Finite-time optimal formation control of multi-agent systems on the Lie group SE(3)

This paper investigates the finite-time optimal formation problem of multi-agent systems on the Lie group SE(3), for the situation when the formation time and/or the cost function need to be considered. Under the condition that the formation time is given according to the task requirement, a finite-time optimal formation controller is proposed for the two-agent case to guarantee that the desired formation is achieved at the given time and the corresponding cost function is optimal. For the systems with multiple agents, the obtained finite-time optimal formation control law has second-order approximation accuracy. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.