Velocity-free attitude coordinated tracking control for spacecraft formation flying

This article investigates the velocity-free attitude coordinated tracking control scheme for a group of spacecraft with the assumption that the angular velocities of the formation members are not available in control feedback. Initially, an angular velocity observer is constructed based on each individual's attitude quarternion. Then, the distributed attitude coordinated control law is designed by using the observed states, in which adaptive control method is adopted to handle the external disturbances. Stability of the overall closed-loop system is analyzed theoretically, which shows the system trajectory converges to a small set around origin with fast convergence rate. Numerical simulations are performed to demonstrate fast convergence and improved tracking performance of the proposed control strategy.     

Relative position finite-time coordinated tracking control of spacecraft formation without velocity measurements

This paper investigates finite-time relative position coordinated tracking problem by output feedback for spacecraft formation flying without velocity measurement. By employing homogeneous system theory, a finite-time relative position coordinated tracking controller by state feedback is firstly developed, where the desired time-varying trajectory given in advance can be tracked by the formation. Then, to address the problem of lack of velocity measurements, a finite-time output feedback controller is proposed by involving a novel filter to recover unknown velocity information in a finite time. Rigorous proof shows that the proposed control law ensures global stability and guarantees the position of spacecraft formation to track a time-varying reference in finite time. Finally, simulation results are presented to illustrate the performance of the proposed controller.     

Observer-based prescribed performance attitude control for flexible spacecraft with actuator saturation

This paper investigates the prescribed performance attitude control problem for flexible spacecraft subject to external disturbances and actuator constraints. By using a new performance function and an error transformation, the attitude control system is transformed into an error system which will be kept bounded to ensure expected dynamic and steady-state responses. Compared with the commonly used performance function, the modified one has an explicit prespecified terminal time which determines the maximum convergence time of the attitude control system. A modal observer and a disturbance observer are designed to deal with the flexible vibration and disturbances, respectively. Furthermore, when considering actuator saturation, an improved control strategy is developed with an auxiliary system utilized to compensate the saturation. The stability of the closed-loop system is analyzed by Lyapunov theory. Simulation results show the effectiveness and performance of the proposed methods.     

Finite-time fault tolerant attitude stabilization control for rigid spacecraft

A sliding mode based finite-time control scheme is presented to address the problem of attitude stabilization for rigid spacecraft in the presence of actuator fault and external disturbances. More specifically, a nonlinear observer is first proposed to reconstruct the amplitude of actuator faults and external disturbances. It is proved that precise reconstruction with zero observer error is achieved in finite time. Then, together with the system states, the reconstructed information is used to synthesize a nonsingular terminal sliding mode attitude controller. The attitude and the angular velocity are asymptotically governed to zero with finite-time convergence. A numerical example is presented to demonstrate the effectiveness of the proposed scheme.     

Robust output feedback distributed model predictive control of networked systems with communication delays in the presence of disturbance

In this work, an output feedback cooperative distributed model predictive control is developed for a class of networked systems composed of interacting subsystems interconnected through their states, in which it handles bounded disturbances and time varying communication delays. A distributed buffer based prediction strategy is used to compensate bounded delays and predict those states, which are coupled between subsystems that their actual values may not available due to delays. In the design of robust distributed model predictive control, distributed moving horizon estimation is employed so that convergence and boundedness of the estimation error are ensured. Furthermore, robust exponential stability of the closed loop system is established. The effectiveness of the proposed method is illustrated using two interconnected continuous stirred tank reactors.     

Distributed finite-time tracking for a team of planar flexible spacecraft

The paper presents a distributed finite-time controller for multiple under-actuated spacecraft with flexible appendages to track a virtual leader with stationary states under an undirected communication graph. Each spacecraft of concern is simplified as a free-floating hub-beam system, which is an under-actuated Euler-Lagrange system by nature since only the hub is driven. In the undirected communication graph, it is assumed that only one spacecraft can receive the information from the virtual leader. A distributed finite-time control law is presented for such a multi-agent system. The closed-loop system is proven to converge to the desired states within a finite time via Lyapunov theory and homogeneous method. Finally, a comparison is made between the proposed controller and the PD controller to show the better performance of the proposed controller.     

