Semi-globally stable formation flight control design in three dimensions

We develop a semi-globally stable nonlinear formation flight control algorithm for a leader-follower configuration in three dimensions. The objective is to maintain the relative distances between the vehicles close to their desired values. It is shown that the conditions under which the control law is well-defined depends on the choice of the reference frame and control inputs. These conditions in the case when the design is carried out in the body frame of the follower are more restrictive than those encountered in the case of the body frame of the leader. The control algorithm is based on a new error formulation in the inertial frame. A detailed analysis and control design procedure are presented.