In the paper, an adaptive collaboration method for multiple robots under localization uncertainty is presented. The multi-agent algorithm makes use of the multiple homogenous wheeled mobile robots whose locations are not known precisely but known to be within uncertainty circles. The workspace is partitioned by using the Guaranteed Power Voronoi Diagram (GPVD or GPD). The weights of the diagram are calculated by the collaboration algorithm in order to assign more regions to the agents with better actuator performances and less regions to the ones with weaker actuators. The robots do not know the performance parameters beforehand. They learn their own parameter vectors online by using the Hopfield Neural Network (HNN) estimator. So, by making use of the proposed control scheme and collaboration algorithm, the agents position themselves to the optimal coverage configuration and at the end configuration, the workspace assignment according to the actuator performances is performed. The proposed algorithm runs online and in a distributed fashion. The simulation results in MATLAB are given with the experimental verification done with Turtlebot 2 robots and ROS.