Robust motion control of quadrotors

In this paper, the robust motion control problem is investigated for quadrotors. The proposed controller includes two parts: an attitude controller and a position controller. Both the attitude and position controllers include a nominal controller and a robust compensator. The robust compensators are introduced to restrain the influence of uncertainties such as nonlinear dynamics, coupling, parametric uncertainties, and external disturbances in the rotational and translational dynamics. It is proven that the position tracking errors are ultimately bounded and the boundaries can be specified by choosing controller parameters. Experimental results on the quadrotor demonstrate the effectiveness of the robust control method.     

Robust output feedback attitude tracking control for rigid-flexible coupling spacecraft

This paper investigates the robust attitude tracking control problem for a rigid-flexible coupling spacecraft. First, the dynamic model for a rigid-flexible coupling spacecraft is established based on the first-order approximation method to fully reveal the coupling effect between rigid movement and flexible displacement when the spacecraft is in rapid maneuver. In the condition that flexible vibration measurements are not available, an robust output feedback controller which is independent of model is presented using Lyapunov method with considering state-independent disturbances. To resolve the chattering problem caused by the discontinuous sign function, a modified continuous output feedback controller is proposed by introducing functions with continuous property. Rigorous proof is achieved showing that the proposed control law ensures asymptotic stability and guarantees the attitude of a rigid-flexible spacecraft to track a time-varying reference attitude based on angle and angular velocity measurements only. Finally, simulations are carried out to verify the simplicity and effectiveness of the proposed control scheme.     

Neural networks-based command filtering control for a table-mount experimental helicopter

This paper presents neural networks based on command filtering control method for a table-mount experimental helicopter which has three rotational degrees-of-freedom. First, the controller is designed based on backstepping technique, and further command filtering technique is used to solve the derivative of the virtual control, thereby avoiding the effects of signal noise. Secondly, the model uncertainty of the table-mount experimental helicopter’s system is estimated by using neural networks. And then, Lyapunov stabilization analysis proves the stability of the table-mount experimental helicopter closed-loop attitude tracking system. Finally, the experiment is carried out to clarify the effectiveness of the proposed method.     

Robust cascaded horizontal-plane trajectory tracking for fixed-wing unmanned aerial vehicles

This paper investigates the problem of horizontal-plane trajectory tracking for fixed-wing unmanned aerial vehicles(UAVs) subjected to external disturbances and uncertainties including coupling and unmodeled dynamics. Under the assumption there exist ideal inner-loop controllers, the 12-state model is reduced to a 6-state translational motion model, which is described by a group of simplified nonlinear equations with equivalent disturbances via introducing general aerodynamic models. Then a new cascaded control structure consisting of an outer-loop controller for position control and inner-loop controllers for attitude and thrust control is proposed. Based on feedback linearization technology and signal compensation theory, the proposed controller applied for position control incorporates a nominal linear time-invariant controller and a robust compensator, the latter of which is introduced to restrain the effects of uncertainties and disturbances. The robust performance of the closed-loop system is proved. Actual experimental results conducted on a small fixed-wing aircraft demonstrate that the proposed control approach is effective.     

Robust homography-based visual servo control for a quadrotor UAV tracking a moving target

In this study, a new robust homography-based visual tracking control approach for the quadrotor unmanned aerial vehicle (UAV) is developed. Specifically, employing the homography matrix as feedback, a hierarchical homography-based visual servoing (HBVS) scheme with a new command attitude extraction method to account for the underactuation of UAV is proposed. On this basis, a smooth hyperbolic tangent function is fulfilled as an augmented part of the backstepping control scheme, which guarantees the non-negative total thrust and avoid singularity. Additionally, a cascaded filter-based estimator and adaptive laws with integrable functions are embedded to counteract uncertainties including external perturbations, unknown acceleration of the moving target, and unknown image depth, and to facilitate the system’s asymptotic stability simultaneously. The theoretical analysis testifies that the whole close-loop system is asymptotically stable. Simulations further verify that the proposed HBVS controller can realize the visual tracking with a superior performance.     

Super twisting control algorithm for the attitude tracking of a four rotors UAV

This paper deals with the design and implementation of a nonlinear control algorithm for the attitude tracking of a four-rotor helicopter known as quadrotor. This algorithm is based on the second order sliding mode technique known as Super-Twisting Algorithm (STA) which is able to ensure robustness with respect to bounded external disturbances. In order to show the effectiveness of the proposed controller, experimental tests were carried out on a real quadrotor. The obtained results show the good performance of the proposed controller in terms of stabilization, tracking and robustness with respect to external disturbances.     

