  Sampling based planners have been successful in robot motion planning, with
many degrees of freedom, but still remain ineffective in the presence of narrow
passages within the configuration space. There exist several heuristics, which
generate samples in the critical regions and improve the efficiency of
probabilistic roadmap planners. In this paper, we present an evaluation of
success probability of one such heuristic method, called obstacle based
probabilistic roadmap planners or OBPRM, using geometric probability theory.
The result indicates that the probability of success of generating free sample
points around the surface of the $n$ dimensional configuration space obstacle
is directly proportional to the surface area of the obstacles.
