Quadrotor Control Research Articles

Quadrotor Trajectory-Tracking Control with Actuator Saturation

As a very serious problem for control systems, actuator saturation often leads to an unstable system. The maneuvering flight of quadrotors may lead to actuator saturation, which commonly affects the flight quality, including trajectory-tracking accuracy. Quadrotors usually adopt double-closed-loop control, of which the outer loop is the position control used to calculate the desired attitude angle and the inner loop is the attitude control used to generate control actions for the vehicle. To address actuator saturation during the maneuvering flight of quadrotors, an attitude controller based on the conditioned super-twisting algorithm (CSTA) was designed. The sign functions in CSTA were replaced by a hyperbolic tangent function, which suppresses the chattering of CSTA. In order to improve the rapidity of the improved controller, the tanh-CSTA (TCSTA), a gain adjustment factor was utilized. The rapidity and smoothness of the controller can be satisfied by adjusting the gain factor. Additionally, a sliding surface was designed according to the characteristics of the quadrotor control structure, so that the TCSTA controller can be applied to the second-order system. The performances of the designed improved controller were simulated using MATLAB, and the results showed that the designed controller is more robust than the PID controller. Moreover, compared with the CSTA controller, the chattering of the designed controller was obviously suppressed without reducing the control accuracy.

Dual Observer Based Adaptive Controller for Hybrid Drones

A biplane quadrotor (hybrid vehicle) benefits from rotary-wing and fixed-wing structures. We design a dual observer-based autonomous trajectory tracking controller for the biplane quadrotor. Extended state observer (ESO) is designed for the state estimation, and based on this estimation, a Backstepping controller (BSC), Integral Terminal Sliding Mode Controller (ITSMC), and Hybrid Controller (HC) that is a combination of ITSMC + BSC are designed for the trajectory tracking. Further, a Nonlinear disturbance observer (DO) is designed and combined with ESO based controller to estimate external disturbances. In this simulation study, These ESO-based controllers with and without DO are applied for trajectory tracking, and results are evaluated. An ESO-based Adaptive Backstepping Controller (ABSC) and Adaptive Hybrid controller (AHC) with DO are designed, and performance is evaluated to handle the mass change during the flight despite wind gusts. Simulation results reveal the effectiveness of ESO-based HC with DO compared to ESO-based BSC and ITSMC with DO. Furthermore, an ESO-based AHC with DO is more efficient than an ESO-based ABSC with DO.

State-Transformation-Based Recursive Design Strategy for Leader-Follower Safety Formation Control of Uncertain Multiple Quadrotors

State-Transformation-Based Recursive Design Strategy for Leader-Follower Safety Formation Control of Uncertain Multiple Quadrotors

Robust Saturated Formation Tracking Control of Multiple Quadrotors With Switching Communication Topologies

This article deals with distributed formation control for a set of quadrotors subject simultaneously to external disturbances and switching communication topologies. The proposed robust controller incorporates position and attitude control laws for each quadrotor. Both control laws have a nominal part for trajectory tracking and a robust part that compensates for the dynamic model uncertainties and time-varying external disturbances. The devised controller guarantees that the thrust force is bounded with respect to the position error by utilizing saturation functions. The directed communication topology among the quadrotors is considered to be switchable. The formation control performance is guaranteed under switching topologies, and it is demonstrated that all error terms, in closed-loop, converge to a ball centered at the origin with an arbitrarily small radius, achieving uniformly ultimate boundedness. Finally, the performance of the proposed strategy is validated through numerous simulation and experimental examples.

Adaptive Formation Control for Multiple Quadrotors with Nonlinear Uncertainties Using Lipschitz Neural Network

This paper proposes a new distributed formation control scheme for multiple quadrotors with uncertainties, which is more practical for real implementation. The proposed design takes into account the inherent nonlinear and coupled dynamics of quadrotor and incorporates the Lipschitz model uncertainty. The multi-quadrotor formation control system is divided into the high-level distributed formation controller for position control, and the low-level attitude controller for desired acceleration tracking. To improve the performance of the low-level system, we employ the Lipschitz neural network (LipNet) adaptation. LipNet adaptation learns the model uncertainty and provides a significant improvement in acceleration tracking by modifying the reference signal of the low-level system. Consequently, the performance of the whole system is enhanced. We provide a stability analysis of the proposed design and validate the performance by some simulation examples.