Quadcopter formation flight control combining MPC and robust feedback linearization

This paper presents an integrated and practical control strategy to solve the leader–follower quadcopter formation flight control problem. To be specific, this control strategy is designed for the follower quadcopter to keep the specified formation shape and avoid the obstacles during flight. The proposed control scheme uses a hierarchical approach consisting of model predictive controller (MPC) in the upper layer with a robust feedback linearization controller in the bottom layer. The MPC controller generates the optimized collision-free state reference trajectory which satisfies all relevant constraints and robust to the input disturbances, while the robust feedback linearization controller tracks the optimal state reference and suppresses any tracking errors during the MPC update interval. In the top-layer MPC, two modifications, i.e. the control input hold and variable prediction horizon, are made and combined to allow for the practical online formation flight implementation. Furthermore, the existing MPC obstacle avoidance scheme has been extended to account for small non-apriorily known obstacles. The whole system is proved to be stable, computationally feasible and able to reach the desired formation configuration in finite time. Formation flight experiments are set up in Vicon motion-capture environment and the flight results demonstrate the effectiveness of the proposed formation flight architecture.     

Integrated guidance and control strategy for homing of unmanned underwater vehicles

This paper presents a novel integrated guidance and control strategy for homing of unmanned underwater vehicles (UUVs) in 5-degree-of-freedom (DOF), where the vehicles are assumed to be underactuated at high speed and required to move towards the final docking path. During the initial homing stage, the guidance system is first designed by geometrical analysis method to generate a feasible reference trajectory. Then, in the backstepping framework, the proposed trajectory tracking controller can achieve all the tracking errors in the closed-loop system convergence to a small neighbourhood of zero. It means that the vehicle's dynamics are consistent with the reference trajectory derived in the previous step. To demonstrate the effectiveness of the proposed guidance and control strategy, the complete stability analysis used Lyapunov's method is given in the paper, and simulation results of all initial conditions are presented and discussed.     

Attitude tracking control of a quadrotor UAV in the exponential coordinates

A new approach to control the attitude of a quadrotor UAV in terms of the exponential coordinates is developed in this paper. The exponential coordinate is a minimal representation of the rotation matrix, but it can avoid singularities. Since the quadrotor UAV can be considered as a rigid body aircraft, the analytic closed-form expressions of a rigid body's attitude kinematics are derived from differential of exponential on SO(3). Furthermore, based on the exponential expressions of attitude kinematics, the controller of a fully actuated rigid body is designed using trajectory linearization control method. The overall attitude controller contains two loops, which are designed according to the torque equation and the angular velocity equation respectively. In the numerical simulation, the proposed attitude controller is compared to a controller in the Euler angles, showing that singularities induced by Euler angles are avoided by using exponential coordinates. The robustness test of the attitude controller is also demonstrated in the simulation. The simulation results indicate that the proposed method can be applied to the attitude tracking control of an aerial robot especially when the robot needs to make aggressive maneuverings.     

Predefined-time control for free-floating space robots in task space

This work mainly studies the position and attitude tracking control of a free-floating space robot. With the attitude represented in modified Rodrigues parameters (MRPs), a task-space controller with predefined-time stability is developed considering the external disturbance. The tuning parameters of a predefined-time controller can be formulated as functions of the prescribed upper bound of the stabilization time. Based on the backstepping technique and a novel predefined-time stabilizing function, a predefined-time control scheme is designed for the space robot system. Moreover, to avoid ’explosion of terms’, an auxiliary variable is introduced such that the controller is independent of the derivative of the virtual control law. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.     

Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer

Over the last decade, considerable interest has been shown from industry, government and academia to the design of Vertical Take-Off and Landing (VTOL) autonomous aerial vehicles. This paper uses the recently developed sliding mode control driven by sliding mode disturbance observer (SMC-SMDO) approach to design a robust flight controller for a small quadrotor vehicle. This technique allows for a continuous control robust to external disturbance and model uncertainties to be computed without the use of high control gain or extensive computational power. The robustness of the control to unknown external disturbances also leads to a reduction of the design cost as less pre-flight analyses are required. The multiple-loop, multiple time-scale SMC-SMDO flight controller is designed to provide robust position and attitude control of the vehicle while relying only on knowledge of the limits of the disturbances. Extensive simulations of a 6 DOF computer model demonstrate the robustness of the control when faced with external disturbances (including wind, collision and actuator failure) as well as model uncertainties.     

