Gravity Gradient Torque Research Articles

Vibration-attitude integrated control of large membrane diffraction space telescope

The development of telescopes with large apertures is driven by the increasing demand for higher imaging resolution and coverage. Large membrane diffraction space telescopes are particularly attractive due to their lightweight nature, ease of folding and unfolding, and high-precision imaging capabilities. However, their substantial size and flexibility make them susceptible to long-duration, low-frequency vibrations during attitude maneuvers, which degrade attitude and imaging accuracy and risk instrument damage. Consequently, an urgent need exists for a high-precision integrated control scheme. In this paper, the integrated control of vibration and attitude in a large space telescope is studied using cable actuators and control moment gyroscopes (CMGs). Since cables can only withstand limited tension, the unilateral and constrained characteristics of the control input are taken into account during the control design process. Firstly, a rigid-flexible coupling dynamic model of the space telescope is established using the velocity variation principle with hybrid coordinates. Additionally, a two-body astrodynamic model is developed to assess the impact of gravity gradient torque. Next, combining the computational torque method and H∞ control theory, an integrated control scheme is proposed, which achieves vibration and attitude control during maneuvers. Then, this paper optimizes the cable actuator positions via the discrete particle swarm optimization (PSO) algorithm and plans various attitude maneuver paths. Finally, numerical simulations are adopted to demonstrate the effectiveness of the control scheme. The results show that this integrated control scheme swiftly suppresses structural vibrations during attitude maneuvers, enabling high-precision attitude control of the space telescope.

Optimal attitude planning along torque equilibrium points using aerodynamic database for deorbiting large space debris

Currently, considerable attention is being directed toward active debris removal (ADR) using small, cost-effective satellites. From high altitude to re-entry, ADR missions use thrusters that consume significant amounts of fuel. The volume of the propulsion system in these satellites can be quite large, and it is difficult for a small satellite to accommodate a large-scale propulsion system. Thus, active utilization of atmospheric drag is being considered for small satellites with low capability. However, the principal challenge for small satellites to remove large debris is to deal with the large disturbance torque caused by strong atmospheric drag on the debris. This paper proposes attitude guidance around an equilibrium (balance) point in attitude dynamics acted on by gravity gradient and aerodynamic torques. The desired attitude is set to optimize two conflicting objectives: maximizing the projection area to generate large aerodynamic force and minimizing the disturbance torque. In this paper, we develop an aerodynamic database (ADDB) by rigorously calculating the aerodynamic torque for each altitude and solar array paddle (SAP) rotation based on an aerodynamic characteristic model of free molecular flow. Using the ADDB, the SAP angle and orbit altitude effects on the torque equilibrium attitude (TEA) are clarified. Then, the mean disturbance torque map at each orbit altitude is introduced to obtain the candidate TEA paths. The effectiveness of the proposed paths for debris descent is demonstrated through numerical simulations.

Neuro-fuzzy system based proportional derivative gain optimized attitude control of CubeSat under LEO perturbations

Prompt attitude stabilization is more challenging in Nano CubeSat due to its minimal capacity, weight, energy, and volume-constrained architecture. Fixed gain non-adaptive classical proportional integral derivative control methodology is ineffective to provide optimal attitude stability in low earth orbit under significant environmental disturbances. Therefore, an artificial neural network with fuzzy inference design is developed in a simulation environment to control the angular velocity and quaternions of a CubeSat by autonomous gain tuning of the proportional-derivative controller according to space perturbations. It elucidates the dynamics and kinematics of the CubeSat attitude model with reaction wheels and low earth orbit disruptions, i.e., gravity gradient torque, atmospheric torque, solar radiation torque, and residual magnetic torque. The effectiveness of the proposed ANFIS-PD control scheme shows that the CubeSat retained the three-axis attitude controllability based on initial quaternions, the moment of inertia, Euler angle error, attitude angular rate, angular velocity rate as compared to PID, ANN, and RNN methodologies. Outcomes from the simulation indicated that the proposed controller scheme achieved minimum root mean square errors that lead towards rapid stability in roll, pitch, and yaw axis respectively within 20 s of simulation time.

