Collective four-group antagonistic formation motion

This paper investigates a new formation motion problem of first-order multi-agent systems with antagonistic interactions. A distributed formation control law is proposed for each agents to realize antagonistic formation motion. A sufficient condition is derived to ensure that all agents make an antagonistic formation motion in a distributed manner. This shows that all agents can spontaneously be divided into four groups, and agents in the same group collaborate while agents in different groups compete. Finally, a numerical simulation is included to demonstrate our theoretical results.