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This paper presents a distributed control framework for multi-agent formations undergoing non-uniform scaling, allowing agents to dynamically join the formation. The control law ensures that the spectral properties of the graph Laplacian are preserved during scaling and agent joining, maintaining formation stability. Simulations demonstrate the framework's ability to incorporate new agents while achieving the desired non-uniform scaling.
Multi-agent formations can now dynamically expand and reshape themselves on the fly, thanks to a new control framework that preserves spectral properties during non-uniform scaling.
Non-uniform scaling control of formation enables multi-agent systems to adjust their shape by scaling with different ratios along different coordinate axes, offering enhanced flexibility in complex environments. However, like most existing formation maneuver strategies, it typically assumes a fixed set of agents, limiting its applicability in scenarios requiring dynamic team expansion. This paper introduces a distributed control framework that enables a formation to incorporate new agents during non-uniform scaling maneuvers in arbitrary dimensions while preserving the spectral properties of the graph Laplacian. Simulation examples validate the effectiveness of the theoretical results.