Distributed Formation Control of Quadrotor UAVs Based on Rotation Matrices without Linear Velocity Feedback

This paper considers the problem of the formation control for multiple underactuated quadrotor UAVs without linear velocity measurements. The objective of this paper is expected to realize smooth formation performances for a quadrotor group. A distributed formation controller is designed directly using rotation matrices to obviate the singularities associated with the Euler-angles or the ambiguity of quaternions. A two-step procedure is adopted for the control development after transforming the dynamics of each quadrotor into a new form. At first, an intermediary control variable is introduced to achieve the formation control, where some auxiliary systems are designed in the presence of lacking linear velocity measurements. Then, based on the thrust force and reference angular velocity decoded from the intermediary control variable, the torque input of each quadrotor is proposed for angular velocity tracking. The case of formation control with a virtual leader is also investigated, where at least one quadrotor has the information of the leader. The asymptotic stability of the proposed control system is analyzed by Lyapunov-like tools, and the effectiveness of the proposed control method is verified by simulation studies. The simulation results show that the proposed method can guide the quadrotor group to form the desired formation smoothly without linear velocity feedback, which has great potentials for the UAV group to execute the challenging mission in hostile environments.