In this work, we examine the distributed coverage control problem for deploying a team of heterogeneous robots with nonlinear dynamics in a partially known environment modeled as a weighted mixed graph. By defining an optimal tracking control problem, using a discounted cost function and state-dependent Riccati equation (SDRE) approach, a new partitioning algorithm is proposed to capture the heterogeneity in robots dynamics. The considered partitioning cost, which is a state-dependent proximity metric, penalizes both the tracking error and the control input energy that occurs during the movement of a robot, on a straight line, to an arbitrary node of the graph in a predefined finite time. We show that the size of the subgraph associated with each robot depends on its resources and capabilities in comparison to its neighbors. Also, a distributed deployment strategy is proposed to optimally distribute robots aiming at persistently monitoring specified regions of interest. Finally, a series of simulations and experimental studies is carried out to demonstrate the viability and efficacy of the proposed methodology in deploying heterogeneous multiagent systems.