Robot navigation using Voronoi diagrams

Abstract eng:
The task of planning trajectories plays an important role in transportation, robotics, etc. In robot motion planning the robot should pass around the obstacles, from a given starting position to a given target position, touching none of them, i.e. the goal is to find a collision-free path from the starting to the target position. This task has many specific formulations depending on the shape of obstacles, allowable directions of movements, knowledge of the scene, etc. Research on path planning has yielded many fundamentally different approaches to its solution, e.g. visibility graph method or the shortest path map method. Assuming movements only in a restricted number of directions (eight directional, horizontal/vertical) the task, with respect to its combinatorial nature, must be solved by heuristic techniques. We propose an application of the Voronoi diagrams to the studied tasks and show that this approach needs only polynomial time and choosing Euclidean or rectilinear metric it can be adapted to tasks with general or directional-constrained movements.

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