Swarm Interpolation Using an Approximate Chebyshev Distribution

In this paper, we describe a novel swarming framework that guides autonomous mobile sensors into a flexible arrangement to interpolate values of a field in an unknown region. The algorithm is devised so that the sensor distribution will behave like a Chebyshev distribution, which can be optimal for certain ideal geometries. The framework is designed to dynamically adjust to changes in the region of interest, and operates well with very little a priori knowledge of the given region. For comparison, we interpolate a variety of nontrivial fields using a standard swarming algorithm that produces a uniform distribution and our new algorithm. We find that our new algorithm interpolates fields with greater accuracy.