Objectives  In order to realize the formation control of swarms of unmanned marine vehicle (UMV) with directed interaction topology, the formation tracking control of unmanned surface vehicle (USV) and unmanned aerial vehicle (UAV) swarms is studied.

  Methods   An inner/outer loop layered control structure of formation is adopted to model the system, and the discrete-time system is used to describe the formation control problem of UMV swarms, improving the compatibility and practicability of the method for heterogeneous swarms. Based on the idea of a virtual leader, a distributed formation control protocol based on neighbor position and velocity error feedback is adopted, and the necessary and sufficient conditions for UMV swarms to realize the desired configuration and path tracking are given.

  Results  The simulation results show that UMV swarms can achieve stable formation control when there is a directed spanning tree in the interaction topology, and the parameters of the control protocol and discrete time period meet the given constraints.

  Conclusions  This method has application value in the formation control of UMV swarms with directed interaction topology.