Here, we aim to find collision-free paths for a point robot in 2D-space
starting from a source configuration. (A) The basic
Single-RRT algorithm provides fast but rough coverage
of unexplored regions, and the target is often missed (red star, top
left). During the run, the tree grows in feasible space (white) among
obstacles (orange rectangles). In biological examples, these obstacles
are high-energy conformations. Each point stands for a two dimensional
conformation, and the tree grows from a source conformation (violet
star, middle of figure), towards random directions (see Methods). (B) In the
Partial-RRT variant, we use partial information to
truncate branches that do not grow towards the target (like the
truncated branch in the grey ellipse, compare to the branch in the
magenta ellipse). The search is more confined to relevant regions, at
the expense of overall coverage of the search space. (C, D) Comparison
between the basic Single-RRT algorithm and RRT with
partial information (Partial-RRT), for the toy example
in a and b. The partial information
used here is the distance to the target. In
SingleRRT-t50 and PartialRRT-t50 the
target is also used as an explicit direction of growth once in 50
iterations, in case the tree reaches the proximity of the target but not
its exact location. This test follows a common assumption that RRT
running time is dominated by the number of collision tests. We compare
the Euclidean distance of the RRT node that is closest to the target
(y-axis) as a function of the number of collision tests (x-axis)
throughout the run. Results are the average distance (in
c) or the minimum distance (in d) over
50 independent runs. PartialRRT performed better than SingleRRT,
especially for a lower number of collision checks. Better performance is
achieved in less running time. As the number of collision checks grows.
All methods converge. Note that this is only a toy example for
illustrative purposes; in many biological examples, the target
conformation might not be given explicitly, and the number of
dofs is in general much higher.