The problem of controlling a group of unmanned aerial vehicles (UAVs) is considered to organize the movement of a swarm along a given trajectory, which ensures the most effective achievement of the flight goal. The issues of choosing a mathematical model of the spatial motion of a group of UAVs, suitable for solving the problem of synthesis of coordinated control of the entire set of aircrafts, are discussed. Taking into account the specifics of the requirements for the space-time position of individual UAVs (agents) in a group, it is proposed to use a model with a leader. A group of agents has a virtual leader who plans the route of the group in accordance with a given task and tracks a specific goal of movement. The virtual leader calculates its own motion control with a trajectory-tracking or target-tracking algorithm to move along the desired trajectory. In this case, the guidance signal can allow individual UAVs to gather at the position of the virtual leader and correspond to the velocity vector of the virtual leader in order to communicate the topology of the multi-agent system and ensure swarm formation.