Predefined‐time guaranteed performance attitude takeover control for non‐cooperative spacecraft with uncertainties

AbstractThis article addresses the predefined‐time guaranteed performance attitude tracking problem for takeover the non‐cooperative target spacecraft with model uncertainties, adversarial control torque and gravity gradient torque. Firstly, a novel prescribed performance function (NPPF) is exploited, and then a new non‐singular predefined‐time terminal sliding mode (NPTSM) surface with the transformed tracking error is constructed. Secondly, a non‐singular predefined‐time prescribed performance control (NPTPC) is designed to achieve the guaranteed performance within predefined‐time. It is proved that the proposed control can ensure that the attitude tracking error satisfies the prescribed performance boundaries all the time and converges to a preset small region centered around the equilibrium point within predefined time and then tends to the equilibrium point asymptotically. The appealing feature of the proposed control is predefined‐time stability with quantified transient performance and steady‐state accuracy. Simulations verify the effectiveness and improved performance of the proposed approach.

Constrained reaction wheel desaturation and attitude control of spacecraft with four reaction wheels

The paper addresses a problem of constrained spacecraft attitude stabilization with simultaneous reaction wheel (RW) desaturation. The spacecraft has a reaction wheel array (RWA) consisting of four RWs in a pyramidal configuration. The developments exploit a spacecraft dynamics model with gravity gradient torques. The linearized dynamics are shown to be controllable at almost all RWA configurations. Configurations that result in the highest Degree of Controllability are elucidated. A strategy that combines an incremental reference governor and time-distributed model predictive control is proposed to perform constrained RW desaturation at low computational cost. Simulation results of successful RW desaturation maneuvers subject to spacecraft pointing constraints, RW zero-speed crossing avoidance and limits on control moments are reported.

Validation and optimization of the GSAMQ analytical propagator for spin-stabilized satellite

The aim of this paper is to validate the analytical propagator through simulations comparing the results with the real data and to optimize the work's source code so that it is processed faster. This work analyzes the use of the quadrupole model in the Earth's magnetic field when an analytical propagator calculates eddy current and residual magnetic torques in spin-stabilized satellites. For that, the components of the gravity gradient torque, the solar radiation torque and aerodynamics torque are also included. The simulations are carried out for a predetermined period and use data from the SCD1 Brazilian satellite, provided by the National Institute for Space Research (INPE). The results are then compared with the real data to validate the propagator. The propagator with the quadrupole model is called GSAMQ and uses the mean deviations of the magnitude of the spin velocity, and the angles of right ascension and declination of the spin axis as evaluation parameters. A statistical approach is included in this analysis and shows the model's accuracy.

Attitude dynamics of satellites with variable shape mechanisms using atmospheric drag torque and gravity gradient torque

Disturbance torques, such as atmospheric drag torque and gravity gradient torque, have always been an issue in attitude control for satellites in low Earth orbit. Although attitude control systems using disturbance torques has been studied with various methods, most previous research has focused on attitude control using aerodynamic stability to remove disturbances. We propose a new attitude control system that actively uses disturbance torque. This system controls the attitude using disturbance torques by changing the equilibrium point of the attitude motion by changing the shape of the satellite. We formulate the attitude dynamics of a variable-shape satellite as a preliminary study. This paper shows that the satellite attitude can be adjusted by varying the equilibrium point of attitude motion by changing the satellite shape. Also, we investigate the stability around the equilibrium point for each shape, and the results show the distribution of the stability index and the equilibrium point for each shape. Finally, we show that the attitude asymptotically converges to an equilibrium point by using the variable shape function and magnetic control.

