Quadrotor Dynamics Research Articles

Performance Evaluation of Different Control Methods for an Underactuated Quadrotor Unmanned Aerial Vehicle (QUAV) with Position Estimator and Disturbance Observer

The main aim of this manuscript is to design and demonstrate the performance of different control algorithms with position estimator and disturbance observer to track the helical trajectory by an underactuated quadrotor craft under the influence of unmodelled dynamic factors and external disturbances. The manuscript consists of the derivations related to the kinematics and dynamics of quadrotor dully derived using the Newton Euler approach. It is one of the strenuous tasks to stabilize and control the quadrotor for helical trajectory tracking since it is an underactuated mechatronic system. In addition to this, with inclusion of unmodelled dynamic factors, it faces some of the serious transient and steady-state issues including Zeno noise. In this research manuscript, dual-loop single-dimension fuzzy sliding mode control (DLSDF-SMC) is proposed to improve the helical trajectory tracking performance, and to tackle the unmodelled dynamic factors, a state feedback controller is proposed consisting of a position estimator and disturbance observer design. The entire system is distributed into two subsystems such that within the angular subsystem, the attitude control is proposed using DLSDF-SMC, and for the translational subsystem, the paper proposes the position control design based on the hyperbolic function to avoid the gimbal lock issue. The overall stability of the proposed closed-loop control scheme is also proved. The simulation work for the proposed algorithm is performed using MATLAB and Simulink software and compared with the conventional sliding mode control (SMC) and fuzzy-based SMC control designs. This work demonstrates that the DLSDF-SMC control technique with position estimator and disturbance observer design in feedback not only improves the aggressive maneuvers while tracking the helical trajectory but also tackles the transient and steady-state issues.

Conditional integrator sliding mode control of an unmanned quadrotor helicopter

Sliding mode control (SMC) is a widely used control law for quadrotor regulation and tracking control problems. The purpose of this article is to solve the tracking problem of quadrotors using a relatively novel nonlinear control law based on SMC that makes use of a conditional integrator. It is demonstrated by a motivation example that the proposed control law can improve the transient response and chattering shortcomings of the previous approaches of similar SMC based controllers. The adopted Newton–Euler model of quadrotor dynamics and controller design is treated separately in two subsystems: attitude and position control loops. The stability of the control technique is demonstrated by Lyapunov’s analysis and the effectiveness and performance of the proposed method are compared with a similar integral law, also based on SMC, and validated by tracking control problems using numerical simulations. Simulations were developed in the presence of external disturbances in order to evaluate the controller robustness. The effectiveness of the proposed controller was verified by performance indexes, demonstrating less accumulated tracking errors and control activity and improvement in the transient response and disturbance rejection when compared to a conventional integrator sliding mode controller.

Improved PID rate control of a quadrotor with a convexity-based surrogated model

PurposeThe purpose of this paper is to develop, extend and propose an improved proportional integral derivative (PID) rate control of a quadrotor unmanned aerial vehicle based on a convexity-based surrogated firefly algorithm.Design/methodology/approachAn improved PID controller structure is proposed for the rate dynamics of the quadrotor. Optimality of the controller is ensured by a recent, simple yet efficient firefly optimization method. The hybrid structure is further enhanced with a convexity-based surrogated model function.FindingsMonte Carlo, transient response, error metrics and histogram distribution analyzes are conducted to show the performance of the proposed controller. The performance of the proposed method is evaluated under various convex combination values to further investigate the effect of the proposed surrogated model. According to the results, the proposed method is capable of controlling the rate quadrotor dynamics with the steady-state error of 0.0023 (rad/s) for P, −0.0024 (rad/s) for Q and 0 (rad/s) for the R state, respectively. Also, the least mean objective value is achieved at = 0 value of convexity in Monte Carlo trials.Originality/valueThe originality of this paper is to propose an improved PID rate controller with a convexity-based surrogated firefly algorithm.

