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Distance-Optimal Navigation in an Unknown Environment without Sensing Distances
- IEEE TRANSACTIONS ON ROBOTICS
"... This paper considers what can be accomplished using a mobile robot that has limited sensing. For navigation and mapping, the robot has only one sensor, which tracks the directions of depth discontinuities. There are no coordinates, and the robot is given a motion primitive that allows it to move t ..."
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Cited by 43 (17 self)
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This paper considers what can be accomplished using a mobile robot that has limited sensing. For navigation and mapping, the robot has only one sensor, which tracks the directions of depth discontinuities. There are no coordinates, and the robot is given a motion primitive that allows it to move toward discontinuities. The robot is incapable of performing localization or measuring any distances or angles. Nevertheless, when dropped into an unknown planar environment, the robot builds a data structure, called the Gap Navigation Tree, which enables it to navigate optimally in terms of Euclidean distance traveled. In a sense, the robot is able to learn the critical information contained in the classical shortest-path roadmap, although surprisingly it is unable to extract metric information. We prove these results for the case of a point robot placed into a simply connected, piecewise-analytic planar environment. The case of multiply connected environments is also addressed, in which it is shown that further sensing assumptions are needed. Due to the limited sensor given to the robot, globally optimal navigation is impossible; however, our approach achieves locally optimal (within a homotopy class) navigation, which is the best that is theoretically possible under this robot model.
Gap navigation trees: Minimal representation for visibility-based tasks
- In Proc. Workshop on the Algorithmic Foundations of Robotics
, 2004
"... Abstract. In this paper we present our advances in a data structure, the Gap Navigation Tree (GNT), useful for solving different visibility-based robotic tasks in unknown planar environments. We present its use for optimal robot navigation in simply-connected environments, locally optimal navigation ..."
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Cited by 30 (9 self)
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Abstract. In this paper we present our advances in a data structure, the Gap Navigation Tree (GNT), useful for solving different visibility-based robotic tasks in unknown planar environments. We present its use for optimal robot navigation in simply-connected environments, locally optimal navigation in multiply-connected environments, pursuit-evasion, and robot localization. The guiding philosophy of this work is to avoid traditional problems such as complete map building and exact localization by constructing a minimal representation based entirely on critical events in online sensor measurements made by the robot. The data structure is introduced from an information space perspective, in which the information used among the different visibility-based tasks is essentially the same, and it is up to the robot strategy to use it accordingly for the completion of the particular task. This is done through a simple sensor abstraction that reports the discontinuities in depth information of the environment from the robot’s perspective (gaps), and without any kind of geometric measurements. The GNT framework was successfully implemented on a real robot platform. 1
Pursuit-Evasion on Trees by Robot Teams
, 2010
"... We present Graph-Clear, a novel pursuit-evasion problem on graphs which models the detection of intruders in complex indoor environments by robot teams. The environment is represented by a graph, and a robot team can execute sweep and block actions on vertices and edges respectively. A sweep action ..."
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Cited by 25 (4 self)
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We present Graph-Clear, a novel pursuit-evasion problem on graphs which models the detection of intruders in complex indoor environments by robot teams. The environment is represented by a graph, and a robot team can execute sweep and block actions on vertices and edges respectively. A sweep action detects intruders in a vertex and represents the capability of the robot team to detect intruders in the region associated to the vertex. Similarly, a block action prevents intruders from crossing an edge and represents the capability to detect intruders as they move between regions. Both actions may require multiple robots to be executed. A strategy is a sequence of block and sweep actions detecting all intruders. When solving instances of Graph-Clear the goal is to determine optimal strategies, i.e. strategies using the least number of robots. We prove that for the general case of graphs the problem of computing optimal strategies is NP-hard. Next, for the special case of trees we provide a polynomial time algorithm. The algorithm ensures that throughout the execution of the strategy all cleared vertices form a connected subtree, and we show it produces optimal strategies.
