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Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Hierarchical Reinforcement Learning with the MAXQ Value Function Decomposition
 Journal of Artificial Intelligence Research
, 2000
"... This paper presents a new approach to hierarchical reinforcement learning based on decomposing the target Markov decision process (MDP) into a hierarchy of smaller MDPs and decomposing the value function of the target MDP into an additive combination of the value functions of the smaller MDPs. Th ..."
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Cited by 439 (6 self)
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This paper presents a new approach to hierarchical reinforcement learning based on decomposing the target Markov decision process (MDP) into a hierarchy of smaller MDPs and decomposing the value function of the target MDP into an additive combination of the value functions of the smaller MDPs. The decomposition, known as the MAXQ decomposition, has both a procedural semanticsas a subroutine hierarchyand a declarative semanticsas a representation of the value function of a hierarchical policy. MAXQ unifies and extends previous work on hierarchical reinforcement learning by Singh, Kaelbling, and Dayan and Hinton. It is based on the assumption that the programmer can identify useful subgoals and define subtasks that achieve these subgoals. By defining such subgoals, the programmer constrains the set of policies that need to be considered during reinforcement learning. The MAXQ value function decomposition can represent the value function of any policy that is consisten...
Simplified Voronoi Diagrams
, 1988
"... We are interested in Voronoi diagrams as a tool in robot path planning, where the search for a path in an r dimensional space may be simplified to a search on an r  1 dimensional Voronoi diagram. We define a Voronoi diagram V based on a measure of distance which is not a true metric. This formulati ..."
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Cited by 36 (5 self)
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We are interested in Voronoi diagrams as a tool in robot path planning, where the search for a path in an r dimensional space may be simplified to a search on an r  1 dimensional Voronoi diagram. We define a Voronoi diagram V based on a measure of distance which is not a true metric
The predicates for the Voronoi diagram of ellipses
 In Proc. 22th Annual ACM Symp. on Computational Geometry
, 2006
"... This paper examines the computation of the Voronoi diagram of a set of ellipses in the Euclidean plane. We propose the first complete algorithms, under the exact computation paradigm, for the predicates of an incremental algorithm: κ1 decides which one of 2 given ellipses is closest to a given exter ..."
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Cited by 12 (6 self)
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This paper examines the computation of the Voronoi diagram of a set of ellipses in the Euclidean plane. We propose the first complete algorithms, under the exact computation paradigm, for the predicates of an incremental algorithm: κ1 decides which one of 2 given ellipses is closest to a given
A Replacement for Voronoi Diagrams of Near Linear Size
 In Proc. 42nd Annu. IEEE Sympos. Found. Comput. Sci
, 2001
"... For a set P of n points in R^d, we define a new type of space decomposition. The new diagram provides an εapproximation to the distance function associated with the Voronoi diagram of P, while being of near linear size, for d ≥ 2. This contrasts with the standard Voronoi diagram ..."
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Cited by 102 (9 self)
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For a set P of n points in R^d, we define a new type of space decomposition. The new diagram provides an εapproximation to the distance function associated with the Voronoi diagram of P, while being of near linear size, for d ≥ 2. This contrasts with the standard Voronoi diagram
Constraint Query Languages
, 1992
"... We investigate the relationship between programming with constraints and database query languages. We show that efficient, declarative database programming can be combined with efficient constraint solving. The key intuition is that the generalization of a ground fact, or tuple, is a conjunction ..."
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Cited by 380 (44 self)
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of constraints over a small number of variables. We describe the basic Constraint Query Language design principles and illustrate them with four classes of constraints: real polynomial inequalities, dense linear order inequalities, equalities over an infinite domain, and boolean equalities. For the analysis
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