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Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
Abstract

Cited by 890 (113 self)
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A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (=150 MIPS), after learning for relatively short periods of time (a few dozen seconds)
Voronoi diagrams  a survey of a fundamental geometric data structure
 ACM COMPUTING SURVEYS
, 1991
"... This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. ..."
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Cited by 560 (5 self)
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This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. The paper puts particular emphasis on the unified exposition of its mathematical and algorithmic properties. Finally, the paper provides the first comprehensive bibliography on Voronoi diagrams and related structures.
Topological Simultaneous Localization and Mapping (SLAM): Toward Exact Localization Without Explicit Localization
 IEEE Transactions on Robotics and Automation
, 2001
"... One of the critical components of mapping an unknown environment is the robot's ability to locate itself on a partially explored map. This becomes challenging when the robot experiences positioning error, does not have an external positioning device, nor the luxury of engineered landmarks placed in ..."
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Cited by 185 (10 self)
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One of the critical components of mapping an unknown environment is the robot's ability to locate itself on a partially explored map. This becomes challenging when the robot experiences positioning error, does not have an external positioning device, nor the luxury of engineered landmarks placed in its free space. This paper presents a new method for simultaneous localization and mapping that exploits the topology of the robot's free space to localize the robot on a partially constructed map. The topology of the environment is encoded in a topological map; the particular topological map used in this paper is the generalized Voronoi graph (GVG), which also encodes some metric information about the robot's environment, as well. In this paper, we present the lowlevel control laws that generate the GVG edges and nodes, thereby allowing for exploration of an unknown space. With these prescribed control laws, the GVG (or other topological map) can be viewed as an arbitrator for a hybrid control system that determines when to invoke a particular lowlevel controller from a set of controllers all working toward the highlevel capability of mobile robot exploration. The main contribution, however, is using the graph structure of the GVG, via a graph matching process, to localize the robot. Experimental results verify the described work. Index TermsExploration, localization, mapping, mobile robots, motion planning, tologoical maps, Voronoi diagrams. I.
Spanning Trees and Spanners
, 1996
"... We survey results in geometric network design theory, including algorithms for constructing minimum spanning trees and lowdilation graphs. 1 Introduction This survey covers topics in geometric network design theory. The problem is easy to state: connect a collection of sites by a "good" network. ..."
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Cited by 143 (2 self)
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We survey results in geometric network design theory, including algorithms for constructing minimum spanning trees and lowdilation graphs. 1 Introduction This survey covers topics in geometric network design theory. The problem is easy to state: connect a collection of sites by a "good" network. For instance, one may wish to connect components of a VLSI circuit by networks of wires, in a way that uses little surface area on the chip, draws little power, and propagates signals quickly. Similar problems come up in other applications such as telecommunications, road network design, and medical imaging [1]. One network design problem, the Traveling Salesman problem, is sufficiently important to have whole books devoted to it [79]. Problems involving some form of geometric minimum or maximum spanning tree also arise in the solution of other geometric problems such as clustering [12], mesh generation [56], and robot motion planning [93]. One can vary the network design problem in many w...
On the Relationship Between Classical Grid Search and Probabilistic Roadmaps
 The International Journal of Robotics Research
, 2004
"... We present, implement, and analyze a spectrum of closelyrelated planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on the quasiMonte Carlo sampling literature, we have developed deterministic variants of the PRM that u ..."
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Cited by 100 (11 self)
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We present, implement, and analyze a spectrum of closelyrelated planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on the quasiMonte Carlo sampling literature, we have developed deterministic variants of the PRM that use lowdiscrepancy and lowdispersion samples, including lattices. Classical grid search is extended using subsampling for collision detection and also the dispersionoptimal Sukharev grid, which can be considered as a kind of latticebased roadmap to complete the spectrum. Our experimental results show that the deterministic variants of the PRM offer performance advantages in comparison to the original, multiplequery PRM and the singlequery, Lazy PRM. Surprisingly, even some forms of grid search yield performance that is comparable to the original PRM. Our theoretical analysis shows that all of our deterministic PRM variants are resolution complete and achieve the best possible asymptotic convergence rate, which is shown to be superior to that obtained by random sampling. Thus, in surprising contrast to recent trends, there is both experimental and theoretical evidence that the randomization used in the original PRM is not advantageous.
Sensor Based Motion Planning: The Hierarchical Generalized Voronoi Graph
, 1996
"... The hierarchical generalized Voronoi graph (HGVG) is a roadmap that can serve as a basis for sensor based robot motion planning. A key feature of the HGVG is its incremental construction procedure that uses only line of sight distance information. This work describes basic properties of the HGVG and ..."
