Spacecraft Inertia Research Articles

Adaptive predefined-time precise anti-unwinding attitude control for a spacecraft with inertia uncertainty

This paper proposes an adaptive predefined-time accurate anti-unwinding attitude controller for a spacecraft with uncertain inertia. The novelty of the proposed algorithm lies in that the spacecraft attitude error is regulated to exact zero after a predefined settling time, which is an explicit parameter in the control algorithm. A time mapping function containing the predefined settling time is introduced, thus transforming the time scale of the original attitude control system. Then a composite barrier Lyapunov function is constructed to avoid the unwinding phenomenon in the attitude control process, and an adaptive backstepping attitude controller is designed based on the attitude system in the new time scale. The stability analysis of the attitude system is carried out based on LaSalle-Yoshizawa theorem, and it is proved that the attitude quaternion and angular rate can converge to zero accurately within the desired predefined time without using the spacecraft inertia information. Numerical simulation results show the effectiveness and superiority of the proposed controller.

Spacecraft attitude control based on generalised dynamic inversion with adaptive neural network

AbstractThis paper proposes a robust generalised dynamic inversion (GDI) control system design with adaptive neural network (NN) estimation for spacecraft attitude tracking under the absence of knowledge of the spacecraft inertia parameters. The robust GDI control system works to enforce attitude tracking, and the adaptive NN augmentation compensates for the lack of knowledge of the spacecraft inertia parameters. The baseline GDI control law consists of a particular part and an auxiliary part. The particular part of the GDI control law works to realise a desired attitude dynamics of the spacecraft, and the auxiliary part works for finite-time stabilisation of the spacecraft angular velocity. Robustness against modeling uncertainties and external disturbances is provided by augmenting a siding mode control element within the particular part of the GDI control law. The singularity that accompanies GDI control is avoided by modifying the Moore-Penrose generalised inverse by means of a dynamic scaling factor. The NN weighting matrices are updated adaptively through a control Lyapunov function. A detailed stability analysis shows that the closed loop system is semi-global practically stable. For performance assessment, a spacecraft model is developed, and GDI-NN control is investigated for its attitude control problem through numerical simulations. Simulation results reveal the efficacy, robustness and adaptive attributes of proposed GDI-NN control for its application to spacecraft attitude control.

Coordinated Attitude Control of Spacecraft Formation Flying via Fixed-Time Estimators under a Directed Graph

This paper mainly studies the distributed fixed-time coordinated attitude tracking control problem of spacecraft formation with a dynamic leader spacecraft under directed communication topology. Follower spacecraft cannot communicate directly with the leader spacecraft; therefore, in order to enable them to obtain the target attitude information, a fixed-time state estimator that can be applied to directed graphs is designed. Based on the estimators, a distributed fixed-time attitude tracking control law is proposed. The settling time of the fixed-time algorithm is only related to the parameters of the control law and independent of the initial state; thus, the proposed control law can reduce the influence of the dynamic leader attitude on the spacecraft formation-coordinated attitude tracking control system. Moreover, external disturbances and spacecraft inertia uncertainty were also considered in the design of the control law. The stability of the system was verified by Lyapunov stability theory, and the effectiveness of the control law was verified by numerical simulation.

Direct-Adaptive Nonlinear MPC for Spacecraft Near Asteroids

In this work, we propose a novel controller based on a simple adaptive controller methodology and model predictive control (MPC) to generate and track trajectories of a spacecraft in the vicinity of asteroids. The control formulation is based on using adaptive control as a feedback controller and MPC as a feed-forward controller. The spacecraft system model, asteroid shape and inertia are assumed to be unknown, with the exception of the estimated total mass and angular velocity of the asteroid. The MPC is used to generate feed-forward trajectories and control input using only the mass and angular velocity of the asteroid combined with obstacle avoidance constraints. However, since the control input from MPC is calculated using only an approximated model of the asteroid, it fails to control the spacecraft in the presence of disturbances due to the asteroid’s irregular gravitational field. Hence, we propose an adaptive controller in conjunction with MPC to handle unknown disturbances. The numerical results presented in this work show that the novel control system is able to handle unknown disturbances while generating and tracking sub-optimal trajectories better than adaptive control or MPC solely.

