Attitude Control Law Research Articles

Quaternion-based adaptive attitude control of asteroid-orbiting spacecraft via immersion and invariance

The design of an attitude control system for an asteroid-orbiting satellite via immersion and invariance is the subject of this paper. It is assumed that the asteroid is rotating with a constant rate, and that the inertia parameters of the satellite and the coefficients in the spherical harmonic gravitational potential of the asteroid are not known. The objective is to regulate the quaternion trajectory of the satellite orbiting in an equatorial orbit. Based on the immersion and invariance (I&I) theory, a noncertainty-equivalence adaptive (NCEA) attitude control law is derived. For the design, a backstepping design process involving two steps is used, and filtered signals are constructed to overcome the difficulty in solving certain matrix inequalities of the I&I methodology. The control law includes a stabilizer and an identifier - designed separately. Unlike the classical certainty-equivalence adaptive (CEA) systems, here the estimated parameters include not only the signals obtained from an integral type update law, but also judiciously chosen nonlinear algebraic signals that yield stronger stability properties. By the Lyapunov stability analysis, it is shown that the quaternion trajectories of the disturbance input-free closed-loop system asymptotically converge to the equilibrium point. The control law is effective in regulating the attitude to the equilibrium point with minimal rotation of spacecraft. Also, for the model with disturbance input, uniform ultimate boundedness of system trajectories is established. Simulation results for the attitude control of spacecraft in orbit around asteroid 433 Eros are presented for illustration. These results show that the spacecraft achieves nadir pointing attitude despite uncertainties in the system dynamics.

Faster Fixed-Time Control of Flexible Spacecraft Attitude Stabilization

The rapid attitude stabilization problem of flexible spacecraft with uncertain inertia and disturbances is investigated. In this article, a sliding mode-based fixed-time control approach is presented with a new fixed-time surface ensuring a faster convergence rate incorporated. This surface has no singularity and can guarantee the settling time to be independent of initial states. An adaptive fixed-time attitude control law is then synthesized, which is continuous and chattering free. It is rigorously proved that the states of the spacecraft attitude system can converge into a small neighborhood after fixed time. A numerical example is presented to validate that the designed scheme is efficient to perform attitude stabilization maneuvers rapidly, whereas high control accuracy is still provided.

Event-triggered backstepping control for attitude stabilization of spacecraft

To decrease the communication frequency between the controller and the actuator, this paper addresses the spacecraft attitude control problem by adopting the event-triggered strategy. First of all, a backstepping-based inverse optimal attitude control law is proposed, where both the virtual control law and the actual control law are respectively optimal with respect to certain cost functionals. Then, an event-triggered scheme is proposed to realize the obtained inverse optimal attitude control law. By designing the event triggering mechanism elaborately, it is guaranteed that the trivial solution of the closed-loop system is globally exponentially stable and there is no Zeno phenomenon in the closed-loop system. Further, the obtained event-triggered attitude control law is modified and extended to the more general case when the disturbance torque cannot be ignored. It is proved that all states of the closed-loop system are bounded, the attitude error can be made arbitrarily small ultimately by choosing appropriate design parameters and the Zeno phenomenon is excluded in the closed-loop system. In the proposed event-triggered attitude control approaches, the control signal transmitted from the controller to the actuator is only updated at the triggered time instant when the accumulated error exceeds the threshold defined elaborately. Simulation results show that by using the proposed event-triggered attitude control approach, the communication burden can be significantly reduced compared with the traditional spacecraft control schemes realized in the time-triggered way.

