TY - CONF

T1 - The visibility-voronoi complex and its applications

AU - Wein, Ron

AU - Van Den Berg, Jur P.

AU - Halperin, Dan

N1 - Funding Information:
✩ This work has been supported in part by the IST Programme of the EU as Shared-cost RTD (FET Open) Project under Contract No IST-2001-39250 (MOVIE—Motion Planning in Virtual Environments) and Contract No IST-006413 (ACS—Algorithms for Complex Shapes), by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Center for Geometric Computing and its Applications), and by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University. * Corresponding author. E-mail addresses: wein@tau.ac.il (R. Wein), berg@cs.uu.nl (J.P. van den Berg), danha@tau.ac.il (D. Halperin).

PY - 2005

Y1 - 2005

N2 - We introduce a new type of diagram called the VV(c)-diagram (the Visibility-Voronoi diagram for clearance c), which is a hybrid between the visibility graph and the Voronoi diagram of polygons in the plane. It evolves from the visibility graph to the Voronoi diagram as the parameter c grows from 0 to ∞, This diagram can be used for planning natural-looking paths for a robot translating amidst polygonal obstacles in the plane. A natural-looking path is short, smooth, and keeps - where possible - an amount of clearance c from the obstacles. The VV(c)-diagram contains such paths. We also propose an algorithm that is capable of preprocessing a scene of configuration-space polygonal obstacles and constructs a data structure called the VV-complex. The VV-complex can be used to efficiently plan motion paths for any start and goal configuration and any clearance value c, without having to explicitly construct the VV(c)-diagram for that c-value. The preprocessing time is O(n2 log n), where n is the total number of obstacle vertices, and the data structure can be queried directly for any c-value by merely performing a Dijkstra search. We have implemented a CGAL-based software package for computing the VV(c)-diagram in an exact manner for a given clearance value, and used it to plan natural-looking paths in various applications.

AB - We introduce a new type of diagram called the VV(c)-diagram (the Visibility-Voronoi diagram for clearance c), which is a hybrid between the visibility graph and the Voronoi diagram of polygons in the plane. It evolves from the visibility graph to the Voronoi diagram as the parameter c grows from 0 to ∞, This diagram can be used for planning natural-looking paths for a robot translating amidst polygonal obstacles in the plane. A natural-looking path is short, smooth, and keeps - where possible - an amount of clearance c from the obstacles. The VV(c)-diagram contains such paths. We also propose an algorithm that is capable of preprocessing a scene of configuration-space polygonal obstacles and constructs a data structure called the VV-complex. The VV-complex can be used to efficiently plan motion paths for any start and goal configuration and any clearance value c, without having to explicitly construct the VV(c)-diagram for that c-value. The preprocessing time is O(n2 log n), where n is the total number of obstacle vertices, and the data structure can be queried directly for any c-value by merely performing a Dijkstra search. We have implemented a CGAL-based software package for computing the VV(c)-diagram in an exact manner for a given clearance value, and used it to plan natural-looking paths in various applications.

KW - Motion planning

KW - Path optimization

KW - Visibility graphs

KW - Voronoi diagrams

UR - http://www.scopus.com/inward/record.url?scp=33244490793&partnerID=8YFLogxK

U2 - 10.1145/1064092.1064104

DO - 10.1145/1064092.1064104

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AN - SCOPUS:33244490793

SP - 63

EP - 72

Y2 - 6 June 2005 through 8 June 2005

ER -