Distributed fixed‐time attitude coordination control for multiple rigid spacecraft

In this paper, the fixed‐time attitude coordination control for multiple rigid spacecraft under an undirected communication graph is investigated. By using the backstepping technique, the distributed fixed‐time observer, and the method of “adding a power integrator,” a distributed fixed‐time attitude coordination control law is designed for a group of spacecraft. The proposed control scheme is nonsingular and can guarantee a group of rigid spacecraft simultaneously tracking a common desired attitude within fixed time even when the time‐varying reference attitude is available only to a subset of the group members. Rigorous analysis is provided to show that the attitude consensus tracking errors can converge to the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Finite‐Time Sliding Mode Trajectory Tracking Control of Uncertain Mechanical Systems

The problem of finite‐time tracking control is studied for uncertain nonlinear mechanical systems. To achieve finite‐time convergence of tracking errors, a simple linear sliding surface based on polynomial reference trajectory is proposed to enable the trajectory tracking errors to converge to zero in a finite time, which is assigned arbitrarily in advance. The sliding mode control technique is employed in the development of the finite‐time controller to guarantee the excellent robustness of the closed‐loop system. The proposed sliding mode scheme eliminates the reaching phase problem, so that the closed‐loop system always holds the invariance property to parametric uncertainties and external disturbances. Lyapunov stability analysis is performed to show the global finite‐time convergence of the tracking errors. A numerical example of a rigid spacecraft attitude tracking problem demonstrates the effectiveness of the proposed controller.     

Multivariable supertwisting fixed‐time approach for RLV re‐entry attitude control

The attitude control problem of reusable launch vehicles (RLVs) is investigated based on multivariable supertwisting fixed‐time comprehensive control strategy. A novel multivariable supertwisting fixed‐time approach, which can guarantee that the states converge to zero within a fixed time, is proposed. According to the multiple time scale principle, the RLV attitude control system is divided into attitude angle subsystem and attitude angle rate subsystem. Based on multivariable supertwisting fixed‐time approach, comprehensive design of fixed‐time disturbance observer and controller is proposed to ensure that the attitude angle tracking error converges to zero within a fixed time. The features of the proposed control scheme contain that the settling time is independent of initial conditions and it has the better property of chattering reduction. Finally, the efficiency of the proposed method is verified through numerical simulation.     

Two‐Layer Terminal Sliding Mode Attitude Control of Satellites Equipped with Reaction Wheels

This paper addresses the global stability and robust attitude tracking problem of a near polar orbit satellite subject to unknown disturbances and uncertainties. It is assumed that the satellite is fully actuated by a set of reaction wheels (RW) as control actuators because of their relative simplicity, versatility and high accuracy. The terminal sliding mode control (TSMC) approach is utilized in a two‐level architecture to achieve control objectives. In the lower layer a detumbling‐like controller is designed which guarantees the finite‐time detumbling and tracking of the desired angular velocities and based on this result a robust attitude tracking controller is designed in the upper layer to achieve 3‐axis attitude tracking in the presence of unknown disturbances and bounded uncertainties. Robust stability and tracking properties of designed controllers are proved using the Lyapunov theory. Finally, a set of numerical simulation results are provided to illustrate the effectiveness and performance of the proposed control method.     

Robust adaptive fixed‐time tracking control of 6‐DOF spacecraft fly‐around mission for noncooperative target

The fixed‐time relative position tracking and attitude synchronization control problem of a spacecraft fly‐around mission for a noncooperative target in the presence of parameter uncertainties and external disturbances is investigated. Firstly, a novel and coupled relative position and attitude motion model for a noncooperative fly‐around mission is established. Subsequently, a novel nonsingular fast terminal sliding mode (NFTSM) surface is developed, and the explicit estimation of the convergence time independent of initial states is provided. Fair and systematic comparisons among several typical terminal sliding modes show that the designed NFTSM has faster convergence performance than the fast terminal sliding mode. Then, a robust integrated adaptive fixed‐time NFTSM control law with no precise knowledge of the mass and inertia matrix and disturbances by combining the nonsingular terminal sliding mode technique with an adaptive methodology is proposed, which can eliminate the chattering phenomenon and guarantee that the relative position and attitude tracking errors can converge into the small regions containing the origin in fixed time. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control schemes.     

