This section introduces an incremental sampling and searching approach that yields good performance in practice without any parameter tuning.5.14The idea is to incrementally construct a search tree that gradually improves the resolution but does not need to explicitly set any resolution parameters. In the limit, the tree densely covers the space. Thus, it has properties similar to space filling curves , but instead of one long path, there are shorter paths that are organized into a tree. A dense sequence of samples is used as a guide in the incremental construction of the tree. If this sequence is random, the resulting tree is called a rapidly exploring random tree (RRT). In general, this family of trees, whether the sequence is random or deterministic, will be referred to as rapidly exploring dense trees (RDTs) to indicate that a dense covering of the space is obtained. This method was originally developed for motion planning under differential constraints [608,611]; that case is covered in Section 14.4.3.