  This paper investigates the formation of fixed-wing UAVs in 3D, which
communicate via a directed acyclic graph. Different from common formation
problems, we consider the roto-translation invariant (RTI) formation, where the
"roto-translation" refers to a rigid-body motion obtained by composing rotation
and translation. Besides, the fixed-wing UAV is modelled by a 3-D nonholonomic
constrained rigid body instead of a particle agent. The main results of this
paper include proposing the formation feasibility conditions and designing the
formation controller. Firstly, we define the RTI formation and propose the
conditions to guarantee that the formations are feasible for the fixed-wing
UAVs under the nonholonomic and input saturation constraints. Secondly, given
feasible formations, we design a formation controller by introducing a virtual
leader and employing the compensation of rotation, followed by proving the
stability of the closed-loop system. Finally, simulation examples are presented
to verify the theoretical results.al with the motion coupling among multiple
robots. Finally, numerical simulations are conducted to verify the theoretical
results.
