RRT

Rapidly-exploring Random Trees (RRT) is a sampling-based motion planning algorithm designed to efficiently explore high-dimensional spaces. The algorithm incrementally builds a tree by randomly sampling points in the configuration space and extending the tree towards these points. The extension is typically done using a steering function that connects the nearest node in the tree to the sampled point while ensuring that the path remains collision-free. RRT is particularly effective in complex environments with obstacles, as it can quickly find feasible paths without exhaustive search. Variants such as RRT* enhance the basic algorithm by incorporating optimization techniques to improve path quality. The mathematical foundation of RRT lies in probabilistic completeness, ensuring that as the number of samples approaches infinity, the algorithm will find a valid path if one exists. This makes RRT a fundamental tool in motion planning and robotics.