Path planning problems and solutions

Path planning has been atopic of research in many areas including robotics and navigation. The purpose of this paper is to explore the problems of three-dimensional path planning in the context of a point-like airplane traveling to avoid circular danger regions. We will explore two distinct problems. The first problem is how to plan a path when the locations of all the dangers are known. The solution to this problem gives the plane an optimal path to follow before it even leaves the ground. We will refer to this as the global path planning case. In the second problem, the locations of the dangers are not known in advance. Instead, the locations of the danger points are known to the plane when they are within a sensor range, The plane changes its path when it senses the danger areas. We will refer to the second problem as the dynamic path planning case. Both of these cases will be subject to turning constraints. For the global path planning case, the problem can be solved with Collins decomposition. The dynamic path planning case, however, is still open ended. This paper outlines several approaches and their pitfalls concluding with subgoal avoidance as a solution for particular classes of reconnaissance scenarios