Rapid Sampling of Molecular Motions with Prior Information Constraints
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.