Spacecraft Dynamics Research Articles

Dynamics and control for spacecraft tracking a displaced orbit around an asteroid exploiting solar sail

This study investigates the displaced orbit around a near-Earth asteroid for spacecraft achieved via a realistic solar sail with a performance based on the existing technology in a low distance. Using the realistic solar sail to achieve the displaced orbit with a short displaced distance is more difficult compared with using a traditional thruster under two main limitations: The force limitation and the position limitation. Firstly, the solar radiation pressure (SRP) force generated by the solar sail is limited by the solar sail’s property and the sunlight direction. Therefore, the feasibility of maintaining a displaced orbit at an equilibrium point around the asteroid at a low distance using a solar sail with realistic performance is investigated analytically. The results demonstrate that the equilibrium point of the displaced orbit can be achieved. Secondly, the usage of the solar sail is also limited by the position of the spacecraft. The SRP force cannot be generated in the eclipse region wherein sunlight is absent; specifically, in a displaced orbit with a low displaced distance, the position limitation is more notable. To address this challenge, spacecraft dynamics and control using a solar sail are investigated to achieve the displaced orbit, and a method of orbit transfer outside the eclipse region is proposed. Numerical simulations reveal that the spacecraft can maintain the displaced orbit using the solar sail without entering the eclipse region. Moreover, spacecraft can achieve orbit transfer between two equilibrium points without entering the eclipse region by using the solar sail. The impact of non-spherical shape of the primary asteroid is also investigated. Results show that the proposed method can maintain a displaced orbit with errors from the reference state less than 10 % during a limited time span when the primary asteroid has a non-spherical shape.

Testing General Relativity with Juno at Jupiter

The Juno spacecraft has been orbiting Jupiter since 2016 July to deepen our comprehension of the solar system by studying the gas giant. The radio science experiment enables the determination of Jupiter’s gravitational field, thus shedding light on its interior structure. The experiment relies on determining the orbit of the spacecraft during its pericenter passages. Previous gravity data analyses assumed the correctness of the general theory of relativity, which was used for trajectory integration and radio signal propagation modeling. In this work, we aim to test general relativity within the unique context of a spacecraft orbiting Jupiter, by employing the parameterized post-Newtonian (PPN) formalism, an established framework for comparing various gravitational theories. Within this framework, we focus our attention toward the PPN parameters γ and β, which offer insights into the curvature of spacetime and the nonlinearity of gravitational effects, respectively. Additionally, we extend our investigation to the Lense–Thirring effect, which models the dragging of spacetime induced by a rotating mass. By measuring the relativistic frequency shift on Doppler observables caused by Jupiter during Juno’s perijove passes, we estimate γ = 1 + (1.5 ± 4.9) × 10−3, consistent with the general theory of relativity. Our estimated γ is primarily influenced by its effect on light-time computation, with a negligible contribution from spacecraft dynamics. Furthermore, we also present a modest level of accuracy for the β parameter, reflecting the minimal dynamical perturbation on Juno from general relativity. This also applies to the Lense–Thirring effect, whose signal is too small to be confidently resolved.

Mass property estimation on TSE(3) via unscented Kalman filter using RCS thrusters

Estimation of spacecraft mass properties in the presence of noise is a nontrivial problem that, when properly addressed, can substantially reduce the crew time devoted to cargo management, control effort expended to manage fuel mass, or both. The estimation of such properties is treated here using a dual unscented Kalman filter (UKF) where the dynamics of the rigid-body spacecraft are formulated on the special Euclidean group SE(3) and its tangent bundle TSE(3) to avoid singularity and nonuniqueness issues found in attitude parameterization sets. The dual UKF on TSE(3) is developed, and a specific methodology is proposed for the estimation of the constant mass properties. An excitation approach is employed in the mass property estimation scheme. Arbitrary sensor suite placements are considered and implemented in the measurement model to capture real-world spacecraft behavior. Furthermore, a reaction control system with duty cycle constraints and noisy thrust values is implemented to account for uncertainty in the excitation inputs. With these features, the methods contained herein are found to be effective at estimating mass properties.

