1. I have chosen to show software that I have previously developed in the
course of my research. It is based on OpenSceneGraph (which is based in
turn on OpenGL). A screenshot follows:
2. The following algorithm is a simple and complete (though not optimal) solution to the R2 path planning problem:
To prove (probabilistic) completeness, it need only be noted that a robot performing a random walk in the plane will eventually visit every point. No upper bound can be given for runtime, but for a finite workspace, the runtime will be finite as well. Since there is no upper bound, the algorithm can never return failure with certainty. Given the size of the world and runtime up to the present, the probability that a solution exists can be computed. Failure could be returned when the probability that a path exists falls below some threshold value.