A Review of Control Algorithms for Autonomous Quadrotors
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paper_title: Attitude Stabilization Control of a Quadrotor UAV by Using Backstepping Approach

paper_content:

The modeling and attitude stabilization control problems of a four-rotor vertical takeoff and landing unmanned air vehicle (UAV) known as the quadrotor are investigated. The quadrotor’s attitude is represented by the unit quaternion rather than Euler angles to avoid singularity problem. Taking dynamical behavior of motors into consideration and ignoring aerodynamic effect, a nonlinear controller is developed to stabilize the attitude. The control design is accomplished by using backstepping control technique. The proposed control law is based on the compensation for the Coriolis and gyroscope torques. Applying Lyapunov stability analysis proves that the closed-loop attitude system is asymptotic stable. Moreover, the controller can guarantee that all the states of the system are uniformly ultimately bounded in the presence of external disturbance torque. The effectiveness of the proposed control approach is analytically authenticated and also validated via simulation study.
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paper_title: Design and control of quadrotors with application to autonomous flying

paper_content:

This thesis is about modelling, design and control of Miniature Flying Robots (MFR) with a focus on Vertical Take-Off and Landing (VTOL) systems and specifically, micro quadrotors. It introduces a mathematical model for simulation and control of such systems. It then describes a design methodology for a miniature rotorcraft. The methodology is subsequently applied to design an autonomous quadrotor named OS4. Based on the mathematical model, linear and nonlinear control techniques are used to design and simulate various controllers along this work. The dynamic model and the simulator evolved from a simple set of equations, valid only for hovering, to a complex mathematical model with more realistic aerodynamic coefficients and sensor and actuator models. Two platforms were developed during this thesis. The first one is a quadrotor-like test-bench with off-board data processing and power supply. It was used to safely and easily test control strategies. The second one, OS4, is a highly integrated quadrotor with on-board data processing and power supply. It has all the necessary sensors for autonomous operation. Five different controllers were developed. The first one, based on Lyapunov theory, was applied for attitude control. The second and the third controllers are based on PID and LQ techniques. These were compared for attitude control. The fourth and the fifth approaches use backstepping and sliding-mode concepts. They are applied to control attitude. Finally, backstepping is augmented with integral action and proposed as a single tool to design attitude, altitude and position controllers. This approach is validated through various flight experiments conducted on the OS4.
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paper_title: Artificial intelligent-based feedforward optimized PID wheel slip controller

paper_content:

Continual improvement of the anti-lock braking system control strategy is the focus of this work. Advances in auto-electronics and sub-systems such as the brake-by-wire technology are the driving forces behind the improvement of the anti-lock braking system. The control strategy has shifted from speed-control to slip-control strategy. In the current slip-control approach, proportional-integral-derivative (PID) controller and its variants: P, PI and PD have been proposed in place of the bang-bang controller mostly used in commercial ABS. Though the PID controller is famous due to its wide applications in industry: irrespective of the nature of the process or system, it might lead to limited performance when applied to the ABS. In order to improve the performance of the PID controller, a neural network inverse model of the plant is used to optimize the reference input slip. The resultant neural network-based PID ABS is then tested in Matlab® /Simulink® simulation environment. The results of the proposed controller, exhibits more accurate slip tracking than the PID-slip controller.
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paper_title: Dynamic analysis and PID control for a quadrotor

paper_content:

In order to analyze the dynamic characteristics and PID controller performance of a quadrotor, this paper firstly describes the architecture of the quadrotor and analyzes the dynamic model of it. Then, based on the classic scheme of PID control, this paper designs a controller, which aims to regulate the posture (position and orientation) of the 6 d.o.f. quadrotor. Thirdly, the dynamic model is implemented in Matlab/Simulink simulation, and the PID control parameters are obtained according to the simulation results. Finally, a quadrotor with PID controllers is designed and made. In order to do the experiment, a flying experiment for the quadrotor has been done. The results of flying experiment show that the PID controllers robustly stabilize the quadrotor.
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paper_title: Hovering control of a quadrotor

paper_content:

This paper deals with the hovering control of a quadrotor. First, we derive the quadrotor model using the Euler-Lagrange equation and perform experiment to identify the model parameter. Second, we divide a quadrotor system into two subsystems: the attitude system and the altitude system. For attitude control, we use PID control method, and for the altitude control, we use dynamic surface control (DSC) method. From the Lyapunov stability theory, we prove that all signals of a quadrotor system are uniformly ultimately bounded(UUB). Finally, we present the simulation and experimental results to verify the effectiveness of the proposed control method.
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paper_title: PID vs LQ control techniques applied to an indoor micro quadrotor

paper_content:

The development of miniature flying robots has become a reachable dream, thanks to the new sensing and actuating technologies. Micro VTOL systems represent a useful class of flying robots because of their strong abilities for small-area monitoring and building exploration. In this paper, we present the results of two model-based control techniques applied to an autonomous four-rotor micro helicopter called quadrotor. A classical approach (PID) assumed a simplified dynamics and a modern technique (LQ) based on a more complete model. Various simulations were performed and several tests on the bench validate the control laws. Finally, we present the results of the first test in flight with the helicopter released. These developments are part of the OS4 project in our lab.
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paper_title: Modeling and control of quadrotor MAV using vision-based measurement

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In this paper we review the mathematics model of quadrotor using Lagrange's equation. We propose a vision-based measurement to stabilize this model. A dual camera method is used for estimating the pose of the quadrotor; positions and attitudes of the quadrotor MAV. One of these cameras is located on-board the quadrotor MAV, and the orther is located on the ground. The control system is developed in Matlab/Simulink. In this paper, we consider a linear controller for our purpose. Linear Quadratic tracking controller with integral action, and Optimal Linear Quadratic Gaussian (LQG) control with integral action are designed for stabilization of the attitude of the quadrotor MAV. Moreover, some measurement noises will be considered in the controller design, too. Finally, this paper will demonstrate how well this control works for a certain flight mission: quadrotor MAV on the ground, and then starting hover, sideway move and keeping the position with a pointing to a certain object fixed in space.
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paper_title: A prototype of an autonomous controller for a quadrotor UAV

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The paper proposes a complete real-time control algorithm for autonomous collision-free operations of the quadrotor UAV. As opposed to fixed wing vehicles the quadrotor is a small agile vehicle which might be more suitable for the variety of specific applications including search and rescue, surveillance and remote inspection. The developed control system incorporates both trajectory planning and path following. Using a differential flatness property the trajectory planning is posed as a constrained optimization problem in the output space (as opposed to the control space), which simplifies the problem. The trajectory and speed profile are parameterized to reduce the problem to a finite dimensional problem. To optimize the speed profile independently of the trajectory a virtual argument is used as opposed to time. A path following portion of the proposed algorithm uses a standard linear multi-variable control technique. The paper presents the results of simulations to demonstrate the suitability of the proposed control algorithm.
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paper_title: Sliding Mode Control of quadrotor

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This paper presents a design method for attitude control of an autonomous quadrotor based sliding Mode Control. We are interested in the dynamic modeling of quadrotor because of it complexity. The dynamic model is used to design a stable and accurate controller to perform the best tracking and attitude results. To stabilize the overall systems, each sliding mode controller is designed based on the Lyapunov stability theory. The advantage of sliding mode control is its not being sensitive to model errors, parametric uncertainties and other disturbances. Lastly, we show that the control law has a good robust and good stability though simulation.
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paper_title: Sliding Mode Control of a Quadrotor Helicopter

paper_content:

In this paper, we present a new design method for the flight control of an autonomous quadrotor helicopter based on sliding mode control. Due to the under-actuated property of a quadrotor helicopter, the controller can make the helicopter move three positions (x, y, z) and the yaw angle to their desired values and stabilize the pitch and roll angles. A sliding mode control is proposed to stabilize a class of cascaded under-actuated systems. The global stability analysis of the closed-loop system is presented. The advantage of sliding mode control is its insensitivity to the model errors, parametric uncertainties and other disturbances. Simulations show that the control law robustly stabilizes a quadrotor.
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paper_title: Attitude Stabilization Control of a Quadrotor UAV by Using Backstepping Approach

paper_content:

The modeling and attitude stabilization control problems of a four-rotor vertical takeoff and landing unmanned air vehicle (UAV) known as the quadrotor are investigated. The quadrotor’s attitude is represented by the unit quaternion rather than Euler angles to avoid singularity problem. Taking dynamical behavior of motors into consideration and ignoring aerodynamic effect, a nonlinear controller is developed to stabilize the attitude. The control design is accomplished by using backstepping control technique. The proposed control law is based on the compensation for the Coriolis and gyroscope torques. Applying Lyapunov stability analysis proves that the closed-loop attitude system is asymptotic stable. Moreover, the controller can guarantee that all the states of the system are uniformly ultimately bounded in the presence of external disturbance torque. The effectiveness of the proposed control approach is analytically authenticated and also validated via simulation study.
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paper_title: Adaptive integral backstepping control of a Micro-Quadrotor

paper_content:

Micro-Quadrotor aerial robots have enormous potential applications in the field of near-area surveillance and exploration in military and commercial applications. However, stabilizing and position control of the robot are difficult tasks because of the nonlinear dynamic behavior and model uncertainties. Backstepping is a widely used control law for under-actuated systems including quadrotor. But general backstepping control algorithm needs accurate model parameters and isn't robust to external disturbances. In this paper, an adaptive integral backstepping control algorithm is proposed to realize robust control of quadrotor. The proposed control algorithm can estimate disturbances online and therefore improve the robustness of the system. Simulation results show that the proposed algorithm performs well against model uncertainties.
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paper_title: Backstepping Control for a Quadrotor Helicopter

paper_content:

This paper presents a nonlinear dynamic model for a quadrotor helicopter in a form suited for backstepping control design. Due to the under-actuated property of quadrotor helicopter, the controller can set the helicopter track three Cartesian positions (x, y, z) and the yaw angle to their desired values and stabilize the pitch and roll angles. The system has been presented into three interconnected subsystems. The first one representing the under-actuated subsystem, gives the dynamic relation of the horizontal positions (x, y) with the pitch and roll angles. The second fully-actuated subsystem gives the dynamics of the vertical position z and the yaw angle. The last subsystem gives the dynamics of the propeller forces. A backstepping control is presented to stabilize the whole system. The design methodology is based on the Lyapunov stability theory. Various simulations of the model show that the control law stabilizes a quadrotor with good tracking.
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paper_title: Adaptive Control of a Quadrotor with Dynamic Changes in the Center of Gravity

paper_content:

Abstract In this paper, we address the problem of quadrotor stabilization and trajectory tracking with dynamic changes in the quadrotor's center of gravity. This problem has great practical significance in many UAV applications. However, it has received little attention in literature so far. In this paper, we present an adaptive tracking controller based on output feedback linearization that compensates for dynamical changes in the center of gravity of the quadrotor. Effectiveness and robustness of the proposed adaptive control scheme is verified through simulation results. The proposed controller is an important step towards developing the next generation of agile autonomous aerial vehicles. This control algorithm enables a quadrotor to display agile maneuvers while reconfiguring in real time whenever a change in the center of gravity occurs.
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paper_title: Position trajectory tracking of a quadrotor helicopter based on L1 adaptive control

paper_content:

We present an adaptive backstepping controller for the position trajectory tracking of a quadrotor. The tracking controller is based on the L1 adaptive control approach and uses a typical nonlinear quadrotor model. We slightly modify the L1 adaptive control design for linear systems to comply with the time-varying nonlinear error dynamics that arise from the backstepping design. Our approach yields a stable adaptive system with verifiable bounds on the tracking error and input signals. The adaptive controller compensates for all model uncertainties and for all bounded disturbances within a particular frequency range, which we specify a priori. The design of this frequency range involves a trade-off between control performance and robustness, which can be managed transparently through the L1 adaptive control design. Simulation results show the powerful properties of the presented control application.
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paper_title: A nonlinear adaptive control approach for quadrotor UAVs

paper_content:

In this paper, a continuous, time varying adaptive controller is developed for an underactuated quadrotor unmanned aerial vehicle (UAV). The vehicle's dynamic model is subject to uncertainties associated with mass, inertia matrix, and aerodynamic damping coefficients. A Lyapunov based approach is utilized to ensure that position and yaw rotation tracking errors are ultimately driven to a neighborhood about zero that can be made arbitrary small. Simulation results are included to illustrate the performance of the control strategy.
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paper_title: Robust control of quadrotor unmanned air vehicles

paper_content:

A robust control approach for a quadrotor helicopter is presented. The controller consists of two parts: an attitude controller and a position controller. The attitude controller is designed based on linear control combined with robust compensation. The linear controller is designed for the nominal system to achieve desired nominal performances, while the robust compensator is applied to restrain the effects of uncertainties and external disturbances. The position controller was realized with classical PD method. Experimental results on the Tsinghua Autonomous Quadrotor System (TAQS) which is developed in our laboratory demonstrate the effectiveness of the designed controller.
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paper_title: Robust attitude tracking control of a quadrotor helicopter in the presence of uncertainty

paper_content:

A robust attitude tracking controller is presented in this paper, which achieves asymptotic tracking of a quadrotor helicopter in the presence of parametric uncertainty and unknown, nonlinear, non-vanishing disturbances, which do not satisfy the linear-in-the-parameters assumption. One of the challenges encountered in the control design is that the control input is premultiplied by a nonlinear, state-varying matrix containing parametric uncertainty. An integral sliding mode control technique is employed to compensate for the nonlinear disturbances, and the input-multiplicative uncertainty is mitigated through innovative algebraic manipulation in the error system development. The proposed robust control law is designed to be practically implementable, requiring no observers, function approximators, or online adaptation laws. Asymptotic trajectory tracking is proven via Lyapunov-based stability analysis, and simulation results are provided to verify the performance of the proposed controller.
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paper_title: Attitude Stabilization Control of a Quadrotor UAV by Using Backstepping Approach

paper_content:

The modeling and attitude stabilization control problems of a four-rotor vertical takeoff and landing unmanned air vehicle (UAV) known as the quadrotor are investigated. The quadrotor’s attitude is represented by the unit quaternion rather than Euler angles to avoid singularity problem. Taking dynamical behavior of motors into consideration and ignoring aerodynamic effect, a nonlinear controller is developed to stabilize the attitude. The control design is accomplished by using backstepping control technique. The proposed control law is based on the compensation for the Coriolis and gyroscope torques. Applying Lyapunov stability analysis proves that the closed-loop attitude system is asymptotic stable. Moreover, the controller can guarantee that all the states of the system are uniformly ultimately bounded in the presence of external disturbance torque. The effectiveness of the proposed control approach is analytically authenticated and also validated via simulation study.
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paper_title: Robust Optimal Control of Quadrotor UAVs

paper_content:

This paper provides the design and implementation of an L1-optimal control of a quadrotor unmanned aerial vehicle (UAV). The quadrotor UAV is an underactuated rigid body with four propellers that generate forces along the rotor axes. These four forces are used to achieve asymptotic tracking of four outputs, namely the position of the center of mass of the UAV and the heading. With perfect knowledge of plant parameters and no measurement noise, the magnitudes of the errors are shown to exponentially converge to zero. In the case of parametric uncertainty and measurement noise, the controller yields an exponential decrease of the magnitude of the errors in an L1-optimal sense. In other words, the controller is designed so that it minimizes the L∞-gain of the plant with respect to disturbances. The performance of the controller is evaluated in experiments and compared with that of a related robust nonlinear controller in the literature. The experimental data shows that the proposed controller rejects persistent disturbances, which is quantified by a very small magnitude of the mean error.
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paper_title: Path following controller for a quadrotor helicopter

paper_content:

A path following controller is presented for a quadrotor helicopter model. The controller relies on input dynamic extension and feedback linearization. The controller allows the designer to specify the speed profile of the quadrotor on the path and its yaw angle as a function of the displacement.
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paper_title: Adaptive Control of a Quadrotor with Dynamic Changes in the Center of Gravity

paper_content:

Abstract In this paper, we address the problem of quadrotor stabilization and trajectory tracking with dynamic changes in the quadrotor's center of gravity. This problem has great practical significance in many UAV applications. However, it has received little attention in literature so far. In this paper, we present an adaptive tracking controller based on output feedback linearization that compensates for dynamical changes in the center of gravity of the quadrotor. Effectiveness and robustness of the proposed adaptive control scheme is verified through simulation results. The proposed controller is an important step towards developing the next generation of agile autonomous aerial vehicles. This control algorithm enables a quadrotor to display agile maneuvers while reconfiguring in real time whenever a change in the center of gravity occurs.
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paper_title: Adaptive Neural Network for a Quadrotor Unmanned Aerial Vehicle

paper_content:

A new adaptive neural control scheme for quadrotor helicopter stabilization at the presence of sinusoidal disturbance is proposed in this paper. The adaptive control classical laws such e-modification presents some limitations in particular when persistent oscillations are presenting in the input. These techniques can create a dilemma between weights drifting and tracking errors. To avoid this problem in adaptive Single Hidden Layer neural network scheme, a new solution is proposed in this work. The main idea is based on the use of two SHL in parallel instead of one in the closed loop in order to estimate the unknown nonlinear function in Quadrotor dynamical model. The learning algorithms of the two SHL Networks are obtained using the Lyapunov stability method. The simulation results are given to highlight the performances of the proposed control scheme.
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paper_title: Intelligent fuzzy controller of a quadrotor

paper_content:

The aim of this work is to describe an intelligent system based on fuzzy logic that is developed to control a quadrotor. A quadrotor is a helicopter with four rotors, that make the vehicle more stable but more complex to model and to control. The quadrotor has been used as a testing platform in the last years for various universities and research centres. A quadrotor has six degrees of freedom, three of them regarding the position: height, horizontal and vertical motions; and the other three are related to the orientation: pitch, roll and yaw. A fuzzy control is designed and implemented to control a simulation model of the quadrotor. The inputs are the desired values of the height, roll, pitch and yaw. The outputs are the power of each of the four rotors that is necessary to reach the specifications. Simulation results prove the efficiency of this intelligent control strategy.
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paper_title: Output Feedback Control of a Quadrotor UAV Using Neural Networks

paper_content:

In this paper, a new nonlinear controller for a quadrotor unmanned aerial vehicle (UAV) is proposed using neural networks (NNs) and output feedback. The assumption on the availability of UAV dynamics is not always practical, especially in an outdoor environment. Therefore, in this work, an NN is introduced to learn the complete dynamics of the UAV online, including uncertain nonlinear terms like aerodynamic friction and blade flapping. Although a quadrotor UAV is underactuated, a novel NN virtual control input scheme is proposed which allows all six degrees of freedom (DOF) of the UAV to be controlled using only four control inputs. Furthermore, an NN observer is introduced to estimate the translational and angular velocities of the UAV, and an output feedback control law is developed in which only the position and the attitude of the UAV are considered measurable. It is shown using Lyapunov theory that the position, orientation, and velocity tracking errors, the virtual control and observer estimation errors, and the NN weight estimation errors for each NN are all semiglobally uniformly ultimately bounded (SGUUB) in the presence of bounded disturbances and NN functional reconstruction errors while simultaneously relaxing the separation principle. The effectiveness of proposed output feedback control scheme is then demonstrated in the presence of unknown nonlinear dynamics and disturbances, and simulation results are included to demonstrate the theoretical conjecture.
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paper_title: Adaptive Control via Backstepping Technique and Neural Networks of a Quadrotor Helicopter

paper_content:

Abstract A nonlinear adaptive controller for the quadrotor helicopter is proposed using backstepping technique mixed with neural networks. The backstepping strategy is used to achieve good tracking of desired translation positions and yaw angle while maintaining the stability of pitch and roll angles simultaneously. The knowledge of all physical parameters and the exact model of the quadrotor are not required for the controller, only some properties of the model are needed. In fact, online adaptation of neural networks and some parameters is used to compensate some unmodeled dynamics including aerodynamic effects. Under certain relaxed assumptions, the proposed control scheme can guarantee that all the signals in the closed-loop system are Uniformly Ultimately Bounded (UUB). The design methodology is based on Lyapunov stability. One salient feature of the proposed approach is that the controller can be applied to any type of quadrotor helicopter of different masses and lengths within the same class. The feasibility of the control scheme is demonstrated through simulation results.
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paper_title: Feedback linearization and high order sliding mode observer for a quadrotor UAV

paper_content:

In this paper, a feedback linearization-based con- troller with a high order sliding mode observer running parallel is applied to a quadrotor unmanned aerial vehicle. The high order sliding mode observer works as an observer and estimator of the effect of the external disturbances such as wind and noise. The whole observer-estimator-control law constitutes an original approach to the vehicle regulation with minimal num- ber of sensors. Performance issues of the controller-observer are illustrated in a simulation study that takes into account parameter uncertainties and external disturbances. I. INTRODUCTION
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paper_title: Backstepping sliding mode controller improved with fuzzy logic: Application to the quadrotor helicopter

paper_content:

In this paper we present a new design method for the fight control of an autonomous quadrotor helicopter based on fuzzy sliding mode control using backstepping approach. Due to the underactuated property of the quadrotor helicopter, the controller can move three positions (x,y,z) of the helicopter and the yaw angle to their desired values and stabilize the pitch and roll angles. A first-order nonlinear sliding surface is obtained using the backstepping technique, on which the developed sliding mode controller is based. Mathematical development for the stability and convergence of the system is presented. The main purpose is to eliminate the chattering phenomenon. Thus we have used a fuzzy logic control to generate the hitting control signal. The performances of the nonlinear control method are evaluated by simulation and the results demonstrate the effectiveness of the proposed control strategy for the quadrotor helicopter in vertical flights.
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paper_title: Design and construction of a novel quad tilt-wing UAV

paper_content:

