Several recent works considered cooperative cleaning in static and dynamic environments, which incorporates a swarm of simple robots cleaning an expanding region of contaminated cells in a 2-D grid. However, even the state of the art strategy requires continuously-updated global domain information. In this work-in-progress we examine a strategy operating truly local. Neither in the beginning of a cleaning process, nor later on will our robot swarm receive any global information in order to perform the cooperative cleaning task. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems—Geometrical Problems and Computations, Computations on Discrete Structures General Terms Algorithms, Theory Keywords Swarm Robotics, Decentral Control