Visibility-Based Pursuit-Evasion with Bounded Speed
"... This paper presents an algorithm for a visibility-based pursuit-evasion problem in which bounds on the speeds of the pursuer and evader are given. The pursuer tries to find the evader inside of a simply-connected polygonal environment, and the evader in turn tries actively to avoid detection. The ..."
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Cited by 23 (1 self)
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This paper presents an algorithm for a visibility-based pursuit-evasion problem in which bounds on the speeds of the pursuer and evader are given. The pursuer tries to find the evader inside of a simply-connected polygonal environment, and the evader in turn tries actively to avoid detection. The algorithm is at least as powerful as the complete algorithm for the unbounded speed case, and with the knowledge of speed bounds, generates solutions for environments that were previously unsolvable. Furthermore, the paper develops a characterization of the set of possible evader positions as a function of time. This characterization is more complex than in the unbound-speed case, because it no longer depends only on the combinatorial changes in the visibility region of the pursuer.
Multi-robot surveillance: an improved algorithm for the graph-clear problem
- In Proc. IEEE Intl. Conf. on Robotics and Automation
, 2008
"... Abstract—The main contribution of this paper is an im-proved algorithm for the GRAPH-CLEAR problem, a novel NP-complete graph theoretic problem we recently introduced as a tool to model multi-robot surveillance tasks. The proposed al-gorithm combines two previously developed solving techniques and p ..."
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Cited by 20 (6 self)
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Abstract—The main contribution of this paper is an im-proved algorithm for the GRAPH-CLEAR problem, a novel NP-complete graph theoretic problem we recently introduced as a tool to model multi-robot surveillance tasks. The proposed al-gorithm combines two previously developed solving techniques and produces strategies that require less robots to be executed. We provide a theoretical framework useful to identify the conditions for the existence of an optimal solution under special circumstances, and a set of mathematical tools characterizing the problem being studied. Finally we also identify a set of open questions deserving more investigations. I.
P.: Simple robots with minimal sensing: From local visibility to global geometry
- In: Proceedings of the TwentySecond National Conference on Artificial Intelligence and the Nineteenth Innovative Applications of Artificial Intelligence Conference, AAAI Press
, 2007
"... We consider problems of geometric exploration and selfdeployment for simple robots that can only sense the combinatorial (non-metric) features of their surroundings. Even with such a limited sensing, we show that robots can achieve complex geometric reasoning and perform many non-trivial tasks. Spec ..."
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Cited by 20 (6 self)
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We consider problems of geometric exploration and selfdeployment for simple robots that can only sense the combinatorial (non-metric) features of their surroundings. Even with such a limited sensing, we show that robots can achieve complex geometric reasoning and perform many non-trivial tasks. Specifically, we show that one robot equipped with a single pebble can decide whether the workspace environment is a simply-connected polygon and, if not, it can also count the number of holes in the environment. Highlighting the subtleties of our sensing model, we show that a robot can decide whether the environment is a convex polygon, yet it cannot resolve whether a particular vertex is convex. Finally, we show that using such local and minimal sensing, a robot can compute a proper triangulation of a polygon, and that the triangulation algorithm can be implemented collaboratively by a group of m such robots, each with Θ(n/m) memory. As a corollary of the triangulation algorithm, we derive a distributed analog of the well-known Art Gallery Theorem: a group of ⌊n/3 ⌋ (bounded memory) robots in our minimal sensing model can self-deploy to achieve visibility coverage of an n-vertex art gallery (polygon). This resolves an open question raised recently by Ganguli et al.
Counting targets with mobile sensors in an unknown environment
- In Proceedings of the 3rd International Workshop in Algorithmic Aspects of Wireless Sensor Networks (ALGOSENSORS), Revised Selected Papers
, 2007
"... Abstract. We consider the problem of counting the number of indistinguishable targets using a simple binary sensing model. Our setting includes an unknown number of point targets in a (simple or multiplyconnected) polygonal workspace, and a moving point-robot whose sensory input at any location is a ..."
