Discovering molecules: Pass planning through a gap

We present a new algorithm for a molecular pass planning through a circle. Our algorithm can solve the given problem with the significant improvement of accuracy for arbitrary shaped molecules in comparison with the method using a minimal bounding sphere. This accuracy is gained by eliminating the overestimation of the substrate size by the bounding volume approaches. Our approach is particularly beneficial in cases where the bounding volume fits poorly to the substrate geometry as is the case with oblong shaped substrates. We are using a sampling-based version of the motion path planning and the Delaunay triangulation to arrange the substrate for the space search. The successor configurations are then computed incrementally from the already known configurations until we find a connected path of the substrate through a circle or we can claim that such path does not exist.