Time-varying formation control for multi-agent systems with uncertainties and switching directed topology

The formation control for multi-agent systems with time-varying uncertainties under directed topology is considered in this paper. By constructing a distributed extended state observer, the uncertainties and external disturbance suffered by the agents during formation process can be estimated. On the basis of the ESO, a distributed formation control protocol is proposed based on switching directed topologies. Further, the necessary and sufficient conditions which the multi-agent systems need to achieve time-varying formation under the designed protocol are proved. An explicit expression of time-varying formation reference function is also presented to reveal the macroscopic motion of the whole formation. The algorithm to clear the protocol is given, and it guarantees that the multi-agent systems with uncertain dynamics and switching directed topologies can hold their positions in the formation. This method help the multi-agent systems reach the desired locations in an expected formation shape with small error.