Stabilizing the spatial position of a quadrotor by the backstepping procedure

<div>The paper considers the problem of synthesizing a control law that stabilizes the spatial position of an airborne object. The control object is a quadrotor with nonlinear dynamics. To solve the stabilization problem, a mathematical model of the quadrotor has been developed, taking into account its positionin the Cartesian and Euler coordinate systems. The new control law has been synthesized using the backstepping procedure. This control law is based on the Lyapunov-type stabilization criterion. New results analysis of the quadrotor dynamics, where has been showing the dependence of the control accuracy on the parameter of the stabilization criterion also presented. An algorithm for the directed search of the procedure parameter also has been proposed. It ensures the desired quality of the transient process. Simulation results confirming the results of the oretical research have been presented as well.</div>

Robust model reference adaptive backstepping sliding-mode control for quadrotor attitude with disturbance observer

Purpose The purpose of this research paper is to design a disturbance observer-based control based on the robust model reference adaptive backstepping sliding-mode control for attitude quadrotor model subject to uncertainties and disturbances. Design/methodology/approach To estimate and reject the disturbance, a disturbance observer is designed for the exogenous disturbances with perturbation while a control criterion is developed for the tracking of desired output. To achieve the control performance, backstepping and sliding-mode control techniques are patched together to obtain robust chattering-free controller. Furthermore, a model reference adaptive control criterion is also combined with the design of robust control for the estimation and rejection of uncertainties and unmodeled dynamics of the attitude quadrotor. Findings The findings of this research work includes the design of a disturbance observer-based control for uncertain attitude quadrotor system with the ability of achieving tracking control objective in the presence of nonlinear exogenous disturbance with and without perturbation. Practical implications In practice, the quadrotor flight is opposed by different kinds of the disturbances. In addition, being an underactuated system, it is difficult to obtain an accurate mathematical model of quadrotor for the control design. Thus, a quadrotor model with uncertainties and disturbances is inevitable. Hence, it is necessary to design a control system with the ability to achieve the control objectives in the presence of uncertainties and disturbances. Originality/value Designing the control methods for quadrotor control without uncertainties and disturbances is a common practice. However, investigating the uncertain quadrotor plant in the presence of nonlinear disturbances is rarely taken into consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the uncertainties and disturbances as well as investigate a control algorithm to achieve tracking performance.

Distributed wind measurements with multiple quadrotor unmanned aerial vehicles in the atmospheric boundary layer

Abstract. In this study, a fleet of quadrotor unmanned aerial vehicles (UAVs) is presented as a system to measure the spatial distribution of atmospheric boundary layer flow. The big advantage of this approach is that multiple and flexible measurement points in space can be sampled synchronously. The algorithm to obtain horizontal wind speed and direction is designed for hovering flight phases and is based on the principle of aerodynamic drag and the related quadrotor dynamics. During the FESST@MOL campaign at the boundary layer field site (Grenzschichtmessfeld, GM) Falkenberg of the Lindenberg Meteorological Observatory – Richard Assmann Observatory (MOL-RAO), 76 calibration and validation flights were performed. The 99 m tower equipped with cup and sonic anemometers at the site is used as the reference for the calibration of the wind measurements. The validation with an independent dataset against the tower anemometers reveals that an average accuracy of σrms<0.3 m s−1 for the wind speed and σrms,ψ<8∘ for the wind direction was achieved. Furthermore, we compare the spatial distribution of wind measurements with the fleet of quadrotors to the tower vertical profiles and Doppler wind lidar scans. We show that the observed shear in the vertical profiles matches well with the tower and the fluctuations on short timescales agree between the systems. Flow structures that appear in the time series of a line-of-sight measurement and a two-dimensional vertical scan of the lidar can be observed with the fleet of quadrotors and are even sampled with a higher resolution than the deployed lidar can provide.

Switched linear parameter‐varying tracking control for quadrotors with large attitude angles and time‐varying inertia

AbstractThis paper is concerned with large‐angle attitude tracking control for quadrotors in the presence of time‐varying inertia and external disturbances using a switched linear parameter‐varying (LPV) system method. The attitude system of the quadrotor is divided into two parts, that is, the outer attitude‐angle loop and inner angular‐velocity loop. A feedback linearization controller is designed in the outer loop to generate the desired angular velocities. In the inner loop, the nonlinear quadrotor dynamics with time‐varying inertia is approximated by a switched LPV system that consists of a series of LPV models. The persistent dwell time (PDT) switching logic is adopted to describe the fast and slow switches coexist among these LPV models. Then, both the continuous‐time state‐feedback and dynamic output‐feedback controllers are designed, which ensure the globally uniformly asymptotically stability and external disturbance attenuation performance of the attitude tracking error system. Finally, the effectiveness of the proposed tracking control method of quadrotors is validated with an example.