Spacecraft attitude control: Application of fine trajectory linearization control

One of the simplest and most popular methods to design a model-based controller for a nonlinear dynamic system is to apply linear control theories to the linearized model of the nonlinear system. For linearization, first-order Taylor series expansion is a straightforward and widely used method. Although the related linearization method is fairly simple, unfortunately, it causes an error in the linearized model, especially in highly nonlinear systems. Different strategies have been proposed to increase the robustness of linearization-based control methods against the linearization error. All of the methods somehow look at the linearization error as uncertainty or disturbance, which has to be rejected. Generally speaking, the lack of the linearization technique reduces the quality of control. One area in which quality and simplicity of control can be necessary is spacecraft attitude control. For the purpose of spacecraft attitude control, this paper improves a well-known trajectory linearization control (TLC) method as a simple and practical nonlinear trajectory tracking control method using an error-less, fine linearization technique. The modified TLC is then used to develop a control law for spacecraft attitude control with only three tunable control parameters and an approximation of the spacecraft inertia matrix. Finally, due to the elimination of uncertainty caused by the linearization error, in a simple way, the novel attitude controller leads to better performance in comparison with the traditional method. The superiority of the new approach is illustrated in numerical simulations.

Управляемый тензор инерции космического аппарата трансформируемой конструкции

A simplified model of a transformable spacecraft is considered, including a rod-type transformation mechanism with movable weights. The mechanism can be used to adapt the dynamic properties of the spacecraft to the environment or the operating conditions of on-board systems, for example, to counter the moments of external disturbances during attitude control and angular stabilization. By changing the position of the transformation mechanism, the spacecraft inertia tensor can be put in diagonal form, which makes it possible to exclude the force interconnections between the channels and to eliminate the constant component of the gravitational moment. For a simplified model of the transformation mechanism, we establish the analytical dependence of the components of the inertia tensor on the parameters determining the position of the transformation mechanism. It is shown that by adjusting the moving mass, which is 0.5% of the entire spacecraft mass, we obtain the spacecraft configuration that ensures the diagonality of the inertia tensor.

Agile Spacecraft Attitude Control: an Incremental Nonlinear Dynamic Inversion Approach

This paper presents an agile and robust spacecraft attitude tracking controller using the recently reformulated incremental nonlinear dynamic inversion (INDI). INDI is a combined model- and sensor-based control approach that only requires a control effectiveness model and measurements of the state and some of its derivatives, making a reduced dependency on exact system dynamics knowledge. The reformulated INDI allows a non-cascaded dynamic inversion control in terms of Modified Rodrigues Parameters (MRPs) where scheduling of the time-varying control effectiveness is done analytically. This way, the controller is only sensitive to parametric uncertainty of the augmented spacecraft inertia and its wheelset alignment. Moreover, we draw some parallels to time-delay control (TDC) —more familiar in the robotics community— which have been shown to be equivalent to the incremental formulation of proportional-integral-derivative (PID) control for second order nonlinear systems in controller canonical form. Simulation experiments for this particular problem demonstrate that INDI has similar nominal performance as TDC/PID control, but superior robust performance and stability.

Model-based FDI for Agile Spacecraft with Multiple Actuators Working Simultaneously

Current and future space missions require agile and reliable spacecraft capable of trailing and keeping the required attitude. Most of the agile spacecraft missions are near-Earth based but some are placed far away from Earth and its influence. One example of such missions is the Athena mission, which requires the spacecraft to perform fast and large-angle attitude slew manoeuvres. Such manoeuvres often imply simultaneous use of multiple actuators such as thrusters and reaction wheels (RWs). A fault in any of these actuators might lead to partial or full damage of sensitive spacecraft instruments. In this research project, a novel model-based Fault Detection and Isolation (FDI) strategy is proposed, which is able to detect and isolate various actuator faults, such as stuck-open/closed thruster, thruster leakage, loss of effectiveness of all thrusters, and change of RW friction torque due to change of Coulomb and/or viscosity factor. Moreover, the proposed FDI strategy is also able to detect and isolate faults affecting the RWs tachometer. The design of the FDI algorithm is based on a multiplicative extended Kalman filter, a generalised likelihood ratio thresholding of the residual signals, and a logic algorithm which unequivocally link the faults to the symptoms. The performance and robustness of the proposed FDI strategy are evaluated using Monte Carlo simulations and carefully defined FDI performance indices. In addition, the influence of faults’ magnitudes, times of fault occurrence, and uncertainties’ magnitudes on the FDI system performance are evaluated. Preliminary results suggest promising performance in terms of detection/isolation times, miss-detection/isolation rates, and false alarm rates. Also, uncertainties on the spacecraft inertia seem to have a negative impact on the FDI performance. In order to fully understand the research project presented here, graduate-level knowledge on rigid body dynamics and kinematics, control theory, and filters applied to estimation might be required. If any of these areas are not known by the reader, it is recommended to read some of the associated literature referenced in the bibliography.

