Trajectory tracking control methods for an autonomous quadcopter

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Dr. Stumpf Péter Pál
Department of Automation and Applied Informatics

The problem of designing a trajectory tracking controller for a quadcopter UAV is addressed

in this document. The motivation is to use the quadrotors in an industrial environment,

where reliable, fast and precise execution of the flight tasks is mandatory.

The goal therefore is to develop a control architecture that is able to satisfy these strict

requirements. The control architecture consists of a trajectory designer and a controller


Two trajectory designing algorithms are going to be introduced, both of them presents a

solution for fitting a trajectory on desired points in the 3D space. The methods have to

give a feasible trajectory (for the quadcopter) for which the requirements originate in the

dynamical and also in the motor and rotor properties of the UAV.

The first solution for the trajectory design fits a third order spline on the desired trajectory

points. The quadcopter accelerates to a constant speed, with which the trajectory is feasible

and is safe to complete. At the end of the path, the quadcopter decelerates to zero speed

and remains in a hovering position. The velocity profile is designed so, that the path will be

carried out under the shortest possible time subject to the actuator and plant constraints.

The second solution connects the desired points with straight lines. The smoothness and

hence the feasibility of the path is achieved with a carefully chosen velocity profile which

is also is also designed so that the path will be carried out under a priori given completion


For the control, three different solutions are going to be introduced, the performance of

which was analyzed via numerical simulations on a high fidelity nonlinear model of an

experimental quadcopter aircraft. The three methods are briefly introduced as follows:

Successive input/output linearization: This method introduces a two level control

architecture based on successive linearization and LQR regulation. The method has

been proposed in in the article of Hernandez published in 2015.

Jacobi linearization and LQG control: Based on the Jacobi linearized model of the

quadcopter around a trim-point, an LQG control can be developed. It can be then

further improved in order to achieve trajectory following capability.

Feedback linearization: Through a change in the input variables, a system can be obtained

which than can be feedback linearized. For the feedback linearized system, an

LQR controller can be applied, making the controller capable of trajectory following

in such way.

The performance of the controllers was analyzed via simulations in the MATLAB-Simulink

environment. In these simulations, the controllers were tested on the different types of

trajectories with different speeds. Simulations with changed quadcopter properties, such

as mass and inertia, were also carried out in order to check the robustness of the controllers.

3D visualization is solved in V-REP and in MATLAB-figure as well.


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