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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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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DOI: https://doi.org/10.1007/978-3-030-15187-4_2
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