Maximizing agility envelopes for reaction wheel spacecraft

Spacecraft agility is limited by the maximum torque that reaction wheels can provide. Therefore, a reaction wheel array is typically configured to maximize the inscribed sphere of the reaction wheel torque envelope. Agility is then determined by dividing the spherical torque by the maximum principal inertia. This industry standard approach can severely underestimate the true capability of an attitude control system. An agility envelope considers the reaction wheel torque envelope along with the spacecraft inertia tensor. The agility envelope can therefore be used as a means to quantify the conservatism associated with the standard approach in order to improve slew performance of a conventional attitude control system without the need for larger, more costly hardware or new control algorithms. This paper, presents a simple approach for constructing the agility envelope of a reaction wheel attitude control system. The agility envelope is applied to determine design curves for limits on angular acceleration and rate for maneuver design and for finding the reaction wheel skew angles that maximize agility for a given spacecraft configuration. A surprising result is the observation that maximizing the inscribed sphere of the reaction wheel torque envelope does not, in general, optimize agility.

Feedback slew algorithms for prolate spinners using Single–Thruster

A number of low-cost open-loop slew control algorithms have been developed for prolate spinning spacecraft using single-thruster actuation. Robustness analysis indicates that these algorithms have high sensitiveness over thruster firing time error, spacecraft inertia error, and especially spin rate perturbations. This paper proposed two novel feedback slew algorithms, Feedback Half-Cone and Feedback Sector-Arc Slew, built on the existing open-loop algorithms and they use attitude and angular velocity feedback to compensate the errors in knowledge of spin rate, without external torques. As presented, after the first thruster actuation initiate the spin-axis precession, the feedback slew algorithms take attitude and spin-rate feedback to estimate the angular momentum and predict the spin-axis attitude during the slew. These techniques contribute to improve the cancelation thrust impulse accuracy and reduce the final nutation error. Simulations for a Penetrator mission scenario validate these feedback algorithms and show their slew performance and robustness over the perturbations mentioned above. It is proved that the attitude feedback greatly improves the slew accuracy and robustness.

Nutation instability of spinning solid rocket motor spacecraft

The variation of mass, and moment of inertia of a spin-stabilized spacecraft leads to concern about the nutation instability. Here a careful analysis on the nutation instability is performed on a spacecraft propelled by solid rocket booster (SRB). The influences of specific solid propellant designs on transversal angular velocity are discussed. The results show that the typical SRB of End Burn suppresses the non-principal axial angular velocity. On the contrary, the frequently used SRB of Radial Burn could amplify the transversal angular velocity. The nutation instability caused by a design of Radial Burn could be remedied by the addition of End Burn at the same time based on the study of the combination design of both End Burn and Radial Burn. The analysis of the results proposes the design conception of how to control the nutation motion. The method is suitable to resolve the nutation instability of solid rocket motor with complex propellant patterns.

Reconfigurable spacecraft attitude takeover control in post-capture of target by space manipulators

Most current research on reconfigurable control system puts emphasis on reconfiguration for adapting to actuator failures. However, the reconfigurable control system is necessitated for spacecraft attitude takeover control in the application of capturing target spacecraft whose fuel is exhausted to extend its operational lifetime by supplying them propulsion, navigation and guidance services. In this scenario, the capture of target spacecraft by space manipulators will cause a large shift in the dynamics of the service spacecraft. Not only do the mass properties change, but also does the thruster configuration. The changes in the mass, center of mass and inertia of the combined spacecraft will cause changes in the equivalent force exerted by each thruster. In this paper, considering the changes of thruster configuration and the control reallocation, a reconfigurable control system is designed for spacecraft attitude takeover control in post-capture of target by space manipulators in order to adapt to changes in the mass properties. The unknown inertia properties of target spacecraft in the system constitute a formidable technical challenge for controller design. Therefore, a modified adaptive dynamic inverse controller is proposed to provide global asymptotic stability in the presence of model uncertainties and nonlinearities. Moreover, by the null-space intersections control reallocation method, the thrust forces of service spacecraft can be redistributed and satisfy some constraints. Numerical simulations validate the feasibility of reconfigurable spacecraft attitude takeover control with large center of mass shifts and unknown inertia properties.