Adaptive Integral Sliding Mode Control Using Fully Connected Recurrent Neural Network for Position and Attitude Control of Quadrotor.

This article proposes an adaptive integral sliding mode control (ISMC) strategy for quadrotor control that ensures faster and finite-time convergence along with chattering attenuation. Quadrotor dynamics are assumed to be unknown because of the high degree of parametric uncertainties, including external disturbances. The equivalent control law obtained by ISMC consists of quadrotor dynamics and, thus, cannot be applied to the quadrotor. A new fully connected recurrent neural network (FCRNN) controller has been proposed to mimic the equivalent control instead of estimating the Quadrotor dynamics separately. The proposed FCRNN architecture consists of output feedback to the input layer and the hidden layer, which enhances the approximation capability of FCRNN. All hidden layer neurons receive self-feedback and feedback from other hidden layer neurons, which further strengthens FCRNN's potential to capture complex dynamic characteristics. As learning should happen in finite time, the finite-time stability of the overall system has been guaranteed using the Lyapunov stability theory, and the update laws for FCRNN weights in real time are derived using the same. To show the effectiveness of the proposed approach, a comprehensive analysis has been done against existing SMC strategy and against well-known function approximation techniques, e.g., the radial basis function network (RBFN) and RNN.

Quadrotor UAV attitude stabilization using fuzzy robust control

In this paper, a robust controller for attitude stabilization of a small quadrotor helicopter is developed. The TS (Takagi-Sugeno) fuzzy model approach and the [Formula: see text] robust control are combined to produce the proposed algorithm. Besides, disturbances and parametric uncertainties are considered. First, the nonlinear model of the vehicle is linearized around several operating points to obtain the representation of a TS fuzzy model, which represents the nonlinearity of the system dynamics. Then, a robust fuzzy controller is synthesized which guarantees desired control performances. The given controller is designed using numerical tools such as linear matrix inequalities (LMI). Finally, simulation results and real-time experiments are presented to validate the performance of the proposed scheme to robustly stabilize the quadrotor dynamics at the desired reference.

SwarmCCO: Probabilistic Reactive Collision Avoidance for Quadrotor Swarms Under Uncertainty

We present decentralized collision avoidance algorithms for quadrotor swarms operating under uncertain state estimation. Our approach exploits the differential flatness property and feedforward linearization to approximate the quadrotor dynamics and performs reciprocal collision avoidance. We account for the uncertainty in position and velocity by formulating the collision constraints as chance constraints, which describe a set of velocities that avoid collisions with a specified confidence level. We present two different methods for formulating and solving the chance constraints: our first method assumes a Gaussian noise distribution. Our second method is its extension to the non-Gaussian case by using a Gaussian Mixture Model (GMM). We reformulate the linear chance constraints into equivalent deterministic constraints, which are used with an MPC framework to compute a local collision-free trajectory for each quadrotor. We evaluate the proposed algorithm in simulations on benchmark scenarios and highlight its benefits over prior methods. We observe that both the Gaussian and non-Gaussian methods provide improved collision avoidance performance over the deterministic method. On average, the Gaussian method requires ~ 5 ms to compute a local collision-free trajectory, while our non-Gaussian method is computationally more expensive and requires ~ 9 ms on average in scenarios with 4 agents.

Antisaturation Command Filtered Backstepping Control-Based Disturbance Rejection for a Quadarotor UAV

This brief investigates the tracking control problem of the quadrotor unmanned aerial vehicle considering the disturbance and input saturation. According to the hierarchical control principle, the quadrotor dynamics is decomposed into position and attitude loops to accommodate the controller design. To overcome the disturbance, two disturbance observer-based state estimators are designed in two loops, respectively. By integrating the filtering-error compensation mechanism and auxiliary control system into the dynamic surface control, the input saturation and filtering errors can be solved. In addition, the tracking errors of the closed-loop system can converge to the origin. Finally, simulation results show the validity of the proposed control formulation.