Robust inertia-free attitude takeover control of postcapture combined spacecraft with guaranteed prescribed performance

In this paper, a robust inertia-free attitude takeover control scheme with guaranteed prescribed performance is investigated for postcapture combined spacecraft with consideration of unmeasurable states, unknown inertial property and external disturbance torque. Firstly, to estimate the unavailable angular velocity of combination accurately, a novel finite-time-convergent tracking differentiator is developed with a quite computationally achievable structure free from the unknown nonlinear dynamics of combined spacecraft. Then, a robust inertia-free prescribed performance control scheme is proposed, wherein, the transient and steady-state performance of combined spacecraft is first quantitatively studied by stabilizing the filtered attitude tracking errors. Compared with the existing works, the prominent advantage is that no parameter identifications and no neural or fuzzy nonlinear approximations are needed, which decreases the complexity of robust controller design dramatically. Moreover, the prescribed performance of combined spacecraft is guaranteed a priori without resorting to repeated regulations of the controller parameters. Finally, four illustrative examples are employed to validate the effectiveness of the proposed control scheme and tracking differentiator.     

A novel body frame based approach to aerospacecraft attitude tracking

In the common practice of designing an attitude tracker for an aerospacecraft, one transforms the Newton-Euler rotation equations to obtain the dynamic equations of some chosen inertial frame based attitude metrics, such as Euler angles and unit quaternions. A Lyapunov approach is then used to design a controller which ensures asymptotic convergence of the attitude to the desired orientation. Although this design methodology is pretty standard, it usually involves singularity-prone coordinate transformations which complicates the analysis process and controller design. A new, singularity free error feedback method is proposed in the paper to provide simple and intuitive stability analysis and controller synthesis. This new body frame based method utilizes the concept of Euleraxis and angles to generate the smallest error angles from a body frame perspective, without coordinate transformations. Global tracking convergence is illustrated with the use of a feedback linearizing PD tracker, a sliding mode controller, and a model reference adaptive controller. Experimental results are also obtained on a quadrotor platform with unknown system parameters and disturbances, using a boundary layer approximated sliding mode controller, a PIDD controller, and a unit sliding mode controller. Significant tracking quality is attained.     

Dual-quaternion based fault-tolerant control for spacecraft formation flying with finite-time convergence

Study results of developing control system for spacecraft formation proximity operations between a target and a chaser are presented. In particular, a coupled model using dual quaternion is employed to describe the proximity problem of spacecraft formation, and a nonlinear adaptive fault-tolerant feedback control law is developed to enable the chaser spacecraft to track the position and attitude of the target even though its actuator occurs fault. Multiple-task capability of the proposed control system is further demonstrated in the presence of disturbances and parametric uncertainties as well. In addition, the practical finite-time stability feature of the closed-loop system is guaranteed theoretically under the designed control law. Numerical simulation of the proposed method is presented to demonstrate the advantages with respect to interference suppression, fast tracking, fault tolerant and practical finite-time stability.     

A class of cooperative relay analysis of multi-agent systems with tracking number switching and time delays

This paper investigates a complicated class of cooperative tracking problems with time-varying number of tracking agents and communication time delays. During the entire tracking process, tracking agents are dynamically changing and the number is not fixed. This results in jumping of tracking errors and dynamic dimensions of the corresponding Laplacian matrices. Consequently, the stability analysis turns to be difficult especially when the effect of communication time delays is taken into consideration. In order to solve this issue, a new type of average Lyapunov function is constructed to compensate the unmatched dimensions of communication topologies over different time intervals. Generalized reciprocally convex Lemma and a more relaxed switched technique are employed to achieve a less conservative switched stability condition for the multi-agent system with variable tracking number and time delays. Finally, through a series of numerical simulations, the effectiveness and feasibility of derived results are verified. The relationship between maximum allowable communication time delays and various control parameters is obtained in a quantitative way.     

Output-feedback super-twisting control for line-of-sight angles tracking of non-cooperative target spacecraft

Without the line-of-sight (LOS) angles rate information, this paper investigates the LOS angles tracking problem of non-cooperative target in chaser’s body frame with the external disturbance force and torque via chaser’s control torque. By integrating with the attitude dynamics of the chaser, a novel coupled LOS-based relative motion model is firstly established, which reveals the redundancy relationship between the LOS angles motion with two Degree-of-Freedom (DOF) and three dimensional control torque. More specially, the LOS angles tracking control problem is formulated as an output-feedback control problem of an uncertain nonlinear system with the actuator redundancy. As a stepping-stone, a fourth order high order sliding mode observer (HOSMO) is proposed to estimate the system state and uncertain terms. A combination of modified super twisting algorithm (STA) with nonsingular fast terminal sliding mode (NFTSM) and control allocation is proposed, the main novelty of modified STA is that the NFTSM is introduced to replace the linear sliding mode (LSM), and the original STA cannot be applied directly, a modified STA is proposed, which can guarantee the fast finite-time convergence. Finally, simulations are conducted to show fine performance of the proposed control scheme.     

