Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Intelligent Control Systems Using Soft Computing Methodologies
Intelligent Control Systems Using Soft Computing Methodologies
Two Heuristics for the Euclidean Steiner Tree Problem
Journal of Global Optimization
Planning Algorithms
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
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A frequent task in transportation, routing, robotics, and communications applications is to find the shortest path between two positions. In robot motion planning, the robot should pass around the obstacles touching none of them, i.e. the goal is to find a collision-free path from a starting to a target position. Research of path planning has yielded many fundamentally different approaches to its solution, mainly based on various decomposition and roadmap methods. In this paper, we show a possible use of geometric data structures in point-to-point motion planning in the Euclidean plane and present an approach using generalised Voronoi diagrams that decreases the probability of collisions with obstacles and generate smooth trajectories. The second application area, investigated here, is focused on problems of finding minimal networks connecting a set of given points in the Euclidean plane and their approximations using the Delaunay triangulation.