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Cited by 19 (3 self)
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Abstract. We consider the problem of counting the number of indistinguishable targets using a simple binary sensing model. Our setting includes an unknown number of point targets in a (simple or multiplyconnected) polygonal workspace, and a moving point-robot whose sensory input at any location is a binary vector representing the cyclic order of the polygon vertices and targets visible to the robot. In particular, the sensing model provides no coordinates, distance or angle measurements. We investigate this problem under two natural models of environment, friendly and hostile, which differ only in whether the robot can walk up to them or not, and under three different models of motion capability. In the friendly scenario we show that the robots can count the targets, whereas in the hostile scenario no (2 − ε)-approximation is possible, for any ε> 0. Next we consider two, possibly minimally more powerful robots that can count the targets exactly. 1 The Problem and the Model
Extracting surveillance graphs from robot maps
- In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems
, 2008
"... Abstract — GRAPH-CLEAR is a recently introduced theo-retical framework to model surveillance tasks accomplished by multiple robots patrolling complex indoor environments. In this paper we provide a first step to close the loop between its graph-based theoretical formulation and practical scenarios. ..."
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Cited by 18 (7 self)
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Abstract — GRAPH-CLEAR is a recently introduced theo-retical framework to model surveillance tasks accomplished by multiple robots patrolling complex indoor environments. In this paper we provide a first step to close the loop between its graph-based theoretical formulation and practical scenarios. We show how it is possible to algorithmically extract suitable so-called surveillance graphs from occupancy grid maps. We also identify local graph modification operators, called contractions, that alter the graph being extracted so that the original surveillance problem can be solved using less robots. The algorithm we present is based on the Generalized Voronoi Diagram, a structure that can be simply computed using watershed like algorithms. Our algorithm is evaluated by processing maps produced by mobile robots exploring indoor environments. It turns out that the proposed algorithm is fast, robust to noise, and opportunistically modifies the graph so that less expensive strategies can be computed. I.
Pursuit-evasion in an unknown environment using gap navigation graphs
- In Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems
, 2004
"... In this paper we present an online algorithm for pursuitevasion in a unknown simply connected environment, for one pursuer that has minimal sensing and carries a set of stationary sentries that it can drop off and pick up during the pursuit. In our sensing model, the pursuer is only able to detect d ..."
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Cited by 17 (7 self)
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In this paper we present an online algorithm for pursuitevasion in a unknown simply connected environment, for one pursuer that has minimal sensing and carries a set of stationary sentries that it can drop off and pick up during the pursuit. In our sensing model, the pursuer is only able to detect discontinuities in depth information (gaps), and it is able to find all of the evaders without any explicit localization or geometric information, by using a Gap Navigation Tree. The strategy is based on growing an evader-free region, by reading “exploration” schedules from the Gap Navigation Tree, that is constructed online. We prove that a pursuer with k +1 sentries can clear any environment that could be cleared by k pursuers using the algorithm in [7], which required a complete map and perfect sensing. I.
S.: The graph-clear problem: definition, theoretical properties and its connections to multirobot aided surveillance
- In: Intelligent Robots and Systems, 2007. IROS
"... Abstract — In this paper we present a novel graph theoretic problem, called GRAPH-CLEAR, useful to model surveillance tasks where multiple robots are used to detect all possible intruders in a given indoor environment. We provide a formal definition of the problem and we investigate its basic theore ..."
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Cited by 17 (6 self)
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Abstract — In this paper we present a novel graph theoretic problem, called GRAPH-CLEAR, useful to model surveillance tasks where multiple robots are used to detect all possible intruders in a given indoor environment. We provide a formal definition of the problem and we investigate its basic theoretical properties, showing that the problem is NP-complete. We then present an algorithm to compute a strategy for the restriction of the problem to trees and present a method how to use this solution in applications. The method is then tested in simple simulations. GRAPH-CLEAR is useful to describe multirobot pursuit evasion games when robots have limited sensing capabilities, i.e. multiple agents are needed to perform basic patrolling operations. I.
