A distributed coverage control strategy is developed for a group of heterogeneous robots in this work. Most existing coverage controllers assume the relation between the underlying density function and the locations of the robots is independent. To relax the condition for more potential applications, a new coverage control strategy that accounts for the dependence between the underlying density function and the locations of the robots is developed, and moreover, it can be extended to the conventional coverage controller by selecting specific system parameters. In addition, the heterogeneity among the robots can also cause various levels of reduction to the underlying density function, and hence, an Enhanced Multiplicatively Weighted Voronoi (EMWV) partition along with the controller is developed, so that optimal coverage can be obtained despite the heterogeneity between the robots. Stability analysis is proven to ensure system convergence, and simulations are conducted to verify the efficacy of the developed controllers.