Formation Maneuver Control Based on the Augmented Laplacian Method

TL;DR

This paper introduces a novel formation maneuver control method using an augmented Laplacian matrix with matrix weights, enabling flexible translation, scaling, and rotation of formations in 2-D and 3-D space, including arbitrary orientation adjustments.

Contribution

It presents a new matrix-weighted augmented Laplacian approach for formation control that allows arbitrary 3-D rotations and dynamic reconfiguration, improving flexibility and scalability.

Findings

The method enables formations to rotate around arbitrary axes in 3-D.

The approach preserves formation configuration during maneuvers.

Simulations confirm effectiveness in 2-D and 3-D spaces.

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.