Objectives  This paper studies a three-dimensional (3D) cooperative path-following control problem in the process of maritime search and rescue for a heterogeneous unmanned cluster system composed of unmanned aerial vehicles (UAVs) and unmanned surface vehicles (USVs).

  Methods  First, kinematic models of the UAVs and USVs are established under a fixed coordinate system and body coordinate system. In order to design a 3D path-following controller suitable for motion control, an air coordinate system is established, and the path tracking error models of the UAVs and USVs are established in the Serret-Frenet coordinate system. Next, a 3D line-of-sight (LOS) guidance law is designed at the kinematic level, and a cooperative path-following control method suitable for heterogeneous clusters of marine vehicles is proposed, allowing the UAVs and USVs to track the preset parameterized path. Finally, the stability of the control system is analyzed based on the Lyapunov stability theory.

  Results  The simulation results verify the effectiveness of the proposed cooperative path-following control method for heterogeneous clusters of marine vehicles.

  Conclusions  The results of this study can provide references for maritime search and rescue by using the proposed cooperative path-following control method.