Dynamic modeling and nonlinear tracking control of a novel modified quadrotor

In this article, a nonlinear tracking controller is designed based on Lyapunov stability for a novel aerial robot. The proposed 6‐rotor configuration improves stability and payload lifting capacity of the robot compared with conventional quadrotors while avoiding further complexities in the robot dynamics and steering principles. The dynamical model of the robot is derived using Newton‐Euler method. The model represents a nonlinear, coupled, and underactuated system. The proposed control strategy includes 2 main parts: an attitude controller and a position controller. Both the attitude and position controls are Lyapunov‐based nonlinear tracking controllers that guarantee the asymptotic convergence of the states' tracking errors to zero. Simulation results are presented to illustrate appropriate performance of the closed‐loop system in terms of position/attitude tracking even in the presence of wind disturbance.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Robust trajectory tracking control for unmanned tail‐sitters in aggressive flight mode transitions

In this paper, the trajectory tracking control problem is investigated for a new typical tail‐sitter. A robust hierarchical control method is proposed to achieve aggressive flight mode transitions. The proposed control method results in a composite controller including a translational controller and a rotational controller to control the position and attitude respectively. Continuous aggressive flight mode transitions can be achieved without switching on the coordinate systems or the controller structures. It is proven that the tracking errors of the designed closed‐loop system can converge into a given neighborhood of the origin in a finite time. Simulation results show the effectiveness of the proposed control strategy.     

Fixed‐Time Synchronization of a Class of Second‐Order Nonlinear Leader‐Following Multi‐Agent Systems

The fixed‐time synchronization problem for a class of second‐order nonlinear multi‐agent systems with a leader‐follower architecture is investigated in this paper. To achieve the fixed‐time tracking task, the design procedure is divided into two steps. At the first step, a distributed fixed‐time observer is designed for each agent to estimate the leader's state in a fixed time. Then, at the second step, based on the technique of adding a power integrator, a fixed‐time tracking controller for each agent is proposed such that the estimate leader's state can be tracked in a fixed time. Finally, an observer‐based fixed‐time controller is developed such that the leader can be tracked by all the followers in a fixed time, which can be predetermined. Simulations are presented to verify the effectiveness of the proposed approach.     

Fixed‐time adaptive sliding mode trajectory tracking control of uncertain mechanical systems

An adaptive fixed‐time trajectory tracking controller is proposed for uncertain mechanical systems in this study. The polynomial reference trajectory is planned for trajectory tracking error. Fractional power of linear sliding mode is applied to design the nonlinear controller, adaptive laws are used to adjust controller parameters. Trajectory planning and fractional power are combined to ensure the tracking‐error convergence in a fixed time. The boundary layer technique is used to suppress the model uncertainties and decrease the chattering phenomenon. The closed‐loop system stability is proved strictly in the Lyapunov framework to show that the trajectory tracking errors and adaptive parameters tend to zero in a fixed time set in advance. Numerical simulation results of robotic manipulators illustrate the effectiveness of the proposed controller.     

Finite‐time geometric control for underactuated aerial manipulators with unknown disturbances

In this article, the finite‐time geometric control for underactuated aerial manipulators is investigated. The dynamics of the aerial manipulator with unknown disturbances is analyzed first. The dynamics of the system is decomposed into the locked subsystem and shape subsystem. The finite‐time controller for the aerial manipulator is then designed based on the analyzed dynamics. In the controller, the attitude tracking error of the aircraft base is expressed from the rotation matrix, which makes the controller continuous and almost globally stable on SO(3). A continuous adaptive term is added in the controller to compensate for the unknown disturbances. Finite‐time filters are designed to ensure the smoothness of the commands on each loop. The convergence of the entire controlled system is strictly proved using Lyapunov theory and the definition of finite‐time stability. The results show that the tracking error and the disturbance bound estimation error of the entire system are finite‐time bounded near origin. Finally, comparative simulation results are presented to show the performance of the proposed controller.     

