RRT With Obstacles

Last week I tried making a rapidly-exploring random tree, or RRT. Instead of starting from a single point as is typical in motion planning, I started from an entire coastline. This produced something vaguely resembling a drainage network of streams and rivers.

Because the tree grows toward each random point from the closest river or shore, it's extremely unlikely that you'd ever replicate South America, with most of the water draining to one side. This can be remedied by adding obstacles (click to enlarge):



Obstacles are defined as line segments which block line of sight between each randomly generated point and the tree. They manually specify some of the ridges on the terrain. Note that rivers will tend to cut quite close to the ends of the obstacles, so the obstacles don't represent just the highest parts of the ridges.

With my brute-force algorithm (coded in a couple of hours) the addition of obstacles slowed it down by a large amount that scales directly with the number of obstacle line segments. As the shape of the obstacles gets more mazelike, the algorithm will require drastically more iterations to fill in the tree, too, since it won't get line of sight to the inner portions for quite some time.

I also did some experiments with RRTs on a grid, where tree edges are all oriented horizontally or vertically. It turns out to bear a strong resemblance to maze-generation algorithms in that context.