Finite-time optimal formation control on Lie groups

This paper studies the problem of finite-time optimal formation control for agents evolving on Lie groups SE(2), for the situation when the formation time and/or the cost function need to be considered. The finite-time optimal formation control laws are proposed for the two-agent case. Considering that disturbances exist after the terminal time, the trajectory tracking control law is given to keep the formation. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.