Linear formation control of multi-agent systems

This paper proposes a new distributed leader–follower control architecture, termed linear formation control, to realize formation variations. The objective is to navigate a group of agents to reach a specific target formation, which is a linear transformation of the pre-defined nominal configuration, whose dimension can be higher than agents’ coordinates. The proposed architecture enables the formation to adjust through arbitrary linear transformations to accommodate the environment, offering a diverse range of feasible formations. First, we introduce the concept of “linear localizability” that leaders can uniquely determine the target formation. Then, using the pre-defined stress matrix, we propose a linear formation control method, which can be regarded as an extension of recent affine formation control approaches. Next, in the situation where the stress matrix is unavailable, distributed estimators are designed to obtain accurate linear formation parameters. We propose an estimation-driven linear formation control method using the graph Laplacian matrix. Finally, simulations are conducted to verify the effectiveness of the proposed linear formation control schemes.