The control problem of the multi-robots with different actuation capabilities has caught the attention of the robotics researchers over the last years. The algorithm proposed in the paper not only makes use of the energy-efficient coverage optimal control scheme but also utilizes Hopfield Neural Networks (HNN) in order to perform collaboration among the agents according to their different actuation performances without knowing them beforehand. The agents estimate their own performances by using HNN estimator and calculate the Power Voronoi Diagram (PVD or PD) weights for each agent. The robots achieve the optimal coverage configuration autonomously. The algorithm can assign the regions from the workspace and in resultant configuration, the robots with strong actuators obtain wider areas allocated from the workspace while the weaker robots obtain smaller areas. Also, by making use of the energy-efficient optimal coverage control scheme, a trade-off between the coverage time and energy consumption of the agents can be made. The MATLAB simulation and experimental results regarding the proposed online and distributed algorithm are given. The novelty of this work lies in the using of HNN-based multi-robot coverage collaboration according to the different actuation capabilities and energy-efficient coverage control laws at the same time. Significant improvements compared with the method utilized in (Pierson et al., 2017) have been observed.