Published in the Proceedings of the International Symposium on Assembly and Task Planning Complete Indexing Strategies for Sparse Sensing Techniques

In structured environments found in manufacturing, a few precise measurements are often su cient to recognize and localize modeled objects. Modeled objects can be recognized and localized by enumerating interpretations of the sensed data in terms of model features, and then validating each hypothesized interpretation by computing the optimal pose estimate and associated error. The task of enumerating hypotheses is termed the correspondence problem, and it is difcult to perform e ciently because only a small fraction of possible interpretations are valid. Indexing is a general approach for solving the correspondence problem in which coordinates are distilled from the sensed data, and then these indexing coordinates are quantized to index a table entry containing the valid interpretations. Indexing table are central to indexing techniques; if the table is complete, i.e., it contains an entry for every valid combination of indexing coordinates and interpretations, then the indexing strategy is correct. For sparse sensing strategies, where each experiment only provides a few measurements, indexing table completeness is critical. The task of constructing complete indexing tables has previously been an open problem. In this paper, we describe a method for constructing complete indexing tables that problem which involves enumerating cells in an arrangement in conguration space.