Trajectory tracking control for uncertain agricultural quadrotor based on combining ASMC and NFTSMC

Trajectory tracking control for uncertain agricultural quadrotor based on combining ASMC and NFTSMC

Trajectory tracking control for uncertain agricultural quadrotor based on combining ASMC and NFTSMC

Trajectory tracking control for uncertain agricultural quadrotor based on combining ASMC and NFTSMC

Fractional Order Sliding Mode Control of Quadrotor Based on Fractional Order Model

Fractional Order Sliding Mode Control of Quadrotor Based on Fractional Order Model

Tracking Control of Quadrotor with Intermittent Target Measurements: A Stochastic Switched Systems Approach

This paper is devoted to the investigation of target tracking control of quadrotor with intermittent measurements, i.e., the measurements of target position are not continuously available. A stochastic switched systems approach is utilized to formulate such a tracking process of quadrotor by splitting it into two modes according to whether the measurements are available. The mode switching of the underlying system is subject to a Markov process to account for the inherent non-memory randomness of the dwell time of each mode, in contrast with the existing studies that impractically require the duration of the measurements to be greater than a given constant. The stability criteria for the underlying system are derived, upon which a switched controller is designed for the quadrotor position control, rather than the determination of the bounds of the dwell time for given pre-designed controllers in each mode. Simulations are presented to demonstrate the effectiveness of the developed theoretical results and the superiority of the designed switched controller for tracking control of quadrotor with intermittent target measurements.

Quadrotor Control for Tracking Moving Target, and Dynamic Obstacle Avoidance Based on Potential Field Method

Quadrotor Control for Tracking Moving Target, and Dynamic Obstacle Avoidance Based on Potential Field Method

A Feedforward Quadrotor Disturbance Rejection Method for Visually Identified Gust Sources Based on Transfer Reinforcement Learning

With the rapid development of urbanization, quadrotors are flying more and more frequently between highdensity buildings. In urban areas, there are many gust sources with obvious visual characteristics, such as ventilation outlet of buildings or subways, outdoor unit of HVAC (heating ventilating and air conditioning), or other artificial gust sources, which can cause sudden gust disturbances to the passing quadrotors. Aiming at reducing the effect of visually identified gust disturbances, this article presents a quadrotor feedforward compensator framework based on transfer reinforcement learning (TRL). In this structure, the Discriminative Model Prediction (DiMP) algorithm is used to extract the visual features of the gust source and achieve tracking of such sources. Then, the TRL algorithm is used to transfer the obtained tracking network to a compensation network, which completes a DiMP-TRL structure. The output of the trained DiMP-TRL compensation network is added to the quadrotor controller as a feedforward part, which will help generate preventive action when encountering the identified gust disturbance. Only a front-facing camera is needed to collect gust information, no additional anemometer or accurate wind model is required. The ultimately uniformly bounding of the quadrotor system can be guaranteed using the Lyapunov stability criteria. The proposed method is compared with Cascade PID and a novel feedback compensation-based method called DCF in a realistic simulation environment built by a physics engine. Two sets of results demonstrate that the proposed method can reject gust disturbance more efficiency.

Development and Application of a Novel High-Order Fully Actuated System Approach—Part I: 3-DOF Quadrotor Control

The quadrotor hierarchical control design (position-attitude) based on the state-space modeling has been widely applied in the past. Although the state-space representation, based on a group of first-order differential equations, is effective in modeling many dynamic systems, inherent high-order dynamics and control of quadrotor systems may not be properly handled by the state-space modeling. This letter proposes a modified high-order fully actuated (HOFA) theory for a group of high-order dynamic systems, including the quadrotor system, without relying on pseudo strict-feedback forms required by the original HOFA approach. Hence, the quadrotor model can be essentially converted into two HOFA subsystems. A nonlinear 3-DOF quadrotor modeling and control is applied as an example to demonstrate the effectiveness of the proposed approach, which can achieve arbitrarily assignable eigenstructure like a stabilized linear system.