Robust Adaptive Global Time-varying Sliding-mode Control for Finite-time Tracker Design of Quadrotor Drone Subjected to Gaussian Random Parametric Uncertainties and Disturbances

The quadrotor has many potential applications such as infrastructure predictive maintenance in mining tunnels of the railway. In order to navigate through those environments by using the quadrotor drone, there are many challenges such as aerodynamics disturbances, parametric uncertainties, and noise measurements. A robust adaptive global time-varying sliding-mode controller (RAGTVSMC) is proposed to address the quadrotor path in the presence of the random disturbances and uncertainties. In order to eliminate the reaching phase and reduce the initial control effort, a novel time-varying sliding mode (TVSM) surface is presented for the quadrotor system. Moreover, the TVSM surface is designed to meet the impact time requirement with a global sliding mode. Adaptive laws are developed to address the upper bound of the additives disturbances on the quadrotor dynamics using only the error position and velocity. The convergence with specific time is assured and the quadrotor stability is proved according to Lyapunov’s theory. Finally, to demonstrate the effectiveness of the proposed controller in this work, simulations are conducted.

Robust Control of Quadrotor using Uncertainty and Disturbance Estimation

In this paper, a robust position and attitude tracking control problem of a quadrotor subject to system nonlinearities, input coupling, aerodynamic uncertainties and external wind disturbances is investigated. An uncertainty and disturbance estimator (UDE) based robustified nonlinear dynamic inversion (NDI) control scheme is proposed for the purpose. The UDE technique robustifies the NDI based controller by providing estimate of the lumped or total disturbance thereby enabling rejection of the same. The effectiveness and benefits of the proposed scheme are confirmed through six–DOF simulations considering nonlinear quadrotor dynamics under ideal as well as perturbed flight conditions. Further, the efficacy and superiority of the proposed control scheme are validated through Monte–Carlo simulations and experimental validation on Quanser’s 3–DOF Hover setup.

Mathematical Modeling of the Coaxial Quadrotor Dynamics for Its Attitude and Altitude Control

In this paper, an easily implementable coaxial quadrotor model and its validation on data from a real unmanned aerial vehicle (UAV), are presented. The proposed mathematical model consists of two parts: description of orientation and position of the UAV in the three-dimensional space. It takes into consideration the gyroscopic effect, influence of the Coriolis force, viscous friction and a several drag-like effects (blade flapping, rotor drag, translational drag and profile drag). In contrast to multirotor models available in the literature, this one is characterized by complementarity in relation to the available control techniques. Depending on selection of these techniques, the model can be narrowed (simplified) to meet the needs without the loss of behaviour adequacy to a real UAV.

Quadrotor Stabilization and Tracking Using Nonlinear Surface Sliding Mode Control and Observer

We propose a control method wherein the estimated angles converge to the desired value for quadrotor attitude stabilization and position tracking. To improve the performance of a quadrotor system, the unmeasured states of the quadrotor are estimated using a sliding mode observer (SMO). We set up a quadrotor dynamic model and augment the quadrotor dynamics by an SMO. We also derive the control inputs by sliding mode control (SMC) and calculate the desired angle of the quadrotor to reach the target position with the control inputs. For fast convergence speed and increased robustness of tracking performance, a nonlinear sliding surface is applied to SMC. The angle of the quadrotor converges to the desired value through the operation of SMC with a nonlinear sliding surface. The target tracking performance is improved by adaptively switching the deceleration curve of the sliding mode surface with a nonlinear curve. Using a tracking system based on a nonlinear surface sliding mode control (NSMC) and SMO, the quadrotor reaches the target position with a decreased settling time. The performance and effectiveness of the proposed system are proved through simulation results.

