Ring Formation Maneuver: Single-Integrator Kinematics


Most conventional formation control algorithms consider convergence towards a specific desired point (or a specific desired displacement) for each vehicle relative to their neighbors. However, this specification restricts the flexibility in the motion of the vehicles. Motivated from this standpoint, this paper considers a formation control problem, where the desired position of each vehicle in the formation is described by a set of points. In particular, we consider relative motion in a two-vehicle system consisting of a leader and a follower, which is scalable to a larger formation in a distributed manner. The leader is free to move in 3-dimensional space while the follower seeks to converge to the desired set of points. We especially consider the desired set to be a ring of a given radius located at a certain distance from the leader in this paper. In addition, we propose two control algorithms. Both of them allow the follower to alter the set point smoothly during the mission and thus increase the follower’s flexibility of motion. The stability of the formation under the proposed control algorithms is analyzed using the Lyapunov theory. Numerical examples are also provided to illustrate the efficacy of the control algorithms.

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