Optimization of spatial turns of «AIST-2» small spacecraft on the basis of the principle of minimum control

The efficiency of using the principle of minimum control in solving the task of synthesizing the system of controlling a spacecraft spatial turn by arbitrarily set angles up to 180 degrees is analyzed, with the Aist-2 small spacecraft taken as an example. The tensor of inertia has the form of a diagonal matrix. Flywheels the rotors of which are parallel to the principal central axes of the spacecraft inertia are used as actuating devices of the system that controls motion round the center of masses. The control moment developed by each flywheel, is proportional to the angular acceleration of its rotor. The energy spent on the control, proportional to the sum of modules of angular accelerations of flywheel rotors is accepted as an index of the optimality of the spacecraft spatial turn. Euler dynamic equations are reduced to finite-difference recurrent relations to model unperturbed spacecraft motion around the center of masses. An auxiliary dynamic system is introduced the parameters of which are chosen on the basis of the solution of the task posed to use the principle of minimum control that ensures minimum costs of control. The results of mathematical modeling confirmed the efficiency of the proposed principle. In comparison with the traditional method of control (acceleration, motion at a constant angular velocity, braking) two-fold economy of electrical power is achieved.

Adaptive integral sliding mode control for spacecraft attitude tracking with actuator uncertainty

The attitude tracking of a rigid spacecraft with actuator uncertainties, such as actuator faults, alignment errors, and saturation constraints is examined. In addition, the unknown external disturbances and spacecraft inertia are also taken into consideration. A novel integral-terminal-sliding mode (ITSM), which is singularity free compared to traditional TSM, is designed such that the attitude tracking error converges to zero in finite time on the ITSM. An adaptive technique is then utilized to develop an adaptive ITSM controller (AITSMC), which achieves finite-time attitude tracking in the presence of some or all of the above uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

Using the inertia of spacecraft during landing to penetrate regoliths of the Solar System

The high inertia, i.e. high mass and low speed, of a landing spacecraft has the potential to drive a penetrometer into the subsurface without the need for a dedicated deployment mechanism, e.g., during Huygens landing on Titan. Such a method could complement focused subsurface exploration missions, particularly in the low gravity environments of comets and asteroids, as it is conducive to conducting surveys and to the deployment of sensor networks. We make full-scale laboratory simulations of a landing spacecraft with a penetrometer attached to its base plate. The tip design is based on that used in terrestrial Cone Penetration Testing (CPT) with a large enough shaft diameter to house instruments for analysing pristine subsurface material. Penetrometer measurements are made in a variety of regolith analogue materials and target compaction states. For comparison a copy of the ACC-E penetrometer from the Huygens mission to Titan is used. A test rig at the Open University is used and is operated over a range of speeds from 0.9 to 3ms−1 and under two gravitational accelerations.The penetrometer was found to be sensitive to the target’s compaction state with a high degree of repeatability. The penetrometer measurements also produced unique pressure profile shapes for each material. Measurements in limestone powder produced an exponential increase in pressure with depth possibly due to increasing compaction with depth. Measurements in sand produced an almost linear increase in pressure with depth. Iron powder produced significantly higher pressures than sand presumably due to the rough surface of the grains increasing the grain-grain friction. Impacts into foamglas produced with both ACC-E and the large penetrometer produced an initial increase in pressure followed by a leveling off as expected in a consolidated material. Measurements in sand suggest that the pressure on the tip is not significantly dependent on speed over the range tested, which suggests bearing strength equations could be applied to impact penetrometry in sand-like regoliths.In terms of performance we find the inertia of a landing spacecraft, with a mass of 100kg, is adequate to penetrate regoliths expected on the surface of Solar System bodies. Limestone powder, an analogue for a dusty surface, offered very little resistance allowing full penetration of the target container. Both iron powder, representing a stronger coarse grained regolith, and foamglas, representing a consolidated comet crust, could be penetrated to similar depths of around two to three tip diameters. Speed tests suggest a linear dependence of penetration depth on impact speed.

Attitude Control with Analytic Disturbance-Rejection Guarantee

Analytic formulas that guarantee a minimum level of disturbance-rejection performance are derived for a class of attitude control problems consisting of linear proportional-derivative quaternion feedback applied to a rigid-body spacecraft plant model. Specifically, a Lyapunov-based disturbance-rejection assessment tool is derived for a general class of perturbed nonlinear systems, and then it is specialized to the linear attitude control class. Although the tool accepts generic Lyapunov function candidates, this paper demonstrates that existing Lyapunov functions (that readily prove asymptotic stability for attitude control systems) are insufficiently parameterized for purposes of estimating disturbance-rejection capability via the proposed tool. In response to this shortcoming, two new Lyapunov functions are proposed, and they are evaluated in the context of two closed-form disturbance-rejection performance assessment algorithms. Both algorithms demonstrate that the magnitude of the allowable disturbance torque is proportional to 1) the magnitude of the allowable angular accuracy, 2) the square of the control bandwidth, and 3) the minimum eigenvalue of the spacecraft inertia matrix. Moreover, the constant of proportionality (coefficient of rejection) is shown to degrade gradually for larger angles, and it eventually goes to zero as the user-specified angular accuracy is increased to 180 deg (for a high-order Lyapunov function) and 12 deg (for a low-order quadratic Lyapunov function).

