Ring Formation Maneuvering with Double Integrator Dynamics

Conventional leader-follower formations restrict the follower to a single desired position relative to the leader. To give the follower more flexibility in motion and to replicate typical human pilot operations, in this paper we propose a control architecture allowing the follower to converge to a ring, which is a set of desired points, relative to the leader. The follower is considered subject to a point-mass aircraft model, which can be transformed into the double integrator kinematics. For that reason, the nonlinear backstepping method is first utilized to design the controller for the double integrator kinematics with input saturation constraints being taken into account. The controller is then converted into control variables for the point-mass model. The stability of the proposed architecture is analyzed. Finally, a numerical example is presented to illustrate the efficacy of the proposed controller.