Hearing the “shape of a drum” refers to a long standing mathematical problem of determining a drum’s membrane geometry from its vibration modes.  This problem relates to applications in pattern recognition and shape identification.  In 1992, it was shown that the shape of the drum cannot be uniquely determined by its vibration modes, but some encouraging results suggest that certain combinations of the Dirichlet eigenvalues can provide reliable, scaling and rotation invariant descriptors for a planar curve.

This project builds on this idea and suggests new ways in which formations of robots can collect data, implement a spatially distributed neural network on their on-board processors, and autonomously classify what “they are looking at” collectively, without any one of them having to piece together the whole picture and perform the computation alone.  The distributed approach to motion control, data collection, and processing gives inherent robustness both against measurement noise and physical failures, and does not necessitate human involvement in the interpretation of the data.

A more comprehensive Final Project Report

This material is based upon work supported by the National Science Foundation under Grant No. 0822845. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.