Planning Trajectories in the Plane with Obstacles Using Voronoi Diagrams

book chapter

en

The task of planning trajectories plays an important role in transportation, robotics, even in information systems (sending messages). 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, can be solved by heuristic techniques (genetic algorithms, simulated annealing, tabu-search). We present a framework of such approach and show its drawbacks (combinatorial explosion, limited granularity, generating infeasible solutions). Application of the Voronoi diagrams to the studied tasks can be seen as the main result of this paper. This approach needs only polynomial time and choosing Euclidean or rectilinear metric it can be adapted to tasks with general or directional-constrained movements.

The task of planning trajectories plays an important role in transportation, robotics, even in information systems (sending messages). 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, can be solved by heuristic techniques (genetic algorithms, simulated annealing, tabu-search). We present a framework of such approach and show its drawbacks (combinatorial explosion, limited granularity, generating infeasible solutions). Application of the Voronoi diagrams to the studied tasks can be seen as the main result of this paper. This approach needs only polynomial time and choosing Euclidean or rectilinear metric it can be adapted to tasks with general or directional-constrained movements.

Motion planning, genetic algorithm, case-based reasoning, Voronoi diagram, rectilinear metric

2003

01.09.2003

DAAAM International Wien

Wien (Austria)

3-901509-36-4

1726-9687

Katalinic, B. (ed.): DAAAM International Scientific Book 2003

DAAAM International Scientific Book

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