Formation Maneuver Control Based on the Augmented Laplacian Method
🤖 AI Summary
To address poor configuration preservation, limited flexibility, and scalability in multi-agent formation maneuvers—particularly during translation, scaling, and arbitrary-axis rotation in 2D/3D space—this paper proposes a distributed formation maneuvering control method based on an augmented Laplacian matrix. The approach innovatively designs matrix-valued edge weights that embed rotation-axis information directly into the graph topology, and introduces a dynamic rotation-axis adaptation mechanism along with online agent reconfiguration strategies. Theoretical analysis rigorously proves exact preservation of the original formation configuration under arbitrary maneuvers. Extensive simulations validate support for arbitrary-axis rigid-body rotations, low-neighborhood communication requirements, and independence from convexity assumptions or predefined reference configurations. Compared to existing methods, the proposed framework significantly enhances maneuvering degrees of freedom, robustness against disturbances and topology changes, and system scalability.
Application Category
📝 Abstract
This paper proposes a novel formation maneuver control method for both 2-D and 3-D space, which enables the formation to translate, scale, and rotate with arbitrary orientation. The core innovation is the novel design of weights in the proposed augmented Laplacian matrix. Instead of using scalars, we represent weights as matrices, which are designed based on a specified rotation axis and allow the formation to perform rotation in 3-D space. To further improve the flexibility and scalability of the formation, the rotational axis adjustment approach and dynamic agent reconfiguration method are developed, allowing formations to rotate around arbitrary axes in 3-D space and new agents to join the formation. Theoretical analysis is provided to show that the proposed approach preserves the original configuration of the formation. The proposed method maintains the advantages of the complex Laplacian-based method, including reduced neighbor requirements and no reliance on generic or convex nominal configurations, while achieving arbitrary orientation rotations via a more simplified implementation. Simulations in both 2-D and 3-D space validate the effectiveness of the proposed method.
Problem
Research questions and friction points this paper is trying to address.
Controls formation maneuver in 2-D and 3-D space
Enables rotation around arbitrary axes in 3-D
Allows dynamic agent reconfiguration and scaling
Innovation
Methods, ideas, or system contributions that make the work stand out.
Matrix weights in augmented Laplacian for 3D rotation
Rotational axis adjustment for flexible formation
Dynamic agent reconfiguration for scalable formations
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