Results 1  10
of
52
Pathplanning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape
 ALGORITHMICA
, 1987
"... The problem of path planning for an automaton moving in a twodimensional scene filled with unknown obstacles is considered. The automaton is presented as a point; obstacles can be of an arbitrary shape, with continuous boundaries and of finite size; no restriction on the size of the scene is impos ..."
Abstract

Cited by 149 (1 self)
 Add to MetaCart
The problem of path planning for an automaton moving in a twodimensional scene filled with unknown obstacles is considered. The automaton is presented as a point; obstacles can be of an arbitrary shape, with continuous boundaries and of finite size; no restriction on the size of the scene is imposed. The information available to the automaton is limited to its own current coordinates and those of the target position. Also, when the automaton hits an obstacle, this fact is detected by the automaton's "'tactile sensor. " This information is shown to be sufficient for reaching the target or concluding in finite time that the target cannot be reached. A worstcase lower bound on the length of paths generated by any algorithm operating within the framework of the accepted model is developed; the bound is expressed in terms of the perimeters of the obstacles met by the automaton in the scene. Algorithms that guarantee reaching the target (if the target is reachable), and tests for target reachability are presented. The efficiency of the algorithms is studied, and worstcase upper bounds on the length of generated paths are produced.
Geometric Shortest Paths and Network Optimization
 Handbook of Computational Geometry
, 1998
"... Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of t ..."
Abstract

Cited by 147 (13 self)
 Add to MetaCart
Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of the edges that comprise it. Efficient algorithms are well known for this problem, as briefly summarized below. The shortest path problem takes on a new dimension when considered in a geometric domain. In contrast to graphs, where the encoding of edges is explicit, a geometric instance of a shortest path problem is usually specified by giving geometric objects that implicitly encode the graph and its edge weights. Our goal in devising efficient geometric algorithms is generally to avoid explicit construction of the entire underlying graph, since the full induced graph may be very large (even exponential in the input size, or infinite). Computing an optimal
The Power of a Pebble: Exploring and Mapping Directed Graphs
, 1998
"... Exploring and mapping an unknown environment is a fundamental problem, which is studied in various contexts. Many works have focused on finding efficient solutions to restricted versions of the problem. In this paper, we consider a model that makes very limited assumptions on the environment and ..."
Abstract

Cited by 104 (4 self)
 Add to MetaCart
Exploring and mapping an unknown environment is a fundamental problem, which is studied in various contexts. Many works have focused on finding efficient solutions to restricted versions of the problem. In this paper, we consider a model that makes very limited assumptions on the environment and solve the mapping problem in this general setting. We model
Navigating In Unfamiliar Geometric Terrain
, 1991
"... . Consider a robot that has to travel from a start location s to a target t in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rath ..."
Abstract

Cited by 88 (3 self)
 Add to MetaCart
. Consider a robot that has to travel from a start location s to a target t in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rather, it finds out about obstacles as it encounters them. We compare the distance walked by the robot in going from s to t to the length of the shortest (obstaclefree) path between s and t in the scene. We describe and analyze robot strategies that minimize this ratio for different kinds of scenes. In particular, we consider the cases of rectangular obstacles aligned with the axes, rectangular obstacles in more general orientations, and wider classes of convex bodies both in two and three dimensions. For many of these situations, our algorithms are optimal up to constant factors. We study scenes with nonconvex obstacles, which are related to the study of mazetraversal. We also show scenes ...
On Information Invariants in Robotics
"... permutation of U can be viewed as follows. Let D U = (C d \Gamma\Delta)=(u ¸ v). D U is the quotient of (C d \Gamma \Delta) under ß . For a partial immersion / to be chosen compatibly with the codesignation constraints, we view permutation as a bijective selfmap of the disjoint equivalence ..."
Abstract

Cited by 81 (6 self)
 Add to MetaCart
permutation of U can be viewed as follows. Let D U = (C d \Gamma\Delta)=(u ¸ v). D U is the quotient of (C d \Gamma \Delta) under ß . For a partial immersion / to be chosen compatibly with the codesignation constraints, we view permutation as a bijective selfmap of the disjoint equivalence classes f ß(ex / \Gamma \Delta) g / 2\Sigma(/): (38) Thus, in general, the group structure for the permutation must respect the quotient structure for codesignation; correspondingly, we call such permutations valid. Below, we define the "diagonal" \Delta, precisely. Now, an unsituated sensor system U could be modeled using a partial immersion / 0 with an empty domain. In this case ex / 0 = C d and Equation (38) specializes to the single equivalence class f D U g. In this "singular" case, we can take several different approaches to defining unsituated permutation. (i) We may define that / 0 = / 0 . Although consistent with situated permutation, (i) is not very useful. We choos...
Robot Navigation in Unknown Terrains: Introductory Survey of NonHeuristic Algorithms
, 1993
"... vii 1 ..."
Information Invariants for Distributed Manipulation
, 1995
"... In (Donald, 1995), we described a manipulation task for cooperating mobile robots that can push large, heavy objects. There, we asked whether explicit local and global communication between the agents can be removed from a family of pushing protocols. In this paper, we answer in the affirmative. We ..."
Abstract

