Sampling-based motion planners provide efficient solutions to a variety of high-dimensional, geometrically complex motion planning problems. Traditionally, these approaches give up formal guarantees, attaining asymptotic properties in terms of completeness and optimality. Recent work argued, based on Monte Carlo experiments, that these approaches also exhibit desirable probabilistic properties in terms of optimality after finite computation. This talk explores these types of guarantees, providing a bound on the probability that the length of solutions In returned by an asymptotically optimal roadmap-based planner after n iterations are within a bound of the optimal path length. This bound gives insight into practial properties, such as providing a probabilistic bound on solution non-existence, which can inform higher-level task planners on where to prune searches. Such a bound can also provide insight into identifying new motion planning methods which provide good practical properties.  Also discussed will be advancements made on sparse representation methods which do provide such good practical properties.  The marriage of sparse methods with finite time properties shows great promise for providing general, robust solutions with very small memory footprints.  This work will strive towards practical application of these methods to humanoid robot manipulation problems.