Flight control of a hexa-rotor airship: Uncertainty quantification for a range of temperature and pressure conditions

The present paper is concerned with the dynamic modeling and design of control laws for a small non-rigid multi-rotor airship constituted of an oblate-spheroid helium balloon coupled with an electric-powered hexa-rotor airframe. The vehicle is assumed to operate in windless and low-speed conditions. A six-degree-of-freedom nonlinear dynamic model is derived for it using the Newton–Euler approach and considering, among other efforts, a restoring torque due to the displacement of the balloon’s center of buoyancy above the vehicle’s center of mass and the added-mass effect resulting from the air–structure interaction. Using the derived model and assuming a time-scale separation between the translational and rotational dynamics, the attitude and position control laws are designed separately from each other. Both laws are formulated using feedback linearization combined with control input saturation within appropriate parallelepipedal sets, which are carefully chosen to respect pre-defined bounds on the control torque, control force and maximum inclination angle. The effect of temperature and pressure fluctuations is taken into account through a parametric probabilistic approach, where Maximum Entropy Principle is used to construct a physically consistent stochastic model and Monte Carlo method is used as the stochastic solver to propagate the uncertainties through the system. Extensive simulation results show the effectiveness of the proposed control system and quantify the uncertainty of its performance over a wide range of local temperature and pressure.

Attitude Stabilization of Tug–Towed Space Target by Thrust Regulation in Orbital Transfer

This paper studies the stability control of a target towed by a space-tug via a tether in orbital transfer. The attitude of the towed target is controlled by thrust regulation at the tug with the consideration of the coupling effect between the attitudes of the tug and towed target and the motion of the flexible and elastic tether. A model-based control scheme is proposed, where the tug and towed target are assumed as rigid bodies and the tether is approximated as a series of extensible but incompressible rods connected by spherical hinges. The governing equations of motion of the coupled rigid–flexible multibody system are derived based on the recursive dynamics algorithm. The attitude motion of the tug with the presence of tether tension disturbance is controlled by a simple proportional–derivative torque controller. The attitude motion of the towed target and the elongation oscillation of the tether are stabilized simultaneously via the tether tension by regulating the thrust at the tug. The thrust control is achieved by first designing an optimal trajectory considering the system constraints based on a reference model, and then the trajectory is tracked by a robust global terminal sliding-mode controller with the consideration of thrust saturation and tether slackness avoidance. Finally, numerical simulation is carried out to demonstrate the effectiveness of the proposed attitude control law based on the thrust regulation.

Dynamic Control Allocation through Kalman Filtering

Control Allocation (CA) in aviation is the problem of distributing the commands among the available actuation means, in order to ensure the achievements of the moments requested by the flight control laws. CA plays a key role in fault-tolerant control systems since it gives robust performances and stability also in presence of faults to one or more aircraft actuators. In this study, a new algorithm is proposed for Control Allocation under both static and dynamic constraints. The proposed algorithm aims at overcoming the most common limitations of the existing algorithms, most of which do not account for actuator dynamics (i.e. they compute a control command that might not be compatible with aircraft performance limitations) and rely on iterative methods. The proposed approach does not need an iterative procedure because it rearranges the CA as a state observer problem in which observer states are the actual commands to actuators and observer measurements are the requested moments by the flight control laws. The observer is implemented through a Kalman Filter (KF), with the actuator dynamics as process model and the algebraic relationships between moments and commands as measurement model. The effectiveness of the proposed CA strategy has been shown through a numerical analysis. The numerical simulations showed that the control commands computed by Control Allocation algorithms guarantee moments that match the ones requested by the attitude control laws. This has been verified in nominal conditions (i.e. no actuator faults) but also in faulty ones, where one or more actuators are subject to malfunctioning and, furthermore, in simulations scenarios in which aggressive maneuvers led to the saturation of one or more control surfaces.

Tube-based Model Predictive Control for Dynamic Positioning of Marine Vessels

This paper focuses on the design of a robust model predictive control law for dynamic positioning (DP) of marine vessels in the presence of actuator saturation and environmental disturbances. The proposed solution is a tube-based MPC ensuring robustness and constraint fulfillment. Formulation of the tube-based MPC relies on a sufficient robust invariant set condition, along with a linear matrix inequality (LMI) synthesis procedure, and an efficient analytical Pontryagin set difference computation. Simulation results show the effectiveness and satisfactory behaviour of the proposed controller.

