Motion planning in environments with danger zones

This paper addresses the problem of path planning for a free-flying object in a (three-dimensional) environment that contains both obstacles and so-called danger zones. The path should (obviously) avoid collisions with the obstacles. The path is allowed to intersect with the danger zones, but this should be avoided as much as possible. We show that under some mild conditions, a path always exists in which the moving object never completely penetrates the danger zones. Based on this result we present a probabilistically complete roadmap method that finds such paths. The methods has been implemented and some experimental results are given.