  In this paper we investigate the asymptotic optimality property of a
randomized sampling based motion planner, namely RRT. We prove that a RRT
planner is not an asymptotically optimal motion planner. Our result, while
being consistent with similar results which exist in the literature, however,
brings out an important characteristics of a RRT planner. We show that the
degree distribution of the tree vertices follows a power law in an asymptotic
sense. A simulation result is presented to support the theoretical claim. Based
on these results we also try to establish a simple necessary condition for
sampling based motion planners to be asymptotically optimal.