Switching disturbance rejection attitude control of near space vehicles with variable structure

A switching disturbance rejection attitude control law is proposed for a near space vehicle (NSV) with variable structure. The multiple flight modes, system uncertainties and disturbances of the NSV are taken into account based on switched nonlinear systems. Compared with traditional backstepping design methods, the proposed method utilizes the added integrals of attitude angle and angular rate tracking errors to further decrease the tracking errors. Moreover, to reduce the computation complexity, a rapid convergent differentiator is employed to obtain the derivative of the virtual control command. Finally, for disturbance rejection, based on the idea from the extended state observer (ESO), two disturbance observers are designed by using non-smooth functions to estimate the disturbances in the switched nonlinear systems. All signals of the closed-loop system are proven to be uniformly ultimately bounded under the Lyapunov function framework. Simulation results demonstrate the effectiveness of the proposed control scheme.

An enhanced anti-disturbance attitude control law for flexible spacecrafts subject to multiple disturbances

As well-known disturbance rejection methods, active disturbance rejection control and disturbance observer-based control can effectively improve the control performances of complex systems in the presence of disturbances. However, the accurate rejection of multiple disturbances for control systems of practical engineering, for example, the attitude control system of flexible spacecraft, is still a bottleneck problem. In order to further improve the anti-disturbance capability and reduce the conservativeness, this paper proposes a novel enhanced anti-disturbance control law for the attitude control system of flexible spacecraft by combining active disturbance rejection control and disturbance observer-based control in a unified framework. More specifically, the disturbance from flexible vibration is described by an uncertain exogenous system based on the partially known information including elastic damping ratios and modal frequencies. The disturbance observer-based control is utilized to estimate and thereby reject this disturbance. On the other hand, the other disturbances such as external environmental disturbance and complex model nonlinearity are merged into a equivalent disturbance with bounded derivative, which is compensated by using the active disturbance rejection control law. Stability and robustness analysis are carried out for the disturbance observer and extended state observer. Finally, simulation results of low-earth-orbit flexible satellite are presented to verify the effectiveness of proposed methods.

Event-triggered fault tolerant control for spacecraft formation attitude synchronization with limited data communication

This paper investigates the leader-following attitude consensus problem of a group of n-th spacecrafts with actuator fault and limited data communication, where the event-triggered based sending mechanism is considered to decrease communication burthen. In this design, unknown actuator faults and external disturbances are considered, and an event-triggered based adaptive distributed cooperative attitude control law is developed to solve the multiple spacecrafts formation control problem. It is shown that leader-following attitude synchronization can be achieved under the designed event-triggered control law. Finally, a simulation example is provided to illustrate the effectiveness of the proposed attitude coordination control techniques.

Tilt-Prioritized Quadrocopter Attitude Control

This paper presents an attitude tracking control law and control allocation strategy for quadrocopters which prioritizes the vehicle’s ability to achieve a desired translational acceleration. The quadrocopter’s attitude error is split into a reduced attitude error, which describes the misalignment of the thrust direction, and a yaw error, which describes the orientation error about the thrust direction. A model-based proportional–derivative control law is derived, where the proportional action is in terms of the reduced attitude and yaw errors, and the derivative action is in terms of the quadrocopter’s angular velocity error. Almost global asymptotic convergence of the reduced attitude error is established, and the convergence of the yaw error is proven. It is further shown that the attitude control law decouples the reduced attitude error dynamics from the yaw error dynamics. A control allocation strategy is derived which exploits the decoupling in order to prioritize the correction of the reduced attitude over the yaw error. The proposed control strategy is computationally lightweight and therefore well-suited to run on board quadrocopters at high rates. Experimental results demonstrate improved error recovery and position tracking performance.

