Curvature based cooperative exploration of three dimensional scalar fields

We develop strategies for controlled motion and filtering performed by a mobile sensor network to cooperatively explore an unknown 3D scalar field. In order to estimate the principal directions and principal curvatures of a desired level surface of the field which are used as feedback by the motion control law, we apply a non-analytic curvature estimation algorithm and prove the sufficient and necessary conditions under which this algorithm can provide reliable estimates. A differential geometric approach is followed in developing provably convergent steering control laws to control the center of the sensor platform formation to track one of the lines of curvature on a detected level surface of the scalar field.