Nonlinear modeling and validation of spacecraft dynamics for space-based gravitational wave detector

The development of the Drag-Free and Attitude Control System is crucial for space-based gravitational wave detectors. The Drag-Free and Attitude Control System includes for spacecraft attitude control, drag-free control, moving optical subassemblies pointing control, and test masses electrostatic control during multiple phases of the mission lifetime. An accurate model of the spacecraft dynamics model is not only a precondition for the control design of Drag-Free and Attitude Control System, but also can serve as a valuable reference to assess the noise budget of gravitational wave detectors. This paper presents a generic, nonlinear mathematical model that describes the multi-body dynamics for the gravitational wave detectors. The model fully considers the couplings between the bodies involved, with a particular focus on the impact of the moving optical subassemblies on the spacecraft attitude. Additionally, a corresponding reduced model for the control design of the science mode is divided. Both models are validated numerically by Monte Carlo simulations and motion analysis, respectively.

Optimal Guidance for Heliocentric Orbit Cranking with E-Sail-Propelled Spacecraft

In astrodynamics, orbit cranking is usually referred to as an interplanetary transfer strategy that exploits multiple gravity-assist maneuvers to change both the inclination and eccentricity of the spacecraft osculating orbit without changing the specific mechanical energy, that is, the semimajor axis. In the context of a solar sail-based mission, however, the concept of orbit cranking is typically referred to as a suitable guidance law that is able to (optimally) change the orbital inclination of a circular orbit of an assigned radius in a general heliocentric three-dimensional scenario. In fact, varying the orbital inclination is a challenging maneuver from the point of view of the velocity change, so orbit cranking is an interesting mission application for a propellantless propulsion system. The aim of this paper is to analyze the performance of a spacecraft equipped with an Electric Solar Wind Sail in a cranking maneuver of a heliocentric circular orbit. The maneuver performance is calculated in an optimal framework considering spacecraft dynamics described by modified equinoctial orbital elements. In this context, the paper presents an analytical version of the three-dimensional optimal guidance laws obtained by using the classical Pontryagin’s maximum principle. The set of (analytical) optimal control laws is a new contribution to the Electric Solar Wind Sail-related literature.

Dynamics and Control of Mass-Variable Liquid-Filled Spacecraft With Combined Nonlinear Slosh

Dynamics and Control of Mass-Variable Liquid-Filled Spacecraft With Combined Nonlinear Slosh

Optimization, guidance, and control of low-thrust transfers from the Lunar Gateway to low lunar orbit

The Lunar Gateway will represent a primary space system useful for the Artemis program, Earth–Moon transportation, and deep space exploration. It is expected to serve as a staging location and logistic outpost on the way to the lunar surface. This study focuses on low-thrust transfer dynamics, from the Near-Rectilinear Halo Orbit traveled by Gateway to a specified Low-altitude Lunar Orbit (LLO). More specifically, this research addresses two closely-related problems: (i) determination of the minimum-time low-thrust trajectory and (ii) design, implementation, and testing of a guidance and control architecture, for a space vehicle that travels from Gateway to LLO. Orbit dynamics is described in terms of modified equinoctial elements, with the inclusion of all the relevant perturbations, in the context of a high-fidelity multibody ephemeris model. The minimum-time trajectory from Gateway to a specified lunar orbit is detected through an indirect heuristic approach, which uses the analytical conditions arising in optimal control theory in conjunction with a heuristic technique. However, future missions will pursue a growing level of autonomy, and this circumstance implies the mandatory design and implementation of an efficient feedback guidance scheme, capable of compensating for nonnominal flight conditions. This research proposes nonlinear orbit control as a viable and effective option for autonomous explicit guidance of low-thrust transfers from Gateway to LLO. This approach allows defining a feedback law that enjoys quasi-global stability properties without requiring any offline reference trajectory. The overall spacecraft dynamics is modeled and simulated, including attitude control and actuation. The latter is demanded to an array of reaction wheels, arranged in a pyramidal configuration. Guidance, attitude control, and actuation are implemented in an iterative scheme. Monte Carlo simulations demonstrate that the guidance and control architecture at hand is effective in nonnominal flight conditions, i.e. with random starting point from Gateway as well as in case of temporary unavailability of the propulsion system. The numerical results also point out that only a modest propellant penalty is associated with the use of feedback guidance and control in comparison to the minimum-time optimal trajectory.