Distributed fixed-time sliding mode control of time-delayed quadrotors aircraft for cooperative aerial payload transportation: Theory and practice

This paper investigates a cooperative fixed-time control for networked-delayed and disturbed quadrotors in payload transportation missions. First, the input time-delayed tracking error system is adequately transformed into a delay-free system via Artstein’s reducing transformation. Second, a novel Distributed Cooperative Fixed-Time Stable Control Protocol (DCFTSCP) is proposed for the multi-quadrotor system to stabilize the geometrical spatial formation while carrying the payload. Furthermore, a disturbance observer is incorporated into the control framework to counteract the lumped disturbances and achieve the transportation task with a minimal swing. Overall, the designed DCFTSCP is able to stabilize the delayed tracking states at the origin in fixed-time uniformly to the Initial Conditions (ICs). It is worth mentioning that the proposed controller belongs to the homogeneous sliding mode control class. The reported related works rely on the bi-limit approximation method to prove the fixed-time convergence of the states. Nevertheless, this method suffers from a crucial shortcoming where it is unable mathematically to provide an explicit expression on the settling (convergence) time. In contrast, in the present study, the stability analysis is thoroughly investigated based on the algebraic Lyapunov tools, namely, Algebraic Lyapunov Equation (ALE) and Lyapunov Quadratic Function (LQF). Consequently, the upper-bound on the convergence-time is explicitly derived for the first time for time-delayed quadrotors aircraft used in cooperative payload transportation. MATLAB® simulations and real flight experiments are conducted to corroborate the theoretical studies of the paper. Overall, the results show that the proposed control protocol yields performance improvement regarding fixed-time tracking stability featuring fast transient, strong robustness, and high steady-state precision. In addition, the undesirable chattering problem of regular linear sliding mode control is noticeably attenuated. Furthermore, unlike conventional terminal sliding mode control techniques, the control input is singularity-free. Finally, several challenging issues in cooperative fixed-time control for networked-delayed quadrotors are highlighted for future research.

A Comparative Study of Nonlinear MPC and Differential-Flatness-Based Control for Quadrotor Agile Flight

Accurate trajectory-tracking control for quadrotors is essential for safe navigation in cluttered environments. However, this is challenging in agile flights due to nonlinear dynamics, complex aerodynamic effects, and actuation constraints. In this article, we empirically compare two state-of-the-art control frameworks: the nonlinear-model-predictive controller (NMPC) and the differential-flatness-based controller (DFBC), by tracking a wide variety of agile trajectories at speeds up to 20 m/s (i.e., 72 km/h). The comparisons are performed in both simulation and real-world environments to systematically evaluate both methods from the aspect of tracking accuracy, robustness, and computational efficiency. We show the superiority of the NMPC in tracking dynamically infeasible trajectories, at the cost of higher computation time and risk of numerical convergence issues. For both methods, we also quantitatively study the effect of adding an inner loop controller using the incremental nonlinear dynamic inversion method, and the effect of adding an aerodynamic drag model. Our real-world experiments, performed in one of the world’s largest motion capture systems, demonstrate more than 78% tracking error reduction of both NMPC and DFBC, indicating the necessity of using an inner loop controller and aerodynamic drag model for agile trajectory tracking.

Modified adaptive discrete-time incremental nonlinear dynamic inversion control for quad-rotors in the presence of motor faults

Unmanned air vehicles are intrinsically non-linear, unstable, uncertain, and prone to a variety of faults, most commonly the motor faults. The main objective of this paper is to develop a fault-tolerant control algorithm for the quadrotors with the motor faults. Accordingly, a novel adaptive modified incremental nonlinear dynamic inversion (MINDI) control is proposed to stabilize and control the quad-rotor with partial motor faults. The controller consists of a MINDI controller augmented with a discrete-time nonlinear adaptive algorithm. Since the incremental nonlinear dynamic inversion (INDI) algorithm is essentially based on the sensor measurements, it necessitates the angular rates differentiation and therefore amplifies the high-frequency noises produced by the gyroscopes. The application of derivative filters causes unavoidable internal state delays in the INDI structure. Henceforth, the performance of the controller developed for the unstable and uncertain quadrotors degrades considerably. To address this drawback, this paper proposes the MINDI controller which basically derives the angular accelerations from the angular moment estimations. Furthermore, to increase the robustness of the MINDI against motor faults, a discrete-time adaptive controller has been incorporated. The performance of the proposed controllers is verified both through the nonlinear simulations and testbed experiments. The results are compared with a recent efficient algorithm, which had been implemented on a quad-rotor model.

Attitude tracking control for quadrotor based on time-varying gain extended state observer

Considering the problems of unknown external disturbances and parametric uncertainties in attitude tracking of a quadrotor, a backstepping sliding mode control method based on the time-varying gain extended state observer is proposed in this article. First, the mathematical model of the attitude system of the quadrotor is introduced. Second, a time-varying gain extended state observer is proposed to observe the unmeasurable states, total disturbance, and reduce the “peaking value” phenomenon, which often occurs in traditional linear extended state observers. It is proved that the observation errors are bounded. Third, a novel controller synthesized by backstepping sliding mode control method and the time-varying gain extended state observer is proposed for the attitude system of the quadrotor. Moreover, the designed controller can ensure that all signals of the closed-loop system are bounded. Finally, the effectiveness and superiority of the proposed control method are verified by simulation.

