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LQR-based affine formation control for multi-agent systems

Affine formation control has been proved to be an effective tool in altering formation shapes for multiple robots to adapt to the change of working space. This paper studies the problem of optimal affine formation control based on LQR performance index. By taking both the internal potential and the control efforts of all agents into consideration, the control gain is uniquely determined under which the cost function is minimized. It is shown that the control gain is dependent on the agents' initial states as well as their connection relationship. Numerical simulations are presented to validate the theoretical results.