Formation control with velocity assignment for second-order multi-agent systems with heterogeneous time-delays

This paper deals with a formation control problem for second-order multi-agent systems with heterogeneous time-delays. We aim to control multiple agents so as to form a desired formation pattern and to move with an assigned velocity in an assigned direction. The assigned velocity and direction are transmitted through long-distance communication from human operators as external signals. Some of the agents, called leaders, can receive the external signals. As shown in this paper, in multi-agent systems with heterogeneous time-delays, there remain formation and velocity errors because of the asymmetry of the time-delays. We investigate how large errors arise in these systems, and propose the best selection of leaders so as to minimize the velocity error. Finally, some numerical results demonstrate the validity of the proposed analyses.