Adaptive neural network based position tracking control for Dual-master/Single-slave teleoperation system under communication constant time delays

The novel trajectory tracking control strategies for trilateral teleoperation systems with Dual-master/Single-slave robot manipulators under communication constant time delays are proposed in this article. By incorporating this design technique into the neural network (NN) based adaptive control framework, two controllers are designed for the trilateral teleoperation systems in free motion. First, with acceleration measurements, an adaptive controller under the synchronization variables containing the position and velocity error is constructed to guarantee the position and velocity tracking errors between the trilateral teleoperation systems asymptotically converge to zero. Second, without acceleration measurements, an adaptive controller under the new synchronization variables is presented such that the trilateral teleoperation systems can obtain the same trajectory tracking performance as the first controller. Third, in term of establishing suitable Lyapunov–Krasovskii functionals, the asymptotic tracking performances of the trilateral teleoperation systems can be derived independent of the communication constant time delays. Moreover, these two controllers are obtained without the knowledge of upper bounds of the NN approximation errors, respectively. Finally, simulation results are presented to demonstrate the validity of the proposed methods.     

An attitude determination algorithm for a spacecraft using nonlinear filter

In this paper, the algorithm for a real time attitude estimation of a spacecraft motion is investigated. The proposed algorithm for attitude estimation is the second order nonlinear filter form not containing truncation error in estimation values. The proposed second order nonlinear filter has improved performance compared with the EKF (extended Kalman filter), because the algorithm does not contain any truncation bias and covariance of the estimator is compensated by the nonlinear terms of the system. Therefore, the proposed second order nonlinear filter is a suboptimal estimator. However, the proposed estimator requires a lot of computation because of an inherent nonlinearity and complexity of the system model. For more efficient computation, this paper introduces a new attitude estimation algorithm using the state divided technique for a real time processing which is developed to provide an accurate attitude determination capability under a highly maneuverable dynamic environment. To compare the performance of the proposed algorithm with the EKF, simulations have been performed with various initial values and measurement covariances. Simulation results show that the proposed second order nonlinear algorithm outperforms the EKF. The proposed algorithm is useful for a real time attitude estimation since it has better accuracy compared with the EKF and requires less computing time compared with any existing nonlinear filters.     

Robust fault-tolerant tracking control design for spacecraft under control input saturation

In this paper, a continuous globally stable tracking control algorithm is proposed for a spacecraft in the presence of unknown actuator failure, control input saturation, uncertainty in inertial matrix and external disturbances. The design method is based on variable structure control and has the following properties: (1) fast and accurate response in the presence of bounded disturbances; (2) robust to the partial loss of actuator effectiveness; (3) explicit consideration of control input saturation; and (4) robust to uncertainty in inertial matrix. In contrast to traditional fault-tolerant control methods, the proposed controller does not require knowledge of the actuator faults and is implemented without explicit fault detection and isolation processes. In the proposed controller a single parameter is adjusted dynamically in such a way that it is possible to prove that both attitude and angular velocity errors will tend to zero asymptotically. The stability proof is based on a Lyapunov analysis and the properties of the singularity free quaternion representation of spacecraft dynamics. Results of numerical simulations state that the proposed controller is successful in achieving high attitude performance in the presence of external disturbances, actuator failures, and control input saturation.     

Rotation matrix based finite-time attitude synchronization control for spacecraft with external disturbances

This paper investigates the anti-unwinding finite-time attitude synchronization control problem for Spacecraft formation flying with external disturbances. Two finite-time controllers are designed based on rotation matrix and terminal sliding mode method. By designing a novel sliding mode surface, the first controller is developed when the upper bound of the external disturbances can be exactly known. However, this value is not always available in reality. In addition, the direct use of the upper bound of the external disturbances can result in the chattering problem. For the purpose of overcoming the disadvantage of the first controller, a modified control law is proposed, in which the adaptive law is applied to estimate the unknown value online. Theoretical analysis and numerical simulations are presented to demonstrate the validity of the proposed controllers.     

