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63
Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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Cited by 1213 (77 self)
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs into the toolkit of every algorithm designer. The purpose of the seminar was to bring together leading experts from all over the world, and from the diverse areas of computer science that have been attracted to this new framework. The seminar was intended as the rst larger international meeting with a specic focus on parameterized complexity, and it hopefully serves as a driving force in the development of the eld. 1 We had 49 participants from Australia, Canada, India, Israel, New Zealand, USA, and various European countries. During the workshop 25 lectures were given. Moreover, one night session was devoted to open problems and Thursday was basically used for problem discussion
Social Potential Fields: A Distributed Behavioral Control for Autonomous Robots
, 1999
"... A Very Large Scale Robotic (VLSR) system may consist of from hundreds to perhaps tens of thousands or more autonomous robots. The costs of robots are going down, and the robots are getting more compact, more capable, and more flexible. Hence, in the near future, we expect to see many industrial and ..."
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Cited by 183 (1 self)
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A Very Large Scale Robotic (VLSR) system may consist of from hundreds to perhaps tens of thousands or more autonomous robots. The costs of robots are going down, and the robots are getting more compact, more capable, and more flexible. Hence, in the near future, we expect to see many industrial and military applications of VLSR systems in tasks such as assembling, transporting, hazardous inspection, patrolling, guarding and attacking. In this paper, we propose a new approach for distributed autonomous control of VLSR systems. We define simple artificial force laws between pairs of robots or robot groups. The force laws are inversepower force laws, incorporating both attraction and repulsion. The force laws can be distinct and to some degree they reflect the 'social relations' among robots. Therefore we call our method social potential fields. An individual robot's motion is controlled by the resultant artificial force imposed by other robots and other components of the system. The approach is distributed in that the force calculations and motion control can be done in an asynchronous and distributed manner. We also extend the social potential fields model to use spring laws as force laws. This paper presents the first and a preliminary study on applying potential fields to distributed autonomous multirobot control. We describe the generic framework of our social potential fields method. We show with computer simulations that the method can yield interesting and useful behaviors among robots, and we give examples of possible industrial and military applications. We also identify theoretical problems for future studies. 1999 Published by Elsevier Science B.V. All rights reserved.
Robot Navigation in Unknown Terrains: Introductory Survey of NonHeuristic Algorithms
, 1993
"... ..."
Statevariable planning under structural restrictions: Algorithms and complexity
 ARTIFICIAL INTELLIGENCE
, 1998
"... Computationally tractable planning problems reported in the literature so far have almost exclusively been defined by syntactical restrictions. To better exploit the inherent structure in problems, it is probably necessary to study also structural restrictions on the underlying statetransition grap ..."
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Cited by 49 (4 self)
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Computationally tractable planning problems reported in the literature so far have almost exclusively been defined by syntactical restrictions. To better exploit the inherent structure in problems, it is probably necessary to study also structural restrictions on the underlying statetransition graph. The exponential size of this graph, though, makes such restrictions costly to test. Hence, we propose an intermediate approach, using a state variable model for planning and defining restrictions on the separate statetransition graphs for each state variable. We identify such restrictions which can tractably be tested and we present a planning algorithm which is correct and runs in polynomial time under these restrictions. The algorithm has been implemented an it outperforms Graphplan on a number of test instances. In addition, we present an exhaustive map of the complexity results for planning under all combinations of four previously studied syntactical restrictions and our five new structural restrictions. This complexity map considers both the optimal and nonoptimal plan generation problem.
Algorithmic Motion Planning
, 1997
"... INTRODUCTION Motion planning is a fundamental problem in robotics. It comes in a variety of forms, but the simplest version is as follows. We are given a robot system B, which may consist of several rigid objects attached to each other through various joints, hinges, and links, or moving independen ..."
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Cited by 47 (6 self)
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INTRODUCTION Motion planning is a fundamental problem in robotics. It comes in a variety of forms, but the simplest version is as follows. We are given a robot system B, which may consist of several rigid objects attached to each other through various joints, hinges, and links, or moving independently, and a twodimensional or threedimensional environment V cluttered with obstacles. We assume that the shape and location of the obstacles and the shape of B are known to the planning system. Given an initial placement Z 1 and a nal placement Z 2 of B, we wish to determine whether there exists a collisionavoiding motion of B from Z 1 to Z 2 , and, if so, to plan such a motion. In this simpli ed and purely geometric setup, we ignore issues such as incomplete information, nonholonomic constraints, control issues related to inaccuracies in sensing and motion, nonstationary obstacles, optimality of the planned motion, and so on. Since the early 1980's, motion planning has been an intensiv
Compaction and Separation Algorithms for NonConvex Polygons and Their Applications
 European Journal of Operations Research
, 1995
"... Given a two dimensional, nonoverlapping layout of convex and nonconvex polygons, compaction can be thought of as simulating the motion of the polygons as a result of applied "forces." We apply compaction to improve the material utilization of an already tightly packed layout. Compaction ..."
