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.

Trajectory Planning of Quadrotor Systems for Various Objective Functions

“…The interactions between the states and the total thrust F T and the torques τ B created by the rotors are visible from the quadrotor dynamics defined by Eqs. (9), (10), and (11). The total thrust F T affects the acceleration in the direction of the z-axis and holds the quadrotor in the air.…”

“…Several researchers have also developed numerous trajectory generation algorithms from a class of motion planning (lines, polynomials, or splines) and respect the quadrotors dynamic constraints. [9][10][11] These algorithms enforce dynamic feasibility by designing trajectories in a two-step process, first determining the geometric trajectory without time information and subsequently determining an appropriate speed profile such that feasibility constraints are not violated.…”

Design of a Multi-Constraint Formation Controller Based on Improved MPC and Consensus for Quadrotors

“…Shadeed et al proposed a trajectory tracking method using a mapped desired output into input sequence based on differential flatness modeling [14]. However, most of the UAV systems in the literature are based on either two-dimensional space or ideal models [15][16][17][18], without considering the disturbances and uncertainties. In addition, the performance of model-based controllers relies heavily on the accuracy of the modeling.…”

Trajectory Generation for Multiagent Point-To-Point Transitions via Distributed Model Predictive Control

“…Distributed model predictive control (DMPC) [14] has been used in coordination tasks such as formation control [15], [16], but not explicitly for point-to-point transitions. Particularly interesting are synchronous implementations of DMPC [17], where the agents simultaneously update their predictions, reducing runtime by parallel computing.…”