Angela Ricciardello

Mathematical modeling and control of a hexacopter

Microcopters are emerging as a popular platform for Unmanned Aerial Vehicle (UAV). The purpose of this paper is to present the basic mathematical modeling of microcopters, which has been used to develop proper methods for stabilization and trajectory control. The microcopter taken into account consists of six rotors, with three pairs of counter-rotating fixedpitch blades. The microcopter is controlled by adjusting the angular velocities of the rotors which are spun by electric motors. It is assumed as a rigid body, so the differential equations of the microcopter dynamics can be derived from both the Newton-Euler and Euler-Lagrange equations. Euler-angle parametrization of three-dimensional rotations contains singular points in the coordinate space that can cause failure of both dynamical model and control. In order to avoid singularities, the rotations of the microcopter are parametrized in terms of quaternions. This choice has been made taking into consideration the linearity of quaternion formulation, their stability and efficiency.

PID Controller Applied to Hexacopter Flight

In the last decades, the increasing interest in unmanned aerial vehicles for both military and civil applications made necessary the development of flight control theory and algorithms more and more efficient and fast. In this paper, an original trajectory controller, like a Proportional Integrative Derivative one, is taken into account and the drone structure assumes a hexacopter configuration, i.e. it consists of six rotors, located on the vertices of a regular hexagon with three pairs of counter-rotating fixed pitch blades. The motion of unmanned aerial vehicle is described by means of the Newton-Euler equations in terms of quaternions, in order to improve the numerical efficiency and stability of the controller algorithm, whose novelty lies in the quaternion error definition. Both model and algorithm have been tested and then validated through a wide experimentation, where the drone keeps going to not elementary trajectories.

Hexacopter trajectory control using a neural network

The modern flight control systems are complex due to their non-linear nature. In fact, modern aerospace vehicles are expected to have non-conventional flight envelopes and, then, they must guarantee a high level of robustness and adaptability in order to operate in uncertain environments. Neural Networks (NN), with real-time learning capability, for flight control can be used in applications with manned or unmanned aerial vehicles. Indeed, using proven lower level control algorithms with adaptive elements that exhibit long term learning could help in achieving better adaptation performance while performing aggressive maneuvers. In this paper we show a mathematical modeling and a Neural Network for a hexacopter dynamics in order to develop proper methods for stabilization and trajectory control.

Genetic algorithm applied to the stabilization control of a hexarotor

An approach to optimize a stabilization controller for an Unmanned Aerial Vehicle (UAV) is presented in this work. In order of stabilizing the altitude and the attitude of a multirotor around its hovering configuration, two controller systems based on Proportional Derivative (PD) and Proportional Integral Derivative (PID) techniques, respectively, tuned by using the Linear Quadratic Regulator (LQR) are investigated. The optimized entries of LQR scheme result from a Genetic Algorithm (GA) implementation based on the minimization of the entire system time settling. The simulations show that, in presence of impulse disturbances, both these approaches lead to the stabilization of the considered multirotor drone flight around an equilibrium configuration, as the hovering one.

An example of quaternion parameterization for dynamical simulations

The dynamical simulation of rigid bodies can be gathered from the classical Newton-Euler differential equations, which commonly make use of the Euler angles parametrization. In this work, the initial value problem associated with motion is presented in terms of quaternion formulation instead of the Euler one. The reason why the quaternion parametrization is proposed lies on the possibility of avoiding singularities that can occur by considering Euler angles. Moreover, the strength of quaternions is represented by the linearity of their formulation, the easiness of their algebraic structure and, overall, on their stability and efficiency. Our proposed application is the mathematical modelling of a small Unmanned Aerial Vehicle dynamics. In particular a multirotor with six blades has been taken into account, its mathematical model is deduced and a comparison between the results obtained by implementing our formulation and the classical one is produced.

An adaptive trajectory control for UAV using a real-time architecture

Multirotor helicopter have generated much interest in recent years as a powerful tool both for civil and military applications. The trajectory of the aircraft is controlled by modifying the angular velocity of the rotors. Among different control techniques the PID controller finds great application due to its simplicity. It uses proportional, integral and derivative regulator to control one or more input signal. In this paper a novel real-time system, based on a real-time Neural Network, is presented to propose an alternative control technique to the PID. In order to prove the validity of the proposed approach simulations are performed through a real experimental test-bed.

A quaternion-based simulation of multirotor dynamics

The main problem addressed in this paper is the quaternion-based trajectory control of a microcopter consisting of six rotors with three pairs of counter-rotating fixed-pitch blades, known as hexacopter. If the hypothesis of rigid body condition is assumed, the Newton–Euler equations describe the translational and rotational motion of the drone. The standard Euler-angle parametrization of three-dimensional rotations contains singular points in the coordinate space that can cause failure of both dynamical model and control. In order to avoid singularities, all the rotations of the microcopter are thus parametrized in terms of quaternions and an original proportional derivative (PD) regulator is proposed in order to control the dynamical model. Numerical simulations will be performed on symmetrical flight configuration, proving the reliability of the proposed PD control technique.

A PSO-PID quaternion model based trajectory control of a hexarotor UAV

A quaternion based trajectory controller for a prototype of an Unmanned Aerial Vehicle (UAV) is discussed in this paper. The dynamics of the UAV, a hexarotor in details, is described in terms of quaternion instead of the usual Euler angle parameterization. As UAV flight management concerns, the method here implemented consists of two main steps: trajectory and attitude control via Proportional-Integrative-Derivative (PID) and Proportional-Derivative (PD) technique respectively and the application of Particle Swarm Optimization (PSO) method in order to tune the PID and PD parameters. The optimization is the consequence of the minimization of a objective function related to the error with the respect to a proper trajectory. Numerical simulations support and validate the proposed method.

Exact Closed-Form Fractional Spectral Moments for Linear Fractional Oscillators Excited by a White Noise

In the last decades the research community has shown an increasing interest in the engineering applications of fractional calculus, which allows to accurately characterize the static and dynamic behaviour of many complex mechanical systems, e.g. the non-local or non-viscous constitutive law. In particular, fractional calculus has gained considerable importance in the random vibration analysis of engineering structures provided with viscoelastic damping. In this case, the evaluation of the dynamic response in the frequency domain presents significant advantages, once a probabilistic characterization of the input is provided. On the other hand, closed-form expressions for the response statistics of dynamical fractional systems are not available even for the simplest cases. Taking advantage of the Residue Theorem, in this paper the exact expressions of the spectral moments of integer and complex orders (i.e. fractional spectral moments) of linear fractional oscillators driven by acceleration time histories obtained as samples of stationary Gaussian white noise processes are determined.

Particle Swarm Optimization Applied to Hexarotor Flight Dynamics

In this work, results obtained by the flight control simulations of a prototype of hexarotor Unmanned Aerial Vehicle (UAV) are shown. The mathematical model and control of the hexacopter airframe are presented. To stabilize the entire system, Linear Quadratic Regulator (LQR) control is used in such a way to set both Proportional Derivative (PD) and Proportional Integral Derivative (PID) controls. Particle Swarm Optimization has been used to set the optimal coefficient matrices of the LQR control algorithm. The simulations are performed to show how LQR tuned PD and PID controllers lead to zero the error of the position along gravity acceleration direction, stop the rotation of UAV around body axes and stabilize the hexarotor. Moreover, the obtained LQR-PD and LQR-PID controllers have been tested by comparing the response to impulse disturbances of the nonlinear dynamical system with the response of the linearized one.