Sliding-Mode-Based Attitude Tracking Control of Spacecraft Under Reaction Wheel Uncertainties

The attitude tracking operations of an on-orbit spacecraft with degraded performance exhibited by potential actuator uncertainties (including failures and misalignments) can be extraordinarily challenging. Thus, the control law development for the attitude tracking task of spacecraft subject to actuator (namely reaction wheel) uncertainties is addressed in this paper. More specially, the attitude dynamics model of the spacecraft is firstly established under actuator failures and misalignment (without a small angle approximation operation). Then, a new non-singular sliding manifold with fixed time convergence and anti-unwinding properties is proposed, and an adaptive sliding mode control (SMC) strategy is introduced to handle actuator uncertainties, model uncertainties and external disturbances simultaneously. Among this, an explicit misalignment angles range that could be treated herein is offered. Lyapunov-based stability analyses are employed to verify that the reaching phase of the sliding manifold is completed in finite time, and the attitude tracking errors are ensured to converge to a small region of the closest equilibrium point in fixed time once the sliding manifold enters the reaching phase. Finally, the beneficial features of the designed controller are manifested via detailed numerical simulation tests.      

Adaptive Fault‐Tolerant Attitude Tracking Control of Rigid Spacecraft on Lie Group with Fixed‐Time Convergence

This paper investigates the fixed‐time attitude tracking problem for rigid spacecraft in the presence of inertial uncertainties, external disturbances, actuator faults, and input saturation constraints. The logarithm map is first utilized to transform the tracking problem on SO(3) into the stabilization one on its associated Lie algebra ( ). A novel nonsingular fixed‐time‐based sliding mode is designed, which not only avoids the singularity but also guarantees that the convergence time of tracking errors along the sliding surface is independent of the state value. Then, an adaptive fault‐tolerant control law is constructed, in which an online adaptive law is incorporated to estimate the upper boundary of the lumped uncertainties. The combined control scheme enforces the system state to reach a neighborhood of the sliding surface in the sense of the fixed‐time concept. The key feature of the resulting control scheme is that it can accommodate actuator failures under limited control torque without the knowledge of fault information. Numerical simulations are finally performed to demonstrate the effectiveness of the proposed fixed‐time controllers.     

交会对接模拟系统姿态位置耦合有限时间控制

针对航天器交会对接模拟系统的姿态同步和位置跟踪控制问题,在存在外界扰动和系统不确定性的情况下,基于改进的快速非奇异终端滑模面和改进的自适应律,采用双闭环控制结构分别设计内环和外环有限时间姿态位置耦合控制器.所提出的自适应律不仅能有效地抑制扰动和不确定性且能保证控制器是连续的.李雅普诺夫理论推导和仿真结果表明,所提出的控制方法能保证系统内环和外环跟踪误差的有限时间稳定性和准确收敛性.     

Reaction wheel fault‐tolerant finite‐time control for spacecraft attitude tracking without unwinding

This article proposes fault‐tolerant finite‐time attitude tracking control of a rigid spacecraft actuated by four reaction wheels without unwinding problem in the presence of external disturbances, uncertain inertia parameter, and actuator faults. First, a novel antiunwinding finite‐time attitude tracking control law is derived with a designed control signal which works within a known actuator‐magnitude constraint using a continuous nonsingular fast terminal sliding mode (NFTSM) concept. Second, a finite‐time disturbance observer (FTDO) is introduced to estimate a lumped disturbance due to external disturbances, uncertain inertia parameter, actuator faults, and input saturation. Third, a composite controller is developed which consists of a feedback control based on the continuous NFTSM method and compensation term based on the FTDO. The global finite‐time stability is proved using Lyapunov stability theory. Moreover, the singularity and unwinding phenomenon are avoided. Simulation results are conducted under actuator constraints in the presence of external disturbances, inertia uncertainty, and actuator faults and results are illustrated to show the effectiveness of the proposed method. In addition, to show the superiority of the proposed control method over the recently reported control methods, comparative analysis is also presented.     