Event-triggered-based adaptive dynamic programming for distributed formation control of multi-UAV

This paper is concerned with the distributed formation control problem of multi-quadrotor unmanned aerial vehicle (UAV) in the framework of event triggering. First, for the position loop, an adaptive dynamic programming based on event triggering is developed to design the formation controller. The critic-only network structure is adopted to approximate the optimal cost function. The merit of the proposed algorithm lies in that the event triggering mechanism is incorporated the neural network (NN) to reduce calculations and actions of the multi-UAV system, which is significant for the practical application. What’s more, a new weight update law based on the gradient descent technology is proposed for the critic NN, which can ensure that the solution converges to the optimal value online. Then, a finite-time attitude tracking controller is adopted for the attitude loop to achieve rapid attitude tracking. Finally, the efficiency of the proposed method is illustrated by numerical simulations and experimental verification.     

Adaptive controller design for spacecraft formation flying using sliding mode controller and neural networks

A spacecraft formation flying controller is designed using a sliding mode control scheme with the adaptive gain and neural networks. Six-degree-of-freedom spacecraft nonlinear dynamic model is considered, and a leader–follower approach is adopted for efficient spacecraft formation flying. Uncertainties and external disturbances have effects on controlling the relative position and attitude of the spacecrafts in the formation. The main benefit of the sliding mode control is the robust stability of the closed-loop system. To improve the performance of the sliding mode control, an adaptive controller based on neural networks is used to compensate for the effects of the modeling error, external disturbance, and nonlinearities. The stability analysis of the closed-loop system is performed using the Lyapunov stability theorem. A spacecraft model with 12 thrusts as actuators is considered for controlling the relative position and attitude of the follower spacecraft. Numerical simulation results are presented to show the effectiveness of the proposed controller.     

Adaptive prescribed performance control of QUAVs with unknown time-varying payload and wind gust disturbance

In this paper, a new robust adaptive prescribed performance control (PPC, for short) scheme is proposed for quadrotor UAVs (QUAVs, for short) with unknown time-varying payloads and wind gust disturbances. Under the presented framework, the overall control system is decoupled into translational subsystem and rotational subsystem. These two subsystems are connected to each other through common attitude extraction algorithms. For translational subsystem, a novel robust adaptive PPC strategy is designed based on the sliding mode control technique to provide better trajectory tracking performance and well robustness. For rotational subsystem, a new robust adaptive controller is constructed based on backstepping technique to track the desired attitudes. Finally, the overall system is proved to be stable in the sense of uniform ultimate boundedness, and numerical simulation results are presented to validate the effectiveness of the proposed control scheme.     

Multivariable uniform finite-time output feedback reentry attitude control for RLV with mismatched disturbance

A continuous multivariable uniform finite-time output feedback reentry attitude control scheme is developed for Reusable Launch Vehicle (RLV) with both matched and mismatched disturbances. A novel finite-time controller is derived using the bi-limit homogeneous technique, which ensures that the attitude tracking can be achieved in a uniformly bounded convergence time from any initial states. A multivariable uniform finite-time observer is designed based on an arbitrary order robust sliding mode differentiator to estimate the unknown states and the external disturbances, simultaneously. Then, an output feedback control scheme is established through the combination of the developed controller and the observer. A rigorous proof of the uniform finite-time stability of the closed-loop system is presented using Lyapunov and homogeneous techniques. Finally, numerical simulation is provided to demonstrate the efficiency of the proposed scheme.     

Experimental validation of a practical nonlinear control method for hydraulic flight motion simulator

The hydraulic flight motion simulator (HFMS), as a key equipment for hardware-in-the-loop (HWIL) simulation in the field of aerospace, is required to have the ability to accurately simulate the aircraft attitude in the laboratory. However, three model uncertainties including nonlinear friction torque, unbalanced gravity torque and time-varying inertia existing in the outer frame of the HFMS at the same time become a main obstacle to achieving its high-precision position control effect. In this paper, according to identification results of friction torque and gravity torque from experiments, combining with simulation result of time-varying inertia of the outer frame from virtual prototype, a disturbance-observer-based nonlinear robust controller with the model compensation was designed on the basis of the mathematical model. Here, since the model compensation has eliminated the main mismatched uncertainties, dual disturbance observers are only necessary to suppress unmodeled mismatched uncertainties and matched uncertainties. Furthermore, the zero bias of the servo valve was also considered to help controller implementation. Finally, the effectiveness and the practicability of the proposed control method were validated by comparative experiments, which demonstrates that the proposed control method is promising and can be applied in the high-precision position control for the HFMS.     

