In this paper, we explore the possibility of applying concepts from general curve evolution theory to the decentralized control of contour-shaped formations of autonomous mobile underwater vehicles commissioned with the task of adapting to certain level sets of environmental fields created by diffusion or similar processes. The robots are assumed to be capable of measuring local gradients on their own. Controllers for individual robots are derived based on the general continuous evolution equation. Basic results on formation stability and convergence are also provided. Simulation results support the effectiveness of this approach.

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