Adaptive fast sliding mode fault tolerant control integrated with disturbance observer for spacecraft attitude stabilization system

In this paper, the problem of fault-tolerant control (FTC) for spacecraft attitude stabilization system with actuator fault and mismatched disturbance is investigated. A novel fault tolerant control strategy based on adaptive fast terminal sliding mode control (AFTSMC) is proposed. Firstly, a novel composite observer is proposed to estimate the disturbance, actuator efficiency factor and partial states of the system. By introducing a sliding mode observer, the bias actuator fault is reconstructed. Subsequently, in accordance with the estimated information, a novel sliding mode fault tolerant controller is designed. The proposed control scheme contains two compensators and two adaptive parameters to attenuate the mismatched disturbance, to compensate actuator fault, and to guarantee fast convergence of the system. Furthermore, the reachability of sliding motion is proved. The simulation results for the spacecraft system illustrate the effectiveness of the proposed method.     

非完整移动机器人领航-跟随编队分布式控制

针对非完整移动机器人运动学模型的特点,并且考虑机器人之间的交互关系是局部的,提出了一种基于领航-跟随的非完整多移动机器人分布式编队控制方法。首先提出了一种分布式估计策略,为每个跟随机器人估计(虚拟)领航机器人的位置、方向、线速度等状态;接着利用每个跟随机器人的跟踪误差设计了编队控制算法;使用Lyapunov工具对算法进行了渐近稳定性和收敛性分析;最后,构建了多移动机器人视觉定位与控制实验平台,通过仿真和实验验证了所提算法的有效性。     

Robust adaptive relative position and attitude control for spacecraft autonomous proximity

This paper provides new results of the dynamical modeling and controller designing for autonomous close proximity phase during rendezvous and docking in the presence of kinematic couplings and model uncertainties. A globally defined relative motion mechanical model for close proximity operations is introduced firstly. Then, in spite of the kinematic couplings and thrust misalignment between relative rotation and relative translation, robust adaptive relative position and relative attitude controllers are designed successively. Finally, stability of the overall system is proved that the relative position and relative attitude are uniformly ultimately bounded, and the size of the ultimate bound can be regulated small enough by control system parameters. Performance of the controlled overall system is demonstrated via a representative numerical example.     

Neural network disturbance observer-based distributed finite-time formation tracking control for multiple unmanned helicopters

The distributed finite-time formation tracking control problem for multiple unmanned helicopters is investigated in this paper. The control object is to maintain the positions of follower helicopters in formation with external interferences. The helicopter model is divided into a second order outer-loop subsystem and a second order inner-loop subsystem based on multiple-time scale features. Using radial basis function neural network (RBFNN) technique, we first propose a novel finite-time multivariable neural network disturbance observer (FMNNDO) to estimate the external disturbance and model uncertainty, where the neural network (NN) approximation errors can be dynamically compensated by adaptive law. Next, based on FMNNDO, a distributed finite-time formation tracking controller and a finite-time attitude tracking controller are designed using the nonsingular fast terminal sliding mode (NFTSM) method. In order to estimate the second derivative of the virtual desired attitude signal, a novel finite-time sliding mode integral filter is designed. Finally, Lyapunov analysis and multiple-time scale principle ensure the realization of control goal in finite-time. The effectiveness of the proposed FMNNDO and controllers are then verified by numerical simulations.     

Attitude maneuver control of flexible spacecraft by observer-based tracking control

A constraint equation-based control law design for large angle attitude maneuvers of flexible spacecraft is addressed in this paper. The tip displacement of the flexible spacecraft model is prescribed in the form of a constraint equation. The controller design is attempted in the way that the constraint equation is satisfied throughout the maneuver. The constraint equation leads to a two-point boundary value problem which needs backward and forward solution techniques to satisfy terminal constraints. An observer-based tracking control law takes the constraint equation as the input to the dynamic observer. The observer state is used in conjunction with the state feedback control law to have the actual system follow the observer dynamics. The observer-based tracking control law eventually turns into a stabilized system with inherent nature of robustness and disturbance rejection in LQR type control laws.