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Mathematical Background

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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

The theory of formation control of distributed agents is developed on the base of mathematical concepts from graph theory. Specifically, algebraic graph theory and graph rigidity theory are two main mathematical backgrounds. But the graph theory acts as a basic topological setup; so to add a control flavor into these theories, we also need to have some background from nonlinear control theory along with consensus dynamics. This chapter provides essential mathematical background that can be used for the developments of distributed formation control theory. The detailed topics included in this chapter are basic concepts in graph theory, rigidity theory (distance rigidity, persistence, bearing rigidity, and weak rigidity), key results in consensus, and basics of nonlinear control theory.

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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). Mathematical Background. In: Formation Control. Studies in Systems, Decision and Control, vol 205. Springer, Cham. https://doi.org/10.1007/978-3-030-15187-4_2

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