Construction of universally rigid tensegrity frameworks and their applications in formation scaling control

This paper first investigates the challenging graph theoretic problem of constructing universally rigid tensegrity frameworks given any generic configuration. We design a numerical algorithm to construct a universally rigid tensegrity framework, such that the resulted eigenvalues of the stress matrix of the tensegrity framework can be selected beforehand. As one application, we then consider the formation scaling problem for multi-agent systems, in which the agents and their interaction relationship are respectively represented by the nodes and the underlying graph of the tensegrity framework. Distributed control laws are developed using the stresses, which render the global exponential convergence to the target formation shape. We also carry out several simulations to validate the theoretical results.

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