Estimation of collision probabilities in dynamic environments for path planning with minimum collision probability

To plan collision-free trajectories for mobile robots among moving obstacles most approaches presume the obstacles´ trajectories to be known. This is contradictory to practice where motions generally are known-at best-as average behaviours. Thus, we proposed to use statistical information for path planning. This paper focuses on the derivation of formulae to estimate collision probabilities. By generalizing elementary collision patterns we develop a method to calculate a collision probability field. For any given goal position, it estimates the collision probabilities for paths starting at arbitrary points in the workspace. This provides a powerful tool for path planning in dynamic environments. Using an algorithm similar to path planning based on potential fields, we can calculate paths with (approximately) minimum collision probability