High-Accuracy Position Control of a Rotary Pneumatic Actuator

Rotary pneumatic actuators provide several advantages over electromechanical actuators (e.g., higher power-to-weight ratio, lower cost, and inherent safety) but are generally inferior in terms of accuracy and robustness when closed-loop position controlled. This paper presents the modeling, controller design, and experimental verification of a high-accuracy position-controlled rotary pneumatic actuator. A novel inverse valve model enables the development of a fast and precise inner-loop pressure control law. The outer-loop position control law combines feedback with model-based feedforward terms, including an adaptive friction compensator. The robust stability of the inner and outer subsystems is analyzed. Experimental results are included for rotating an arm in the vertical plane. The hardware features low-cost ON / OFF solenoid valves and low-cost pressure sensors. For a multiple cycloidal reference trajectory covering a 90° range, the root-mean-square error (RMSE) averaged over five tests was 0.156°. Steady-state errors less than or equal to 0.0045° were achieved for these moves and for moves as small as 0.045°. Robustness to unknown payloads was achieved using an improved payload estimator. For example, for a payload 53% less than nominal, the RMSE with the estimator was 75% less than without it. The experimental results are superior to those reported in the prior literature.

Multi-objective optimal design of flexible-joint parallel robot

PurposeThis paper aims to present the optimal design procedure of a symmetrical 2-DOF parallel planar robot with flexible joints by considering several performance criteria based on the workspace size, dynamic dexterity and energy of the control.Design/methodology/approachConsequently, the optimal design consists in determining the dimensional parameters to maximize the size of the workspace, maximize the dynamic dexterity and minimize the energy of the control action. The design criteria are derived from the kinematics, dynamics, elastodynamics and the position control law of the robot. The analysis of the design criteria is performed by means of the design space and atlases.FindingsFinally, the multi-objective design optimization derived from the optimal design procedure is solved by using multi-objective genetic algorithms, and the results are analyzed to assess the validity of the proposed approach.Originality/valueAn alternative approach to the design of a planar parallel robot with flexible joints that permits determining the structural parameters by considering kinematic, dynamic and control operational performance.

Rigid-flexible coupling dynamic modeling and vibration control for flexible spacecraft based on its global analytical modes

In this study, we used global analytical modeswfny (GAMs) to develop a rigid-flexible dynamic modeling approach for spacecraft with large flexible appendages (SwLFA). This approach enables the convenient and precise calculation of the natural characteristics for designing an attitude control law for the spacecraft while simultaneously suppressing the active vibration of its flexible appendages. We simplify the flexible spacecraft as a rigid-flexible coupling hub-beam system with tip mass and derive the system’s governing equations of motion based on Hamilton’s principle. By solving the linearized form of those equations with their associated boundary conditions, we obtain the frequencies as well as the corresponding GAMs of flexible spacecraft, which we use to discretize the equations of motion. Using this approach, we performed numerical simulations to investigate the system’s global modes and assess the performance of the controller based on the GAM model. The results reveal that the GAM model can be used to directly calculate the exact global modes of SwLFAs and that the controller based on the discrete GAM model can achieve a control-index for a SwLFA in a shorter time with less input energy than other methods.

Extended state observer-based third-order sliding mode finite-time attitude tracking controller for rigid spacecraft

In this paper, the attitude tracking control problem for a rigid spacecraft in the presence of systemparameter uncertainties and external disturbances is addressed. First, a new nonsingular finite-time sliding surface is introduced and third-order sliding mode finite-time attitude control law is designed to achieve precise accurate tracking responses and robustness against inertia uncertainties and external disturbances.The stability of the closed-loop system is rigorously proved using the Lyapunov stability theory.Then, a new finite-time extended state observer is established to estimate total disturbances of the system.The extended stated observer-based sliding mode control technique yields improved disturbance rejection and high-precision attitude tracking. Moreover, this control law can avoid the unwinding phenomenon and overcome the input saturation constraint by introducing an auxiliary variable to compensate for the overshooting.A Lyapunov based analysis is provided to guarantee sufficiently small observation error and stabilization of the closed-loop system in finite time. Numerical simulations are conducted to verify the effectiveness of the proposed control method.

