Rapidlyexploring

Rapidlyexploring is a term used to describe a class of probabilistic motion planning methods designed to find feasible paths for robots in high-dimensional, continuous configuration spaces. The most common embodiment is the rapidly-exploring Random Tree (RRT). The central idea is to grow a tree of configurations by repeatedly sampling random configurations from the space, locating the nearest node in the tree, and extending toward the sample if the resulting path is collision-free. The random sampling drives rapid exploration of large or cluttered spaces, helping to locate feasible trajectories even when deterministic search methods struggle. The basic approach is probabilistically complete: if a solution exists, the probability of finding one approaches one as the number of samples increases.

The concept originated with Steven M. LaValle and J. J. Kuffner Jr., who introduced Rapidly-exploring Random Trees in 1998. Since then, numerous variants have been developed to address practical needs. Notable examples include RRT-Connect, which aims to quickly connect two trees, and RRT*, which provides asymptotic optimality by rewiring connections to reduce path cost.

Applications of rapidly-exploring methods span robotics, autonomous vehicles, and computer animation, particularly in complex environments where obstacles and high dimensionality complicate exhaustive search. They are often used for kinodynamic planning, where system dynamics constrain feasible motions, and for real-time planning when a quick feasible path is preferred over exact optimality.

Limitations include potential suboptimality for the basic RRT and sensitivity to parameters such as step size and sampling distribution. Post-processing, path smoothing, or switching to optimal variants like RRT* can mitigate these issues. Related approaches include probabilistic roadmaps and other sampling-based planners.