal is to design a parallel algorithm minimizing the competitive ratio, represented by the worst case ratio between the time of arrival of the first reliable robot at the target, and the distance from the source to the target. If n ≥ 2f+2, there is a simple algorithm with competitive ratio 1. For f Our search algorithm is easily seen to be optimal for the case n=f+1. We also show that as @math tends to ∞ the competitive ratio of our algorithm for the case $n = 2f+1 approaches 3 and this is optimal. More precisely, we show that asymptotically, the competitive ratio of our proportional schedule algorithm A(2f+1,f) is at most 3 + 4ln n n , while any search algorithm has a lower bound 3 + 2ln n n on its competitive ratio. In this paper we describe a novel path planning approach for mobile robots operating in indoor environments. In such scenarios, robots must be able to maneuver in crowded spaces, partially filled with static and dynamic obstacles (such as people). Our approach produces smooth, complex maneuvers over large distances through the use of an anytime graph search algorithm applied to a novel multi-resolution state lattice, where the resolution is adapted based on both environmental characteristics and task characteristics. In addition, we present a novel approach for generating fast globally optimal trajectories in constrained spaces (i.e. rooms connected via doors and hallways). This approach exploits offline precomputation to provide extremely efficient online performance and is applicable to a wide range of both indoor and outdoor navigation scenarios. By combining an anytime, multi-resolution lattice-based search algorithm with our precomputation technique, globally optimal trajectories in up to four dimensions (2D position, heading and velocity) are obtained in real-time. A common assumption made in multi-robot research is the connectedness of the underlying network. Although this seems a valid assumption for static networks, it is not realistic for mobile robotic networks, where communication between robots usually is distance dependent. Motivated by this fact, we explicitly consider the communication limitations. This paper extends the LFIP based exploration framework previously developed by (Cogn. Comput. doi: 10.1007 s12559-012-9142-7 , 2012), to address the Multi-Agent Territory Exploration (MATE-n k ) task under severe communication constraints. In MATE-n k task agents have to explore their environment to find and visit n checkpoints, which only count as "visited" when k agents are present at the same time. In its simplest form, the architecture consists of two layers: an "Exploration layer" consisting of a selection of future locations for the team for further exploring the environment, and "Exploration and CheckpointVisit layer", consisting of visiting the detected checkpoints while continuing the exploration task. The connectivity maintenance objective is achieved via two ways: (1) The first layer employs a leader-follower concept, where a communication zone is constructed by the leader using a distance transforms method, and (2) In the second layer we make use of a graph theory for characterizing the communication, which employs the adjacency and Laplacian matrices of the graph and their spectral properties. The proposed approach has been implemented and evaluated in several simulated environments and with varying team sizes and communication ranges. Throughout the paper, our conclusions are corroborated by the results from extensive simulations. For many robotics applications (such as robotic search and rescue), information about the environment must be gathered by a team of robots and returned to a single, specific location. Coordination of robots and sharing of information is vital, and when environments have severe communication limitations, approaches must be robust to communication drop-out and failure. The difficulties are compounded in dynamic environments, where paths previously believed to be free can suddenly become blocked. In this paper, we introduce a novel way of calculating rendezvous points for robots to meet and share information. Using role-based exploration, some robots continuously explore the environment while others ferry information back and forth to a central command centre. Optimal rendezvous point selection leads to more efficient exploration, and allows robots to replan when one of them has unexpected obstacles in its path. 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 LOOK-COMPUTE-MOVE model for a set of autonomous robots has been thoroughly studied for over two decades. Each robot repeatedly LOOKS at its surroundings and obtains a snapshot containing the positions of all robots; based on this information, the robot COMPUTES a destination and then MOVES to it. Previous work assumed all robots are present at the beginning of the computation. What would be the effect of robots appearing asynchronously? This paper studies thisquestion, for problems of bringing the robots close together, andexposes an intimate connection with combinatorial topology. A central problem in the mobile robots area is the gathering problem. In its discrete version, the robots start at vertices in some graph G known to them, move towards the same vertex and stop. The paper shows that if robots are asynchronous and may crash, then gathering is impossible for any graph G with at least two vertices, even if robots can have unique IDs, remember the past, know the same names for the vertices of G and use an arbitrary number of lights to communicate witheach other. Next, the paper studies two weaker variants of gathering: edge gathering and 1-gathering. For both problems we present possibility and impossibility results. The solvability of edge gathering is fully characterized: it is solvable for three or more robots on a given graph if and only if the graph is acyclic. Finally, general robot tasks in a graph are considered. A combinatorial topology characterization for the solvable tasks is presented, by a reduction of the asynchronous fault-tolerant LOOK-COMPUTE-MOVE model to a wait-free read write shared-memory computing model, bringing together two areas that have been independently studied for a long time into a common theoretical foundation. In this paper we study the problem of gathering a collection of identical oblivious mobile robots in the same location of the plane. Previous investigations have focused mostly on the unlimited visibility setting, where each robot can always see all the others regardless of their distance.In the more difficult and realistic setting where the robots have limited visibility, the existing algorithmic results are only for convergence (towards a common point, without ever reaching it) and only for semi-synchronous environments, where robots' movements are assumed to be performed instantaneously.In contrast, we study this problem in a totally asynchronous setting, where robots' actions, computations, and movements require a finite but otherwise unpredictable amount of time. We present a protocol that allows anonymous oblivious robots with limited visibility to gather in the same location in finite time, provided they have orientation (i.e., agreement on a coordinate system).Our result indicates that, with respect to gathering, orientation is at least as powerful as instantaneous movements.