Consensus-Based Distributed Formation Control of Multi-Quadcopter Systems: Barrier Lyapunov Function Approach

Abstract

The problem of formation tracking control for a group of quadcopters with nonlinear dynamics using Barrier Lyapunov Functions (BLFs) is studied in this paper where the quadcopters are following a desired predefined trajectory in a predefined formation shape. The BLFs are employed to formulate the problem of formation trajectory tracking with a predefined accuracy. For this purpose, logarithmic BLFs including both the trajectory errors and the errors between the quadcopters' distances with the desired ones (for the formation goal) are proposed. The method is firstly developed in a centralized scheme and then extended to a distributed framework using appropriate asymptotically convergent consensus algorithms. Therefore, the asymptotic convergence of the designed distributed algorithm to the centralized one is guaranteed. Moreover, due to the under-actuated feature of a quadcopter system, a general hierarchical scheme is considered for designing the controller. To this end, firstly a formation altitude tracking control is designed and then using the generated control signal, the formation translational tracking control is developed with the assumption of virtual inputs which are then employed to generate desired trajectory signals for the attitude control subsystem. Finally, attitude controllers are designed separately for each agent using the generated desired signals through logarithmic BLFs to consider a predefined accuracy. The efficiency of the proposed method is demonstrated through simulations and comparisons with the similar approaches in MATLAB-Simulink environment.