3D-printed, electrically conductive structures for magnetic attitude control

The use of embedded current loops for the attitude control of large, flexible spacecraft is investigated. Length-scaling laws are derived by determining what fraction of a planar spacecraft’s mass would need to be allocated to the conductive current loops in order to produce a torque at least as large as the gravity gradient torque. Simulations are then performed of a flexible truss structure, modelled as a spring–mass system, for a range of structural flexibilities and a variety of current loop geometries. Simulations demonstrate rotation of the structure via the electromagnetic force on the current carrying elements, and are also used to characterise the structural deformations caused by the various current loop geometries. An attitude control simulation is performed, demonstrating a 90∘ slew manoeuvre of a 250 × 250 m flexible structure through the use of three orthogonal sets of current loops embedded within the spacecraft.

Distributed magnetic attitude control for large space structures

The utility of distributed magnetic torque rods for the attitude control of a large space structure is investigated. Distributed arrays of actuators offer advantages such as distributing structural loads, increasing fault tolerance, allowing structures to be designed modularly, and additionally the actuators may be integrated with on-orbit fabrication strategies. First, distributed torques are shown to effectively rotate highly flexible structures. This is compared with torques applied to the centre-of-mass of the structure, which cause large surface deformations and can fail to enact a rotation. This is demonstrated using a spring–mass model of a planar structure with embedded actuators. A distributed torque algorithm is then developed to control an individually addressable array of actuators. Attitude control simulations are performed, using the array to control a large space structure, again modelled as a spring–mass system. The attitude control system is demonstrated to effectively detumble a representative 75 × 75 m flexible structure, and perform slew manoeuvres, in the presence of both gravity-gradient torques and a realistic magnetic field model.

Novel orbit-attitude combination mode for solar power satellites to reduce mass and fuel

Solar power satellite receives great attention because it can release the energy crisis and environmental problems in the future. However, the launch and maintenance costs are tremendous due to the large system mass and large fuel consumption to counteract space perturbations. To reduce mass and fuel, a novel quasi-Sun-pointing attitude in Sun-frozen orbit is proposed. The Sun-frozen orbit has a nonzero eccentricity vector that always points towards the Sun. The quasi-Sun-pointing attitude is a periodic solution of the Sun-pointing attitude angle. Although about 3 % electricity must be given up because of the variation of Sun-pointing attitude angle, little control action is required to deal with the solar radiation pressure and gravity-gradient torque. The algorithm to obtain initial conditions is proposed. The influences of system parameters and structural flexibilities are studied. Simulation results reveal that the quasi-Sun-pointing attitude in Sun-frozen orbit dramatically reduce fuel consumption, the dry mass, and complexity of the control system. In addition, structural vibration is hardly induced by the gravity-gradient torque. Thus, the bending stiffness as well as the mass of the supporting structure can be reduced.

Prescribed-time time-varying sliding mode based integrated translation and rotation control for spacecraft formation flying

<p style='text-indent:20px;'>This paper studies the prescribed-time spacecraft formation flying problem. The coupled 6-degrees-of-freedom kinematics and dynamics for spacecraft are modeled on Lie group SE(3), where the gravity-gradient torque, the perturbing forces caused by Earth's oblateness and unknown external disturbances are all taken into account. The relative configuration is expressed by using exponential coordinates of SE(3). In order to regulate the relative motion between the leader spacecraft and follower spacecraft, a novel prescribed-time control law is given based on a prescribed-time time-varying high-gain sliding mode method. Numerical simulations verify the effectiveness of the proposed control scheme.</p>

Structural process and testing of tunneling attitude sensor based on gravity gradient torque measurements

The function of determining the orientation of a satellite in orbit is known as attitude determination. Depending on the missions, this important function is typically performed by different optical instruments. Due to the limited field of view, multiple optical sensors are placed in all directions to ensure large coverage. A kind of inertial sensor that uses the gravity gradient torque as a reference for attitude determination was proposed recently. At present, the volume of this kind of sensors is large and the accuracy is not high enough. In this paper, we propose an attitude sensor, which is composed of a barbell-shaped sensitive structure with larger moment of inertia and a small displacement detection module based on the tunneling effect. The sensitive structure is fabricated by silicon-on-glass process based on micro-electro-mechanical system technology. As a result, the sensitive structure has a smaller size, and the accuracy of angle measurement can reach 7.3° (3σ) in the range of −20° to +20°.