A novel single thruster control strategy for spacecraft attitude stabilization

Feasibility of achieving three axis attitude stabilization using a single thruster is explored in this paper. Torques are generated using a thruster orientation mechanism with which the thrust vector can be tilted on a two axis gimbal. A robust nonlinear control scheme is developed based on the nonlinear kinematic and dynamic equations of motion of a rigid body spacecraft in the presence of gravity gradient torque and external disturbances. The spacecraft, controlled using the proposed concept, constitutes an underactuated system (a system with fewer independent control inputs than degrees of freedom) with nonlinear dynamics. Moreover, using thruster gimbal angles as control inputs make the system non-affine (control terms appear nonlinearly in the state equation). This necessitates the control algorithms to be developed based on nonlinear control theory since linear control methods are not directly applicable. The stability conditions for the spacecraft attitude motion for robustness against uncertainties and disturbances are derived to establish the regions of asymptotic 3-axis attitude stabilization. Several numerical simulations are presented to demonstrate the efficacy of the proposed controller and validate the theoretical results. The control algorithm is shown to compensate for time-varying external disturbances including solar radiation pressure, aerodynamic forces, and magnetic disturbances; and uncertainties in the spacecraft inertia parameters. The numerical results also establish the robustness of the proposed control scheme to negate disturbances caused by orbit eccentricity.

Adaptive Spacecraft Attitude Tracking and Parameter Estimation with Actuator Uncertainties

This paper studied the attitude tracking control of a spacecraft using variable speed control moment gyros (VSCMGs) as the actuator. The dynamics of the spacecraft with uncertainties was established. These uncertainties included the moment of spacecraft inertia, the configuration of the VSCMGs, and the moment of the rotator inertia. To solve the problem, the uncertainties were classified into two types. Type I included installation misalignment angles and some part of the rotator inertia, which could impact the character of the output of the VSCMGs. The rest of the uncertainties were categorized as Type II, which could impact the response of the spacecraft attitude control. Different parameter estimation methods were designed for the uncertainties of the two types. For Type-I uncertainties, their relationship with the output-torque error was established based upon which the estimation of Type-I uncertainties was designed. Based on the Lyapunov theory, the estimation of Type-II uncertainties and the adaptive attitude tracking controller were proposed. In this way, the estimation value of Type-I uncertainties could achieve the actual value, and the impact of Type-II uncertainties imposed on the system could be counteracted by the proposed attitude controller. The simulation results showed that the proposed methods could reduce output torque errors. Therefore, attitude tracking performance would be improved.

Magnetic Control of Dual-Spin and Bias-Momentum Spacecraft

This paper examines simultaneous attitude control and momentum-wheel management of dual-spin and biasmomentum spacecraft using magnetic actuation. Transformations of variables are presented, leading to the derivation of control laws that yield proven stability and asymptotic convergence under appropriate assumptions on theEarth’smagneticfield. The results remain valid in the presence ofmagnetic torquer saturation. Furthermore, it is shown that for a spacecraft equipped with three orthogonal magnetic torquers, the control laws are tolerant to the failure of a single magnetic torquer in the case of a dual-spin spacecraft and tolerant to the failure of two magnetic torquers in the case of a bias-momentum spacecraft, provided that the remainingmagnetic torquer does not generate its dipolemoment parallel to themomentum-wheel spin axis.Additionally, the stability analyses show that the control laws remain stabilizing under the effects of control quantization. The theoretical results rely on the assumption that the spacecraft principal and body axes coincide. Robustness to uncertainties in the spacecraft inertia matrix and to disturbance torques are demonstrated with a numerical example.

L 2 disturbance attenuation control for input saturated spacecraft attitude stabilization without angular velocity measurements

This work explores a novel efficient and low-cost control scheme for rigid spacecraft attitude stabilization problem, in which the unavailability of angular velocity measurements is considered. The resulting controller is independent on spacecraft inertia parameters, and explicit accounts for control input saturation with angular velocity measurements eliminated. Moreover, the proposed control law allows L 2 gain of the closed-loop attitude system to be chosen arbitrarily small so as to achieve any level of L 2 disturbance attenuation. Numerical simulation results are also presented to highlight those highly desirable features.