Decentralized polynomial trajectory generation for flight formation of quadrotors

Abstract

This paper deals with the decentralized polynomial trajectory generation for the formation flight of a leader–follower network of quadrotors. The proposed decentralized trajectory planning method guarantees stability of the formation in missions with aggressive trajectories or low information exchange frequencies or data loss. Moreover, designed formation protocol ensures robustness of the formation against variations of the network communication topology. First, quadrotor translational dynamics is represented as a quadruple integrator by linearizing and differentiating its equations of translational motion. Then, a formation control law for a leader–follower network of the quadruple integrators is designed by implementing robustness properties of linear quadratic regulator design method and special characteristics of the network graph. Moreover, sufficient condition for the robustness of the formation against possible variations of the communication topology is addressed. According to the represented trajectory generation algorithm, once a follower receives information from its neighbors (e.g. coefficients of their intended polynomial trajectories), it plans a polynomial trajectory. To generate proper trajectories, integral of squared magnitude of error between the snap of the trajectory and its determined value by the formation control law over a finite horizon time should be minimized. The optimization problem can be formulated as a quadratic problem, which can be solved in real time. Furthermore, actuators limits can be imposed on the optimization problem as inequality constraints. As it is validated in the simulations, this predictive model of the trajectory generation provides stability of the formation in operations with aggressive trajectories or low information update frequencies or probability of data packets loss. Additionally, the quadrotors track the planned trajectories via implementing a hierarchical nonlinear trajectory tracking controller including a position controller and a geometrical attitude controller. Stability of the tracking error dynamics is proven by Lyapunov stability theorem. Expected capabilities of the formation control law, trajectory generation method and nonlinear trajectory tracking controller are examined in numerical simulations. In all of the simulations, an experimentally verified full model of a specific quadrotor taken from literatures is used.