Cited by 69 (16 self)
 Add to MetaCart
In (Donald, 1995), we described a manipulation task for cooperating mobile robots that can push large, heavy objects. There, we asked whether explicit local and global communication between the agents can be removed from a family of pushing protocols. In this paper, we answer in the affirmative. We do so by using the general methods of (Donald, 1995) analyzing information invariants. We discuss several measures for the information complexity of the task: (a) How much internal state should the robot retain? (b) How many cooperating agents are required, and how much communication between them is necessary? (c) How can the robot change (sideeffect) the environment in order to record state or sensory information to perform a task? (d) How much information is provided by sensors? and (e) How much computation is required by the robot? To answer these questions, we develop a notion of information invariants. We develop a technique whereby one sensor can be constructed from others by adding...
The power of team exploration: Two robots can learn unlabeled directed graphs
 In Proceedings of the Thirty Fifth Annual Symposium on Foundations of Computer Science
, 1994
"... We show that two cooperating robots can learn exactly any stronglyconnected directed graph with n indistinguishable nodes in expected tame polynomial in n. We introduce a new type of homing sequence for two robots which helps the robots recognize certain previouslyseen nodes. We then present an ..."
Abstract

Cited by 66 (5 self)
 Add to MetaCart
We show that two cooperating robots can learn exactly any stronglyconnected directed graph with n indistinguishable nodes in expected tame polynomial in n. We introduce a new type of homing sequence for two robots which helps the robots recognize certain previouslyseen nodes. We then present an algorithm in which the robots learn the graph and the homing sequence simultaneously by wandering actively through the graph. Unlike most previous learning results usang homing sequences, our algorithm does not require a teacher to provide counterexamples. Furthermore, the algorithm can use efficiently any additional information available that distinguishes nodes. We also present an algorithm in which the robots learn by taking random walks. The rate at which a random walk converges to the stationary distribution is characterized by the conductance of the graph. Our randomwalk algorithm learns in expected time polynomial in n and in the inverse of the conductance and is more eficient than the homingsequence algorithm for highconductance graphs. 1
Distributed covering by antrobots using evaporating traces
 IEEE Transactions on Robotics and Automation
, 1999
"... 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 unmapped building, or an ..."
Abstract

Cited by 56 (1 self)
 Add to MetaCart
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 unmapped 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 model is a decentralized multiagent adaptive system with a shared memory, moving on a graph whose vertices are the floortiles. 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—Antrobotics, covering, exploration, multiagent systems, robotics.
LabelGuided Graph Exploration by a Finite Automaton
"... A finite automaton, simply referred to as a robot, has to explore a graph, i.e., visit all the nodes of the graph. The robot has no a priori knowledge of the topology of the graph or of its size. It is known that, for any kstate robot, there exists a graph of maximum degree 3 that the robot cannot ..."
Abstract

Cited by 48 (24 self)
 Add to MetaCart
A finite automaton, simply referred to as a robot, has to explore a graph, i.e., visit all the nodes of the graph. The robot has no a priori knowledge of the topology of the graph or of its size. It is known that, for any kstate robot, there exists a graph of maximum degree 3 that the robot cannot explore. This paper considers the effects of allowing the system designer to add short labels to the graph nodes in a preprocessing stage, and using these labels to guide the exploration by the robot. We describe an exploration algorithm that given appropriate 2bit labels (in fact, only 3valued labels) allows a robot to explore all graphs. Furthermore, we describe a suitable labeling algorithm for generating the required labels, in linear time. We also show how to modify our labeling scheme so that a robot can explore all graphs of bounded degree, given appropriate 1bit labels. In other words, although there is no robot able to explore all graphs of maximum degree 3, there is a robot R, and a way to color in black or white the nodes of any boundeddegree graph G, so that R can explore the colored graph G. Finally, we give impossibility results regarding