Distributed safe formation tracking control of multiquadcopter systems using barrier Lyapunov function

Abstract

Coordinating the movements of a robotic fleet using consensus-based techniques is an important problem in achieving the desired goal of a specific task. Although most available techniques developed for consensus-based control ignore the collision of robots in the transient phase, they are either computationally expensive or cannot be applied in environments with dynamic obstacles. Therefore, we propose a new distributed collision-free formation tracking control scheme for multiquadcopter systems by exploiting the properties of the barrier Lyapunov function (BLF). Accordingly, the problem is formulated in a backstepping setting, and a distributed control law that guarantees collision-free formation tracking of the quads is derived. In other words, the problems of both tracking and interagent collision avoidance with a predefined accuracy are formulated using the proposed BLF for position subsystems, and the controllers are designed through augmentation of a quadratic Lyapunov function. Owing to the underactuated nature of the quadcopter system, virtual control inputs are considered for the translational (x and y axes) subsystems that are then used to generate the desired values for the roll and pitch angles for the attitude control subsystem. This provides a hierarchical controller structure for each quadcopter. The attitude controller is designed for each quadcopter locally by taking into account a predetermined error limit by another BLF. Finally, simulation results from the MATLAB-Simulink environment are provided to show the accuracy of the proposed method. A numerical comparison with an optimization-based technique is also provided to prove the superiority of the proposed method in terms of the computational cost, steady-state error, and response time.