Rotorcraft with a 3DOF Rigid Manipulator: Quaternion-based Modeling and Real-time Control Tolerant to Multi-body Couplings

This paper proposes a simple solution for the stabilization of a mini-quadcopter carrying a 3DoF (degrees of freedom) manipulator robot in order to enhance its achievable workspace and application profile. Since the motion of the arm induces torques which degrade the stability of the system, in the present work, we consider the stabilization of both subsystems: the quadcopter and the robotic arm. The mathematical model of the system is based on quaternions. Likewise, an attitude control law consisting of a bounded quaternion-based feedback stabilizes the quadcopter to a desired attitude while the arm is evolving. The next stage is the translational dynamics which is simplified for control (nonlinear) design purposes. The aforementioned controllers are based on saturation functions whose stability is explicitly proved in the Lyapunov sense. Finally, experimental results and a statistical study validate the proposed control strategy.

Fractional-order controllers optimized via heterogeneous comprehensive learning pigeon-inspired optimization for autonomous aerial refueling hose–drogue system

Dynamic modeling and control system design for the hose–drogue system (HDS) in the docking stage of autonomous aerial refueling (AAR) are investigated in this paper. The dynamics and kinematics of hose are modeled via a finite-segment multi-body method, which describes the hose–drogue assembly as a link-connected system. A controllable drogue is connected to the hose for automatically stabilizing the drogue's relative position under the influences of tanker trailing vortex, receiver bow wave, atmospheric turbulence, gust, and wind shear. Thus, a drogue position control law based on fractional-order method is designed to resist the multi-wind disturbances. Noting that it is difficult to tune the parameters of fractional-order controller (FOC), a modified pigeon-inspired optimization (PIO), the hybrid of heterogeneous comprehensive learning strategy and PIO (HCLPIO), is carried out to optimize the parameters of FOC. The simulation results show that the proposed optimized fractional-order feedback controllers effectively stabilize the controllable drogue to swing within an acceptable range.

Anti-disturbance attitude control of combined spacecraft with enhanced control allocation scheme

In this paper, we propose a novel anti-disturbance attitude control law for combined spacecraft with an improved closed-loop control allocation scheme. More specifically, a saturated approach is adopted to guarantee the global asymptotic stability under control input saturation. To enhance the robustness of the system, a nonlinear disturbance observer is constructed to compensate the disturbances caused by inertial parameter uncertainty and unmodeled dynamics. Next, the quadratic programming algorithm is used to obtain an optimal open-loop control allocation scheme, where both energy consumption and actuator saturation have been considered in the allocation of the virtual control command. Then, a modified closed-loop control allocation scheme is proposed to reduce the allocation error under the actuator uncertainty. Finally, stability analysis of the closed-loop system with the proposed allocation scheme is provided. Simulation results confirm the effectiveness of the proposed control scheme.

Distributed Formation Control based on Orientation Alignment and Position Estimation

Formation control is studied for single-and double-integrators on the plane based on orientation alignment and position estimation. It is assumed that agents measure the relative positions of their neighbors with respect to their own local body-fixed reference frames without any common sense of orientation. The proposed control strategy consists of an orientation alignment, a position estimation, and a position control law. It is shown that the proposed control strategy allows the agents to achieve the desired formation if the interaction graph is uniformly connected and the orientation angles belong to an interval with arc length less than π.

Observer-based continuous finite-time attitude control for rigid–flexible coupling satellites

ABSTRACTIn this paper, a novel finite-time attitude control law is proposed for rigid–flexible coupling satellites in large angle manoeuver. First, the rigid–flexible coupling dynamic model is set up to reflect the coupling effect between the deformation of flexible appendages and the spatial movement of the rigid hub. Then an extended state observer (ESO) is designed to estimate and compensate the total perturbation including high-order flexible coupling terms, external disturbances and uncertain inertia. Following this, a continuous finite-time attitude controller is designed based on non-singular fast terminal sliding mode (NFTSM) and fast power reaching law, which is introduced to smooth the control input and eliminate the chattering. Numerical simulation is designed to verify the finite-time stability, high accuracy, disturbance rejectionand vibration damping of the proposed control scheme and then a ground experimental system is set to further test the controller's practicability.