Design of a H∞ model reference tracking control for interconnected nonlinear systems by decentralized dynamic output-feedback

This study investigates the problem of robust tracking control for interconnected nonlinear systems affected by uncertainties and external disturbances. The designed H_∞ dynamic output-feedback model reference tracking controller is parameterized in terms of linear matrix inequalities (LMIs), which is formulated within a convex optimization problem readily implementable. The resolution of such a problem, guarantying not only the quadratic stability but also a prescribed performance level of the resulting closed-loop system, enables to calculate concurrently the robust decentralized control and observation gain matrices. The established LMI conditions are computed in a single-step resolution to obtain all the controller/observer parameters and therefore to overcome the problem of iterative algorithm based on a multi-stage resolution leading in most cases to conservative and suboptimal solutions. Numerical simulations on diverse applications ranging from a numerical academic example to coupled inverted double pendulums and a 3-strongly interconnected machine power system are provided to corroborate the merit of the proposed control scheme.     

Hyperbolic tangent function-based fixed-time event-triggered control for quadrotor aircraft with prescribed performance

In this paper, the prescribed performance trajectory tracking problem of quadrotor aircraft with six degrees of freedom is addressed. Firstly, for the sake of facilitating the construction of controller, the aircraft is decomposed into position loop and attitude loop through time scale decomposition method. A fixed-time sliding mode controller is proposed to guarantee the convergence time of the aircraft system regardless of initial states. After that, to enhance security of control system, the hyperbolic tangent performance function is designed as performance index function to maintain the error within a prescribed range. Then, the event-triggered strategy is adopted to attitude subsystem which can significantly save communication resources, and the stability of control system is analyzed by Lyapunov method. In addition, the Zeno phenomenon is avoided which can be proved by ensuring the two consecutive trigger events have a positive lower limit. Finally, the validity of the constructed controller is confirmed by simulation results.     

A yaw stability-guaranteed hierarchical coordination control strategy for four-wheel drive electric vehicles using an unscented Kalman filter

A novel hierarchical coordination control strategy (HCCS) is offered to guarantee the stability of four-wheel drive electric vehicles (4WD-EVs) combining the Unscented Kalman filter (UKF). First, a dynamics model of the 4WD-EVs is established, and the UKF-based estimator of sideslip angle and yaw rate is constructed concurrently. Second, the equivalent cornering stiffness coefficients are jointly estimated to consider the impact of vehicle uncertainty parameters on the estimator design. Afterwards, a HCCS with two-level controller is presented. The sideslip angle and yaw rate are controlled by an adaptive backstepping-based yaw moment controller, and the computational burden is relieved by an improved adaptive neural dynamic surface control technology in the upper-level controller. Simultaneously, the optimal torque distribution controller of hub motors is developed to optimize the adhesion utilization ratio of tire in the lower-level controller. Finally, the proposed HCCS has shown effective improvement in the trajectory tracking capability and yaw stability of the 4WD-EVs under various maneuver conditions compared with the traditional Luenberger observer-based and the federal-cubature Kalman filter-based hierarchical controller.     

Decentralized sampled-data fuzzy controller design for a VTOL UAV

This study focuses on a sampled-data fuzzy decentralized tracking control problem for a quadrotor unmanned aerial vehicle (UAV) under the variable sampling rate condition. To this end, the overall dynamics of the quadrotor is expressed as a decentralized Takagi–Sugeno (T–S) fuzzy model interconnected with each other. Although the proposed decentralized control technique divides the overall UAV control system into attitude and position subsystems, the stability of the entire control system is guaranteed. Besides, in this paper, the model uncertainty, interconnection, and reference trajectory are considered as disturbances acting on the tracking error. To attenuate these disturbances, a novel sampled-data tracking control design technique is derived based on a linear reference model to be tracked and the time-dependent Lyapunov–Krasovskii functional (LKF). By doing so, both the stability of the tracking error dynamics and the minimization of tracking performance are guaranteed. Also, the proposed tracking control design method is derived as a linear matrix inequality (LMI)-based optimal problem. Finally, a simulation example is provided to demonstrate the effectiveness and feasibility of the proposed design methodology.