Probabilistic Analysis of Manipulation Tasks: A Conceptual Framework

This article addresses the problem of manipulation planning in the presence of uncertainty. We begin by reviewing the worst-case planning techniques introduced by Lozano-Pérez et al. (1984) and show that these methods are limited by an information gap inherent to worst-case analysis techniques. As the task uncertainty increases, these methods fail to produce useful information, even though a high-quality plan may exist. To fill this gap, we present the notion of a probabilistic backprojection, which describes the likelihood that a given action will achieve the task goal from a given initial state. We provide a constructive definition of the probabilistic backprojection and related probabilistic models of manipulation task mechanics and show how these models unify and enhance several past results in manipulation planning. These models capture the fundamental nature of the task behavior but appear to be very complex. We present the results of laboratory experiments, comprising over 100,000 grasping trials, that measured the probabilistic backprojection of a grasping task under varying conditions. The resulting data support the probabilistic backprojection model and illustrate a task in which probabilistic analysis is required. We sketch methods for computing these models and using them to construct multiple-step plans.