Collision-free formation tracking control for multiple quadrotors under switching directed topologies: Theory and experiment

Multiple quadrotors are becoming increasingly attractive in many fields, and the formation tracking control of multiple quadrotors is the foundation for performing complex tasks. In this paper, the collision-free formation tracking control problem for multiple quadrotors under switching topology is studied, and the leader has the control command, which is unknown to the followers. A formation tracking control protocol is firstly constructed utilizing local neighboring information, in which the neighbors of the quadrotors can change. Then, inspired by the spring-damping system, a collision avoidance mechanism based on Hooke's law with damping is proposed to avoid collision of multiple quadrotors in a cluttered flight. By using the Lyapunov based stability analysis, it is proved that multiple quadrotors can track the dynamic leader in a dynamic formation using the proposed protocol under formation feasibility and the existence of spanning trees in communication topology. Finally, a lightweight communication protocol is designed in the experimental platform. Several groups of visual simulations are carried out based on the Gazebo simulator. The proposed method is compared with two potential field methods in two scenarios through quantitative studies of task efficiency and error analysis. Overall, the completion time is improved by 86.02% and 31.98%, and the minimum tracking error is improved by 57.24% and 46.20% in scenario 1. The completion time is improved by 86.88% and 30.34%, and the minimum tracking errors are improved by 82.20% and 42.62% in scenario 2. Outdoor experiments on formation tracking are performed to verify the effectiveness of the proposed methods. Furthermore, several outdoor experiments are conducted in the same scenarios to validate the proposed algorithm.

Optimal Control of Quadrotor with a Novel Madgwick/Extended Kalman Observer to Track a Spline Trajectory for Obstacle Avoidance

Optimal Control of Quadrotor with a Novel Madgwick/Extended Kalman Observer to Track a Spline Trajectory for Obstacle Avoidance

Target Enclosing and Coverage Control for Quadrotors with Constraints and Time-Varying Delays: A Neural Adaptive Fault-Tolerant Formation Control Approach.

This paper investigates the problem of formation fault-tolerant control of multiple quadrotors (QRs) for a mobile sensing oriented application. The QRs subject to faults, input saturation and time-varying delays can be controlled to perform a target-enclosing and covering task while guaranteeing the state constraints will not be exceeded. A distributed formation control scheme is proposed, using a radial basis function neural network (RBFNN)-based time-delay position controller and an adaptive fault-tolerant attitude controller. The Lyapunov–Krasovskii approach is used to analyze the time-varying delay. Barrier Lyapunov function is deployed to handle the prescribed constraints, and an auxiliary system combined with a command filter is designed to resolve the saturation problem. An RBFNN and adaptive estimators are deployed to provide estimates of disturbances, fault signals and uncertainties. It is proven that all the closed-loop signals are bounded under the proposed protocol, while the prescribed constraints will not be violated, which enhances the flight safety and QR formation’s applicability. Comparative simulations based on application scenarios further verify the effectiveness of the proposed method.

A predictive sliding mode control for quadrotor’s trackingtrajectory subject to wind gusts and uncertainties

<p>In this paper, a predictive sliding mode control (PSMC) strategy for the quadrotors tracking trajectory problem is proposed. This strategy aims to combine the advantages of sliding mode control (SMC) and non-linear model predictive control (NMPC) to improve the tracking control performance for quadrotors in terms of optimality, inputs/states constraints satisfaction, and strong robustness against disturbances. A comparative study of three popular controllers: the SMC, NMPC, and the integral backstepping control (IBC) is performed with different criteria. Accordingly, IBC and SMC show less computational time and strong robustness, while NMPC has minimum control effort. The discrete Dryden turbulence model is used as a benchmark model to represent the wind effect on the trajectory tracking accuracy. The effectiveness of the proposed method PSMC has been proven and compared with discrete-time slidingmode control (DSMC) and NMPC in several scenarios. Simulation results show that under both wind turbulence and time-variant uncertainties, the PSMC outperforms the other controllers by providing simultaneously disturbance rejection and guarantee that the control inputs are within bounded constraints.</p>