Synchronization of coupled quadcopters using contraction theory

In this paper, the synchronization of coupled quadcopters using contraction theory principles is presented. In order to synchronize the roll and pitch angles of the quadcopter models, contraction theory application is a pivotal tool. Despite the fact that all of the quadcopters used in this study have identical characteristics, their behaviour greatly depends on their initial conditions. Because of the inherently nonlinear nature of quadcopters, slight variations in the initial conditions can have a significant impact on the trajectory of the quadcopters in the future. Contraction theory is a useful technique for addressing this problem. By using the contraction theory, synchronization has been done for two quadcopters as well as for three quadcopters. Finally, a generalized method for synchronizing any number of quadcopters using contraction theory is presented. For the synchronization of two quadcopters, roll angles and pitch angles were synchronized in 3.2 and 3.6 seconds, respectively whereas for the synchronization of three quadcopters, roll angles and pitch angles were synchronized in 3.2 and 3.4 seconds, respectively. MATLAB® is used to carry out the mathematical modelling of the quadcopters and the synchronization procedure.