A Foundation for the "Flexible-Trajectory" Approach to Numeric Path Planning

This paper describes the development of a new type of non- collision constraint function for use in numeric path planning. It is valid even when computed for configurations in collision. This allows for greater freedom in hypothesizing trajectories to be relaxed intact into admissibility. The motivation lead ing to its development is discussed, along with its theory and properties. By way of example, its application in a naive path planning algorithm is described, which leads to surprising results when compared with a contemporary subdivision method.