Using Backprojections for Fine Motion Planning with Uncertainty

Abstract

This paper outlines a method for planning motions in the presence of uncertainty. Tasks are modeled as geometrical goals in configuration space. The planning process consists of determining regions from which particular motions are guar anteed to reach a desired goal successfully. An algorithm is presented for backprojecting from desired goal states. The backprojection regions are computed by erecting constraints that geometrically capture the uncertainty in motion. The relationship of backprojections to goal recognizability is discussed within the formal framework of preimages. This relationship suggests a partitioning of desired goal states into recognizable goal states. Backprojections are actually per formed from this partitioning.