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Cited by 79 (9 self)
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The hierarchical generalized Voronoi graph (HGVG) is a roadmap that can serve as a basis for sensor based robot motion planning. A key feature of the HGVG is its incremental construction procedure that uses only line of sight distance information. This work describes basic properties of the HGVG and the procedure for its incremental construction using local range sensors. Simulations and experiments verify this approach. 1 Introduction Sensor based motion planning incorporates sensor information, reflecting the current state of the environment, into a robot's planning process, as opposed to classical planning, which assumes full knowledge of the world's geometry prior to planning. Sensor based planning is important for realistic deployment of robots because: (1) the robot often has no a priori knowledge of the world; (2) the robot may have only a coarse knowledge of the world because of limited computer memory; (3) the world model is bound to contain inaccuracies which can be overcom...
Optimal motion planning for multiple robots having independent goals
 IEEE Transactions on Robotics and Automation
, 1998
"... Abstract — This work makes two contributions to geometric motion planning for multiple robots: 1) motion plans are computed that simultaneously optimize an independent performance measure for each robot; 2) a general spectrum is defined between decoupled and centralized planning, in which we introdu ..."
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Cited by 76 (7 self)
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Abstract — This work makes two contributions to geometric motion planning for multiple robots: 1) motion plans are computed that simultaneously optimize an independent performance measure for each robot; 2) a general spectrum is defined between decoupled and centralized planning, in which we introduce coordination along independent roadmaps. By considering independent performance measures, we introduce a form of optimality that is consistent with concepts from multiobjective optimization and game theory literature. Previous multiplerobot motion planning approaches that consider optimality combine individual performance measures into a scalar criterion. As a result, these methods can fail to find many potentially useful motion plans. We present implemented, multiplerobot motion planning algorithms that are derived from the principle of optimality, for three problem classes along the spectrum between centralized and decoupled planning: 1) coordination along fixed, independent paths; 2) coordination along independent roadmaps; 3) general, unconstrained motion planning. Computed examples are presented for all three problem classes that illustrate the concepts and algorithms. Index Terms — Gametheory, mobile robots, motion planning, multiobjective optimization, multiple robots, obstacle avoidance, path planning, scheduling. I.
Sensor Based Planning, Part I: The Generalized Voronoi Graph
 In Proc. IEEE Int. Conf. on Robotics and Automation
, 1995
"... . This paper introduces a 1dimensional network of curves termed the Generalized Voronoi Graph (GVG) and its extension, the Hierarchical Generalized Voronoi Graph (HGVG), which can be used as a basis for a roadmap or retractlike structure. The GVG and HGVG provide a basis for sensor based path pla ..."
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Cited by 54 (19 self)
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. This paper introduces a 1dimensional network of curves termed the Generalized Voronoi Graph (GVG) and its extension, the Hierarchical Generalized Voronoi Graph (HGVG), which can be used as a basis for a roadmap or retractlike structure. The GVG and HGVG provide a basis for sensor based path planning in an unknown static environment. In this paper, the GVG and HGVG are defined and some of their properties are exploited to show their utility for motion planning. A companion paper describes how to use the GVG and HGVG for the purposes of sensor based planning. 1 Introduction Sensor Based Planning incorporates sensor information, reflecting the current state of the environment, into a robot's planning process, as opposed to Classical Planning, which assumes full knowledge of the world's geometry prior to planning. This paper and its companion [7] introduce a sensor based motion planning scheme that is useful for two closely related motion planning problems: (1) to determine the path...
Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions
 In Proc. 14th Annu. ACM Sympos. Comput. Geom
, 1998
"... The straight skeleton of a polygon is a variant of the medial axis, introduced by Aichholzer et al., defined by a shrinking process in which each edge of the polygon moves inward at a fixed rate. We construct the straight skeleton of an ngon with r reflex vertices in time O(n 1+" +n 8=11+" r ..."
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Cited by 46 (0 self)
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The straight skeleton of a polygon is a variant of the medial axis, introduced by Aichholzer et al., defined by a shrinking process in which each edge of the polygon moves inward at a fixed rate. We construct the straight skeleton of an ngon with r reflex vertices in time O(n 1+" +n 8=11+" r 9=11+" ), for any fixed " ? 0, improving the previous best upper bound of O(nr log n). Our algorithm simulates the sequence of collisions between edges and vertices during the shrinking process, using a technique of Eppstein for maintaining extrema of binary functions to reduce the problem of finding successive interactions to two dynamic range query problems: (1) maintain a changing set of triangles in IR 3 and answer queries asking which triangle would be first hit by a query ray, and (2) maintain a changing set of rays in IR 3 and answer queries asking for the lowest intersection of any ray with a query triangle. We also exploit a novel characterization of the straight skeleton as a ...
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 32 (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. This formulation has lower algebraic complexity than the usual definition, which is a considerable advantage in motion planning problems with many degrees of freedom. In its simplest form, the measure of distance between a point and a polytope is the maximum of the distances of the point from the hMfspaces which pass through faces of the polytope. More generally, the measure is defined in configuration spaces which represent rotation. The Voronoi diagram defined using this distance measure is no longer a strong deformation retract of free space, but it has the following useful property: any path through free space which starts and ends on the diagram can be continuously deformed so that it lies entirely on the diagram. Thus it is still complete for motion planning, but it has lower algebraic complexity than a diagram based on the euclidean metric.