Non-integrability of a model of elastic dumbbell satellite

We study the integrability of a model of elastic satellite whose centre of mass moves in a circular Keplerian orbit around a gravity centre. The satellite is modelled by two point masses connected by an extensible massless spring that obeys Hooke’s law. It is assumed that the distance between point masses is much smaller than the radius of the orbit, so the orbital motion of the satellite is not perturbed by its rotational motion. The gravity potential of the satellite is expanded into a series with respect to its size up to quadratic terms which describe the gravity gradient torque acting on the satellite. Two cases are considered with Hooke’s centre localised in the centre of mass of the dumbbell and at an arbitrary point along a line connecting both masses. It is shown that the first case appears to be integrable and super-integrable for selected values of the parameter of the system. In the second case, model depends effectively only on one parameter and is non-integrable. In the proof, differential Galois integrability obstructions are used. For the considered sysem, these obstructions are deduced thanks to the recently developed symplectic Kovacic’s algorithm in dimension 4. According to our knowledge, this is the first application of this tool to a physical model.

Adaptive torque equilibrium attitude guidance for rapid deorbit of space debris by aerodynamic drag considering model uncertainty

Currently, considerable research is directed toward active debris removal (ADR) in space, especially by small, cost-effective satellites. However, a drawback to effective ADR missions has been that they use thrusters to move from a high altitude for reentry, which consumes a great deal of fuel. Thus, the propulsion system for these satellites is quite large, so designing the propulsion system for a small satellite is quite difficult. This paper proposes a new guidance design based on the altitude-dependent mean torque equilibrium attitude (TEA) and centered on determining the equilibrium point in a satellite’s attitude dynamics with respect to aerodynamic and gravity gradient torques. To correct guidance errors, the adaptive TEA guidance technique learns the actuator inputs during one orbital revolution. The controller is designed to guarantee robustness against disturbances and modeling uncertainties. Finally, the proposed adaptive guidance system and the robust controller’s effectiveness are demonstrated through numerical simulations to enhance the feasibility of an ADR mission.

Roto-Translational Control of Spacecraft in Low Earth Orbit Using Environmental Forces and Torques

In this paper, relative orbit and attitude adaptive controllers are integrated to perform roto-translational maneuvers for CubeSats equipped with a Drag Maneuvering Device (DMD). The DMD enables the host CubeSat with modulation of aerodynamic forces/torques and gravity gradient torque. Adaptive controllers for independent orbital and attitude maneuvers are revisited to account for traslational-attitude coupling while compensating for uncertainty in parameters such as atmospheric density, drag/lift coefficients, location of the Center of Mass (CoM) and inertia matrix. Uniformly ultimately bounded convergence of the attitude error and relative orbit states is guaranteed by Lyapunov-based stability analysis for the integrated roto-translational maneuver. A simulation example of an along-track formation maneuver between two CubeSats with simultaneous attitude control using only environmental forces and torques is presented to validate the controller.

Attitude dynamics of a rigid body in Keplerian motion

This paper studies the attitude dynamics of a rigid body in a Keplerian orbit. We show that the use of Classical Rodrigues Parameters for the attitude motion of the rigid body subject to gravity-gradient torques enables us to characterize the equilibria associated with the rotational motion about its mass center. A parametric study of the stability of equilibria is conducted to show that large oscillations are induced due to the energy exchange between the pitch and roll–yaw motions, specifically near the 2:1 resonant commensurability regions. A visualization tool is developed to study these pitch oscillations and gain insight into the rigid body motion near internal resonance conditions. A measure of coupling between the pitching and roll–yaw motions is developed to quantify the energy exchange utilizing information from the state transition matrix.

