Computational Geometry Data Structures in Logistics and Navigation Tasks

Abstract

Computational geometry data structures have many applications, such as network optimisation, location tasks, but they can also be used in robot motion planning when a path of the shortest length must be found between the start and target positions that guarantee movements without the risk of collisions with obstacles. The paper deals with visibility graphs, strip and cell decompositions, Voronoi diagrams and compares their properties and efficiency in the investigated area. Since cell decomposition-based approaches give exponential complexity depending on the number of cells, and the knowledge base makes it possible to reduce it mostly only insignificantly, Voronoi diagrams with their polynomial complexity are more efficient for large instances. In addition, their generalized version allows them to generate smooth trajectories.