Abstract This paper presents aerodynamic and mechanical design, prototyping and flight control system design of a new unmanned aerial vehicle SUAVI ( S abanci University U nmanned A erial V eh I cle). SUAVI is an electric powered quad tilt-wing UAV that is capable of vertical takeoff and landing (VTOL) like a helicopter and long duration horizontal flight like an airplane. Aerodynamic and mechanical designs are optimized to enhance the operational performance of the aerial vehicle. Both of them have great importance for increasing efficiency, reaching the flight duration goals and achieving the desired tasks. A full dynamical model is derived by utilizing Newton–Euler formulation for the development of the flight control system. The prototype is constructed from carbon composite material. A hierarchical control system is designed where a high level controller (supervisor) is responsible for task decision, monitoring states of the vehicle, generating references for low level controllers, etc. and several low level controllers are responsible for attitude and altitude stabilization. Results of several simulations and real flight tests are provided along with flight data to show performance of the developed UAV.
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paper_title: Modeling and control of a novel tilt — Roll rotor quadrotor UAV

paper_content:

The use of unmanned aerial vehicles (UAVs) for military, scientific, and civilian sectors are increasing drastically in recent years. The quadrotor platform has been used for many applications and research studies, as well. One of the limiting factors that prevents further implementation of the quadrotor system into applications, is the way quadrotor moves. It needs to tilt along the desired direction of motion. By doing this it can have necessary acceleration towards that direction. But tilting has the undesired effect of moving the onboard cameras' direction of view. This becomes an issue for surveillance and other vision based tasks. This study presents the design and control of a novel quadrotor system. Unlike previous study that uses regular quadrotor, this study proposes an alternative propulsion system formed by tilting rotors. This design eliminates the need of tilting the airframe, and it suggests superior performance with respect to regular quadrotor design. The mathematical model of the tiltable-rotor type quadrotor and designed control algorithms are explained. Various simulations are developed on MATLAB, in which the proposed quadrotor aerial vehicle has been successfully controlled. Comparison of the proposed system to regular quadrotor suggests better performance.
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Title: A Review of Control Algorithms for Autonomous Quadrotors

Section 1: Introduction
Description 1: Introduce the significance and applications of quadrotors, and outline the focus and structure of the review.

Section 2: Mathematical Model
Description 2: Explain the key mathematical equations and models used to describe the dynamics of quadrotors.

Section 3: Survey of Control Algorithms
Description 3: Provide an overview of the various control algorithms applied to quadrotors, categorizing them into linear and non-linear control schemes.

Section 4: Proportional Integral Derivative (PID)
Description 4: Discuss the PID control algorithm and its applications, strengths, and limitations in controlling quadrotors.

Section 5: Linear Quadratic Regulator/Gaussian-LQR/G
Description 5: Examine the LQR and LQG control algorithms, their methodologies, and their effectiveness in quadrotor control.

Section 6: Sliding Mode Control (SMC)
Description 6: Describe the implementation of sliding mode control, its benefits, and its challenges when applied to quadrotors.

Section 7: (Integrator) Backstepping Control
Description 7: Analyze the backstepping control algorithm and its integrator variant, focusing on their convergence and disturbance handling capabilities.

Section 8: Adaptive Control Algorithms
Description 8: Explore adaptive control techniques used for quadrotors, highlighting how they adapt to parameter changes and uncertainties.

Section 9: Robust Control Algorithms
Description 9: Review robust control strategies designed to handle system uncertainties and disturbances, and discuss their limitations in terms of tracking.

Section 10: Optimal Control Algorithms
Description 10: Provide insights into optimization-based control methods like LQR and H∞, emphasizing their application to quadrotors and their robustness issues.

Section 11: Feedback Linearization
Description 11: Explain feedback linearization control methods, their application to quadrotors, and their sensitivity to model inaccuracies.

Section 12: Intelligent Control (Fuzzy Logic and Artificial Neural Networks)
Description 12: Cover intelligent control approaches such as fuzzy logic and neural networks, discussing their complexity and computational requirements.

Section 13: Hybrid Control Algorithms
Description 13: Discuss hybrid control schemes that combine multiple control philosophies to overcome individual limitations and enhance overall performance.

Section 14: Discussion and Conclusion
Description 14: Summarize the findings of the review, discuss the strengths and weaknesses of different control algorithms, and outline future research directions in quadrotor control.