Fully distributed affine formation control of general linear systems with uncertainty

This paper considers the distributed affine formation control problem of general linear systems with uncertainty. In affine formation manoeuvre control, the agents are to be capable of producing specified geometric patterns and simultaneously accomplish required manoeuvres, such as scales, translations and rotations. Here, the formation control problem is studied using the stress matrix approach which has similar properties as the Laplacian matrix of a graph, with a major difference being that the edge weights can have positive or negative values. The system stability is analysed using Lyapunov theory. Novel affine formation control laws for general linear systems are presented. Four control laws are presented to address different cases. The proposed laws consider the general linear case, the case with uncertainty and the fully distributed case using robust and adaptive strategies. Under the proposed laws, the collection of agents can track any targets that are affine transforms of a defined reference configuration. Experimental results are presented to demonstrate the effectiveness of the proposed control laws.