Robust Nonlinear Model Predictive Control Based Visual Servoing of Quadrotor UAVs

In this article, a robust nonlinear model predictive control (NMPC) scheme is proposed for the visual servoing of quadrotors subject to external disturbances. By using the virtual camera approach, the image moments are defined in the virtual camera plane and adopted as visual features to derive the decoupled image kinematics. As a result, the image-based visual servoing (IBVS) system model is established by integrating the image kinematics and quadrotor dynamics. To handle the visibility constraint, a robust NMPC scheme is developed for the IBVS of the quadrotor such that the visual target can stay within the field of view of the camera. In addition, based on the Lipschitz condition, the tightened state constraints are constructed to tackle external disturbances. The sufficient conditions on guaranteeing recursive feasibility of the proposed NMPC algorithm are derived. Furthermore, we theoretically show that the tracking error will converge to a small set around the origin in finite time under some derived conditions. Finally, simulation studies and experimental tests are conducted to verify the efficacy of the proposed method.

Data-Driven Fault-Tolerant Control for Attitude Synchronization of Nonlinear Quadrotors

In this article, the data-driven fault-tolerant synchronization control problem is investigated for unknown cooperative quadrotors subject to nonlinearities and multiple actuator faults in the quadrotor dynamics. A distributed observer is provided to estimate the state of the virtual leader. Based on the reinforcement learning theory, the optimal control policy is learned for each quadrotor without any knowledge of the quadrotor dynamic information. Then, the learned control policy is used to construct a data-based fault-tolerant controller to restrain the effects of quadrotor actuator faults. Stability of the constructed controller is proven and the simulation results illustrate the effectiveness of the proposed controller.

Modified Gaussian process regression based adaptive control for quadrotors

Robustness is crucial for flight vehicle control, which is directly related to control performance and mission security. Adaptive control methods are effective for handling perturbations, but most rely on expert knowledge in choosing parametric estimator structures. These uncertainties in quadrotor dynamics own complex representation form, so the structure of the estimator is difficult to determine. Our work integrates modified Gaussian process regression (GPR) with a quaternion-based command filtered backstepping framework, such that quadrotors subjected to perturbations can rapidly and accurately track the desired trajectory. GPR-based control architecture applies Bayesian nonparametric representation to estimate the distribution of perturbations; the nonparametric estimation method requires no prior knowledge about uncertainties and can inherently manage measurement noises. The zero-mean prior of GPR is modified by using the error integral, which compensates for the estimation bias of constant and/or low-frequency disturbances. Furthermore, to estimate the rapidly changing perturbations, a time-dependent form regarding state point selection is applied to increase the influence of recent measurements. Simulation results demonstrate the effectiveness of these modifications and the superiority of the proposed control system.

A Unified SO(3) Approach to the Attitude Control Design for Quadrotors

This paper proposes a two-phased problem reformulation approach to solve the quadrotor UAV attitude control problem. Given an initial attitude, the objective is to design a control to drive it toward a desired value. The first phase begins with the definition of three types of errors pertaining to attitude discrepancy, followed by the utilization of virtual control with which the dynamics of quadrotor’s attitude and angular velocity are then unified under the framework of SO(3), rendering the original control problem much more transparent to tackle. Through cancellation of certain unwanted terms emerging from the unification process, entry-wise treatment of the remaining matrix dynamics is then employed in the second phase to transform it further into the stabilization problem of a 3-dimensional linear time-invariant system that is fairly easy to solve since to which standard feedback designs such as linear quadratic regulator and pole placement are readily applicable. In addition to the classical designs, a specialized and structurally simple controller is provided to reduce the number of gains. To account for system parametric uncertainties, external disturbances, and sensor measurement errors and noises, a second controller based on classical $H_{\infty }$ theory is presented to enhance the robustness of the design. A numerical example is given, and computer simulations are conducted to generate error and control trajectories to assess and compare the effectiveness of the presented designs.

Trajectory Tracking Control of Quadrotor via Minimum Projection Method

Abstract In this paper, we consider a nonlinear tracking controller design problem for a quadrotor. For the controller design, we design a tracking control Lyapunov function (TCLF) based on the minimum projection method. However, it is not clear whether we can design the TCLF for a quadrotor by the method. In particular, it is difficult to calculate the TCLF without reducing the amount of computation. We show that the use of the orthogonal property of the direction cosine matrix in the quadrotor dynamics has the effect of reducing the computation. Finally, we demonstrate the computer simulation for a given trajectory.