This paper introduces a novel method for the coordinated control of heterogeneous multi-robot systems composed of a UGV and a UAV and focuses on cooperative exploration in unknown environments. The proposed approach utilizes a numerical optimization solver to manage the non-linear dynamics and constraints of both agents. We introduce a weighting parameter to adapt the team behavior either prioritizing proximity between the agents or independently pursuing the exploration. The proposed solution has been extensively tested in a simulation environment and the experimental results demonstrate the method’s computational efficiency, adaptability, and suitability for real-time deployment in autonomous exploration missions. This approach advances multi-robot coordination by providing a flexible and robust framework for heterogeneous agent collaboration in complex, unstructured environments.