With the increased use of robots with different performance characteristics in areas such as search and rescue, patrolling and surveillance, the control of multiple robots with unequal capabilities have gained a lot of interest among robotics researchers. Also, the uncertainty of the sensors utilized on the robots for localization has made the problem of imprecise localization attractive. This paper aims to present the development and implementation of a multi-agent collaboration algorithm under localization uncertainty using Hopfield neural networks, guaranteed power Voronoi diagrams (GPVD or GPD), and coverage control. The agents are considered non-holonomic wheeled mobile robots under the assumption that their locations are not known precisely, but they are known to be in uncertain circles. The workspace is partitioned with a Guaranteed Power Voronoi Diagram (GPVD or GPD) algorithm which takes imprecise localization into account. Also, it is assumed that the actuation capabilities of the robots are different from each other and the agents do not know those performances beforehand. The performance parameters of the robots are learned by using the collaboration algorithm with Hopfield Neural Network (HNN) and then passed to the GPD algorithm. The GPD algorithm together with the HNN provides workspace partitioning for the robots so that the agents with poor actuation performances take smaller regions from the workspace while the agents with strong performances take greater regions. Thus, a collaborative coverage task is achieved which enables the robots to deploy themselves to an optimal configuration minimizing the total coverage cost. The simulation results in MATLAB show the efficiency of the algorithm. The experimental results with the Robot Operating System (ROS) are given. The results obtained are satisfactory since the algorithm has faster convergence and has the capability to assign the regions from the workspace considering the imprecise localization resulting from sensor characteristics. Finally, the algorithm is compared to the base collaboration method, important performance improvements had been observed.