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Local Stabilization

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Formation Control

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 205))

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Abstract

In Chap. 3, solutions for global stabilization of formation systems with several specific topologies have been presented. In this chapter, generalized formations with n-agents are studied. However, it is difficult to guarantee a global convergence for general n-agent formations without any communication. This chapter provides analysis for local convergence of general n agents under the traditional gradient control laws. Following Chap. 3, it is assumed that agents can sense locations of neighboring agents with respect to their own coordinate frames; but they cannot exchange information or cannot communicate with other neighboring agents. So, the control goal is to achieve the desired distances only based on the relative measurements. Since the control variables are distances, the formation control problems studied in this chapter are classified as distance-based control. By satisfying all the desired distances of rigid graphs, we can achieve a unique configuration in d-dimensional (\(d=2,3\)) space, or in general d-dimensional space, up to translations and rotations. This chapter presents a generalized gradient control law for n agents on the basis of Sect. 3.2.

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Notes

  1. 1.

    However, it is hard to image an aligned virtual axis in 3- or higher dimensional spaces. In higher dimensional spaces, we may have to define an aligned virtual manifold rather than an axis.

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Authors and Affiliations

  1. School of Mechanical Engineering, Gwangju Institute of Science and Technology, Buk-gu, Gwangju, Korea (Republic of)

    Hyo-Sung Ahn

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  1. Hyo-Sung Ahn
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Correspondence to Hyo-Sung Ahn .

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Ahn, HS. (2020). Local Stabilization. In: Formation Control. Studies in Systems, Decision and Control, vol 205. Springer, Cham. https://doi.org/10.1007/978-3-030-15187-4_4

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