Distributed finite‐time formation control for multiple quadrotors via local communications

This paper investigates finite‐time formation tracking control problem for multiple quadrotors with external disturbance. The states of the virtual leader are not available to all the followers and the network topology is described by a directed graph. The model of each quadrotor is divided into position subsystem and attitude subsystem. Firstly, novel distributed finite‐time state observers are designed to estimate the relative state errors between followers and the virtual leader. Secondly, the values of these observers are used to design controllers that achieve finite‐time robust coordinated tracking in the position subsystem. Thirdly, the terminal sliding mode disturbance observers and finite‐time attitude tracking controllers are proposed, respectively, in the attitude subsystem to estimate the external disturbance and achieve attitude tracking control. The finite‐time stability analysis of the control algorithms is carried out using the Lyapunov theory and the homogeneous technique. Finally, the efficiency of the proposed algorithm is illustrated by numerical simulations.     

Adaptive fixed‐time fault‐tolerant control for rigid spacecraft using a double power reaching law

In this paper, an adaptive fixed‐time fault‐tolerant control scheme is presented for rigid spacecraft with inertia uncertainties and external disturbances. By using an inverse trigonometric function, a novel double power reaching law is constructed to speed up the state stabilization and reduce the chattering phenomenon simultaneously. Then, an adaptive fixed‐time fault‐tolerant controller is developed for the spacecraft with the actuator faults, such that the fixed‐time convergence of the attitude and angular velocity could be guaranteed, and no prior knowledge on the upper bound of the lumped uncertainties is required anymore in the controller design. Comparative simulations are provided to illustrate the effectiveness and superior performance of the proposed scheme.     

Velocity-free adaptive nonsingular fast terminal sliding mode finite-time attitude tracking control for spacecraft

Aiming at the attitude tracking control problem of rigid spacecraft under the condition of unmeasurable angular velocity information, a velocity-free adaptive nonsingular fast terminal sliding mode finite-time tracking control method is proposed. The finite-time extended-state observer is used to estimate the attitude tracking speed errors and the integrated disturbances. Combined with the above control method, a fast nonsingular terminal sliding mode controller with attitude measurement is designed and the adaptive technology is introduced to compensate for the influence of observation errors on the controller. The finite-time convergence of the observer and the control method was demonstrated based on Lyapunov theory, and the effectiveness of the proposed method is verified by numerical simulations.     

Robust control of nonlinear semi‐strict feedback systems using finite‐time disturbance observers

The output tracking controller design problem is dealt with for a class of nonlinear semi‐strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances, and uncertain nonlinear virtual control coefficients of the subsystems. The controller is designed in a backstepping manner, and to avoid the shortcoming of ‘explosion of terms’, the dynamic surface control technique that employs a group of first‐order low‐pass filters is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input‐to‐state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite‐time disturbance observer that estimates the disturbance term in a finite‐time. The properties of the composite control system are analyzed theoretically. Furthermore, by exploiting the cascaded structure of the control system, a simplified robust controller is proposed where only the first subsystem employs a disturbance observer. The performance of the proposed methods is confirmed by numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.     

Adaptive fault‐tolerant spacecraft attitude control using a novel integral terminal sliding mode

The attitude tracking of a rigid spacecraft is approached in the presence of uncertain inertias, unknown disturbances, and sudden actuator faults. First, a novel integral terminal sliding mode (ITSM) is designed such that the sliding motion realizes the action of a quaternion‐based nonlinear proportional‐derivative controller. More precisely, on the ITSM, the attitude dynamics behave equivalently to an uncertainty‐free system, and finite‐time convergence of the tracking error is achieved almost globally. A basic ITSM controller is then designed to ensure the ITSM from onset when an upper bound on the system uncertainties is known. Further, to remove this requirement, adaptive techniques are employed to compensate for the uncertainties, and the resultant adaptive ITSM controller stabilizes the system states to a small neighborhood around the sliding surface in finite time. The proposed schemes avoid the singularity intrinsic to terminal sliding mode‐based controllers and the unwinding phenomenon associated with some quaternion‐based controllers. Numerical examples demonstrate the advantageous features of the proposed algorithm. Copyright © 2017 John Wiley & Sons, Ltd.