Model Predictive Control with Gaussian-Process-Enhanced Dynamics for Spacecraft Attitude Takeover Maneuvers

This paper aims to deal with the attitude takeover control for combined spacecraft with unknown dynamics and attitude maneuverability of the target. Generally, the dynamics of combined spacecraft executing an on-orbit servicing task is highly nonlinear and costly to identify. To address this issue, a sparse variational Gaussian process (GP)-based model predictive control (MPC) strategy is proposed to achieve efficient attitude takeover maneuvers under multiple constraints and target attitude maneuverability. The GP regression performs a model completion behavior, where the unknown dynamics is compensated by the sparse variational GP with a low computational load. This enhances the control performance of the combined spacecraft during the takeover task execution. Numerical simulations are used to demonstrate the effectiveness of the proposed strategy.

General Dynamics for Single- and Dual-Axis Rotating Rigid Spacecraft Components

Deriving and propagating a spacecraft’s equations of motion is fundamental to describing its behavior accurately. These equations of motion depend on the spacecraft’s configuration, which includes any physical subsystem such as attitude control devices, solar panels, gimbals, etc. Prior work introduced the backsubstitution method to yield a modular and scalable formulation to develop complex spacecraft dynamics specific to rotating components attached to a rigid hub as effectors. This paper relaxes assumptions made in deriving effector components in prior work, such as mass properties and frame definitions. This produces a general architecture that uses common equations of motion for physically equal parts. The result is an analytical solution of a set of general rotating effector equations of motion that greatly expand the configuration space of spacecraft that can be simulated with the backsubstitution method. In contrast to prior work where the rotations are highly constrained, rigid-body components can rotate about one or two general axes, and the component mass distribution can be general, no longer requiring the component’s principal axis to align with the center of mass or hinge axis. A numerical software solution demonstrates and verifies how these effectors can mimic a range of dynamic spacecraft components.

Berthing proximity maneuvers and trajectory planning of a space manipulator via Kane’s formulation

On-orbit servicing is one of the most challenging tasks of the recent space era. Space Manipulator Systems (SMS) can represent viable technological solutions for several space operations, such as in-situ refueling, repairing of operating spacecraft, or debris grappling. Regardless of the specific task, SMS must approach the target object and then establish a physical connection with it using a single or more robotic arms. This work considers a space vehicle equipped with a pair of two-link robotic arms, with the intent of efficiently designing and simulating the overall spacecraft dynamics until contact takes place. The links that compose each arm are modeled as rigid bodies, assuming relatively slow dynamics. Instead, flexibility is introduced in the model of the rotary joints. The overall dynamics is investigated using Kane’s methodology, which is general, highly systematic, and joins the advantages of both the Newton/Euler and the Lagrange formulation. Both SMS and the target, assumed as noncooperative, are placed in low Earth orbit, in close proximity. Trajectory planning of the robotic arm is investigated, while considering the effect of the arm motion on the overall attitude dynamics. Precise attitude maneuvering is mandatory in order that grappling be successfully completed. To do this, a quaternion-based, globally stable attitude feedback law is designed, implemented, and tested. Actuation is demanded to an arrangement of control momentum gyroscopes. These devices are modeled with the inclusion of gyroscopic coupling effects, and are driven by means of suitable steering laws, for the purpose of pursuing the desired attitude control action. Accurate modeling of SMS, with also the inclusion of disturbances due to joint flexibility, in conjunction with the use of suitable feedback attitude control and steering laws for both the robotic arms and the actuation devices, allows obtaining the desired variables, i.e. (i) the motor torques (for steering both the joints and the attitude devices) and (ii) the constraint actions (forces and torques). A Monte Carlo analysis points out effectiveness of the control architecture proposed in this study in the challenging mission scenario of interest.