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Cited by 37 (10 self)
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Given a two dimensional, nonoverlapping layout of convex and nonconvex polygons, compaction can be thought of as simulating the motion of the polygons as a result of applied "forces." We apply compaction to improve the material utilization of an already tightly packed layout. Compaction can be modeled as a motion of the polygons that reduces the value of some functional on their positions. Optimal compaction, planning a motion that reaches a layout that has the global minimum functional value among all reachable layouts, is shown to be NPcomplete under certain assumptions. We first present a compaction algorithm based on existing physical simulation approaches. This algorithm uses a new velocitybased optimization model. Our experimental results reveal the limitation of physical simulation: even though our new model improves the running time of our algorithm over previous simulation algorithms, the algorithm still can not compact typical layouts of one hundred or more polygons in ...
The Complexity of the Free Space for a Robot Moving Amidst Fat Obstacles
 Comput. Geom. Theory Appl
, 1993
"... We propose a new definition of fatness of a geometric object and compare it with alternative definitions. We show that, under some realistic assumptions, the complexity of the free space for a robot with any fixed number of degrees of freedom moving in a ddimensional Euclidean workspace with fat ob ..."
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Cited by 32 (13 self)
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We propose a new definition of fatness of a geometric object and compare it with alternative definitions. We show that, under some realistic assumptions, the complexity of the free space for a robot with any fixed number of degrees of freedom moving in a ddimensional Euclidean workspace with fat obstacles is linear in the number of obstacles. The complexity of motion planning algorithms depends, to a large extent, on the complexity of the robot's free space, and theoretically, the complexity of the free space can be very high. Thus, our result opens the way to devising efficient motion planning algorithms in certain realistic settings. 1 Introduction It has been recently noted that, in certain problems in computational geometry, the relatively high complexity implied by worstcase lower bound constructions, can be avoided if we assume that the objects at hand have a certain "fatness" property. This paper discusses fatness in the context of algorithmic motion planning. 1.1 Background:...
Compaction Algorithms for NonConvex Polygons and Their Applications
, 1994
"... Given a twodimensional, nonoverlapping layout of convex and nonconvex polygons, compaction refers to a simultaneous motion of the polygons that generates a more densely packed layout. In industrial twodimensional packing applications, compaction can improve the material utilization of already ti ..."
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Cited by 29 (2 self)
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Given a twodimensional, nonoverlapping layout of convex and nonconvex polygons, compaction refers to a simultaneous motion of the polygons that generates a more densely packed layout. In industrial twodimensional packing applications, compaction can improve the material utilization of already tightly packed layouts. Efficient algorithms for compacting a layout of nonconvex polygons are not previously known. This dissertation offers the first systematic study of compaction of nonconvex polygons. We start by formalizing the compaction problem as that of planning a motion that minimizes some linear objective function of the positions. Based on this formalization, we study the complexity of compaction and show it to be PSPACEhard. The major contribution of this dissertation is a positionbased optimization model that allows us to calculate directly new polygon positions that constitute a locally optimum solution of the objective via linear programming. This model yields the first ...
Randomized Robot Navigation Algorithms
, 1996
"... We consider the problem faced by a mobile robot that has to reach a given target by traveling through an unmapped region in the plane containing oriented rectangular obstacles. We assume the robot has no prior knowledge about the positions or sizes of the obstacles, and acquires such knowledge only ..."
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Cited by 28 (0 self)
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We consider the problem faced by a mobile robot that has to reach a given target by traveling through an unmapped region in the plane containing oriented rectangular obstacles. We assume the robot has no prior knowledge about the positions or sizes of the obstacles, and acquires such knowledge only when obstacles are encountered. Our goal is to minimize the distance the robot must travel, using the competitive ratio as our measure. We give a new randomized algorithm...
Approximation Algorithms for CurvatureConstrained Shortest Paths
, 1996
"... Let B be a point robot in the plane, whose path is constrained to have curvature of at most 1, and let\Omega be a set of polygonal obstacles with n vertices. We study the collisionfree, optimal pathplanning problem for B. Given a parameter ", we present an O((n 2 =" 2 ) log n)time a ..."
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Cited by 24 (4 self)
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Let B be a point robot in the plane, whose path is constrained to have curvature of at most 1, and let\Omega be a set of polygonal obstacles with n vertices. We study the collisionfree, optimal pathplanning problem for B. Given a parameter ", we present an O((n 2 =" 2 ) log n)time algorithm for computing a collisionfree, curvatureconstrained path between two given positions, whose length is at most (1 + ") times the length of an optimal robust path (a path is robust if it remains collisionfree even if certain positions on the path are perturbed). Our algorithm thus runs significantly faster than the previously best known algorithm by Jacobs and Canny whose running time is O(( n+L " ) 2 + n 2 ( n+L " ) log n), where L is the total edge length of the obstacles. More importantly, the running time of our algorithm does not depend on the size of obstacles. The path returned by this algorithm is not necessarily robust. We present an O((n=") 2:5 log n) time algorithm that...