ABSTRACT
Theorem 6 If a connection sequence of length k ex ists, then the expected number of iterations required to connect qinn to qgoai is no more than k/p.
Proof: If an RRT vertex lies in A i-1, and a random sample, x , falls in Ai, then the RRT will be connected to x. This is true because using the first property in the definition of a basin, it follows that one of the ver tices in Bi must be selected for extension. Using the second property of the basin, inputs will be chosen that ultimately generate a vertex in Ai.
