In the Rapidly Exploring Random Tree (RRT) [41] algorithm, the
motion model is used to create the roadmap. The RRT represents
the roadmap as a tree T rooted in qinit . The tree is grown as follows.
In each iteration, a random sample qrand ∈ C is generated. The
nearest node qnear ∈ T in the tree is found and is expanded to
obtain a set S of free configurations reachable from qnear . From
this set, a configuration qnew which is nearest to qrand is selected
and stored into the tree. The qnear is marked as its parent node.
The algorithm terminates if the goal region defined by radius dgoal
is approached. The basic RRT algorithm is listed in Alg. 1. The
RRT algorithm has been employed for motion planning of various
robotic systems, and many modifications have been proposed; we
refer to [38,50] for a survey of the modifications of this algorithm.