Control of multiple left-invariant systems on Lie groups using less control inputs

In this paper, we discuss control problems of multiple left-invariant systems on Lie groups, such as SE(2), SO(3) and SE(3). If each robot were supposed to be controlled independently, the total number of control inputs would be the number of individual inputs times the number of robots. On the other hand, it is possible for the system to remain controllable even if some artificial constraints are imposed. We show that systems of multiple agents on Lie groups can be controlled using less number of control inputs.