Affine formation maneuver control of multi-agent systems

A multi-agent formation control task usually consists of two subtasks. The first is to steer the agents to form a desired geometric pattern and the second is to achieve desired collective maneuvers so that the centroid, orientation, scale, and other geometric parameters of the formation can be changed continuously. This paper proposes a novel affine formation maneuver control approach to achieve the two subtasks simultaneously. The proposed approach relies on stress matrices, which can be viewed as generalized graph Laplacian matrices with positive, negative, and zero edge weights. The proposed control laws can track any target formation that is a time-varying affine transformation of a nominal configuration. The centroid, orientation, scales in different directions, and even geometric pattern of the formation can all be changed continuously. The desired formation maneuvers are only known by a small number of agents called leaders, and the rest agents called followers only need to follow the leaders. The proposed control laws are globally stable and do not require global reference frames if the required measurements can be measured in each agent's local reference frame.