Aerodynamic and gravity gradient based attitude control for CubeSats in the presence of environmental and spacecraft uncertainties

In this paper, the problem of controlling the attitude of a CubeSat in low Earth orbit using only the environmental torques is considered. The CubeSat is equipped with a Drag Maneuvering Device (DMD) that enables the spacecraft to modulate its experienced aerodynamic and gravity gradient torques. An adaptive controller is designed to achieve attitude tracking of the spacecraft in the presence of uncertain parameters such as the atmospheric density, drag and lift coefficients, and the time-varying location of the Center of Mass (CoM). The proposed controller also accounts for modeling inaccuracy of the inertia matrix of the spacecraft. A Lyapunov-based analysis is used to prove that the quaternion-based attitude trajectory tracking error is uniformly ultimately bounded. The designed controller is also examined through numerical simulations for a spacecraft with time-varying uncertain drag, lift coefficients and CoM location parameters and the NRLMSISE-00 model for the atmospheric density.

Rotation–translation coupling analysis on perturbed spacecraft relative translational motion

This paper explores an accurate and complete spacecraft six-degree-of-freedom coupled relative motion model using the dual quaternion representation. Based on this technique, we build a scheme capable of describing both kinematic and dynamic coupling effects on the spacecraft relative translational motion through a further combination with the chaser’s precise absolute translational and rotational dynamics. This new model generalizes the existing nonlinear spacecraft relative translational model to include both the kinematic coupling effect due to the displacements of selected feature points relative to the spacecraft centers of mass and the dynamic coupling effect induced by the gravity gradient torque and the orbital perturbations. Several numerical simulations are implemented to validate the feasibility of the proposed model, for analyzing both the kinematic and dynamic coupling effects, on the relative translational motion of two arbitrary feature points in either Keplerian or $$J_2$$ perturbed orbits. The results are further compared against the $$J_2$$ perturbation effect.

Design and development of prototype carpal wrist cold gas propulsion system for attitude control applications

In recent years, the Philippine space program has launched several small-scale satellites, and lately has commissioned its own space program. Research on improving the subsystems of these satellites would be beneficial to future space programs in the Philippines. This paper will detail the process of designing, validating, fabricating, and testing a prototype Carpal Wrist Cold Gas Propulsion System (CW-CGPS). By making use of a carpal wrist’s (CW) hemispherical movement capabilities, the sixteen thrusters could theoretically be replaced by four mounted on opposite ends. Optimization of the propulsion system is based on finding the nozzle design with the most adequate values for thrust, Mach number, and specific impulse while the CW design is validated when it can be calibrated to move as the program dictates. This study uses multiple programs to simulate and verify the design. The conditions of the testing environment are established by resources from international space organizations. Assembly and feasibility are assessed based on the results of the research. It was found that the final optimized system had a model torque of 0.247 N-m, more than enough to overcome the maximum combined influence of the gravity gradient torque of 2.34E-06 N-m and aerodynamic torque of 1.57E-25 N-m. The design, development, and test campaign for the thruster system is presented.

Attitude control of space solar power satellite with large range of relative motion among subsystems

The transmitting antenna needs to be oriented to the Earth, while the PV cell array of the SSPS-OMEGA system rotates in a large range inside the concentrator for the orientation to the Sun, so that there is a large range of unfixed relative movement among the subsystems. For the study of dynamic characteristics and attitude control problem of the space solar power satellite, the multi-body dynamics model of the system is built, and the gravity gradient torque equation applied on the PV cell array is derived in the process of relative motion. A simple attitude control system and the corresponding electric thrusters configuration scheme are designed. The simulation results show that the attitude of 2-GW SSPS-OMEGA in roll and yaw direction is well controlled. However, due to the large range rotation of the PV cell array, the attitude in the pitch direction is controlled to converge to the microwave beam pointing accuracy of mechanical adjustment in longer time with the residual gravity gradient torque. In the long period, the attitude deviation angle in the pitch direction would stabilize periodically within ±0.018 degree. This provides a reference for further study of beam-control of the transmitting antenna.