Onboard estimation of unknown dynamics of flexible spacecraft

Attitude control methods of highly flexible spacecraft have seen increased interest over the last decades thanks to the technological development of flexible solar panels and deployables, which improves the capabilities of satellites. However, a high-fidelity model of the flexible dynamics is hard to obtain on-ground testing because not all modes can be observed, complicating the controller design. This paper proposes a method to develop a high-fidelity model of a spacecraft with a flexible appendage subject to large deformations by modeling it as a finite series of rigid links connected by torsional springs and dampers. To overcome the uncertainties or unknowns in the flexible dynamics, an onboard estimation through an adaptive controller is performed for these unknowns while the spacecraft is maneuvered. The controller uses integral concurrent learning (ICL), an adaptive scheme that records inputs and outputs provided by sensors mounted on the flexible body. The novelty of this investigation is the development of self-adapting control gains for the learning matrix obtained from ICL. This approach achieves the objective of tracking a desired trajectory while accurately learning the unknown physical parameters of the flexible appendage by only using the recorded measurements of the appendage displacements and the spacecraft attitude and velocities. It was observed that for a finer discretization of the flexible appendage and therefore a higher fidelity model of the flexible dynamics, the estimation algorithm is able to observe all the frequencies necessaries to learn the unknown mechanical properties of the flexible body.

State‐dependent indirect hp‐pseudospectral method for rigid spacecraft attitude optimal control problem

AbstractThe state‐dependent indirect ‐pseudospectral (SDIHP) method for rigid spacecraft attitude control is presented in this paper. The optimal controller is obtained by the SDIHP method through classifying the attitude optimal control problem as a nonlinear quadratic optimal control problem. In the proposed control scheme, successive state‐dependent coefficient (SDC) parameterization is initially applied to the spacecraft dynamics to derive an available linear system to decrease the calculation cost and speed. Then, the indirect ‐adaptive spectral discretization is developed to convert the resultant optimal control problem into a sequence of linear equations, which can improve the global computational efficiency and guarantee the solving precision. Hence, the optimal control can be efficiently solved using basic matrix operations under the necessary collocation points based on the ‐adaptive features. Considering the inertia uncertainties and external disturbances, a state feedback controller is generated by the receding horizon control (RHC) framework to improve the robustness. Simulation results are included to show the effectiveness and performance of the suggested optimal method.

A generalized super-twisting algorithm-based adaptive fixed-time controller for spacecraft pose tracking

Abstract A generalized super-twisting second-order sliding mode adaptive fixed-time control law, which is used for spacecraft pose tracking in the presence of internal and external uncertainties, is proposed. Lie group SE(3) (for special Euclidean group), which is the configuration space for rigid body motion, is used for modeling the six-degrees-of-freedom dynamics of spacecraft. A fixed-time sliding mode surface is proposed and applied to design an generalized super-twisting sliding mode control law. A novel dual-layer adaption law for the controller is proposed to the ensure the gains varying rapidly with the disturbance. The adaptive second-order sliding mode controller guarantees a uniform exact convergence for the closed-loop tracking control system with less energy consumption. Numerical simulations are performed to demonstrate the excellent performances of the control law.

Inertia matrix identification of combined spacecraft using a deep neural network with optimized network structure

After the space robot captures the out-of-control spacecraft, they form a combined spacecraft. For the parameter identification problem of combined spacecraft with complex angular rate measurement noise, deep learning could provide a new solution, due to its ability to extract robust features from noisy data. However, the deep neural network (DNN) has substantial computing resource requirements, which restricts its application in spacecraft systems. To solve the above problems, an inertia matrix identification approach combining a structure optimization strategy of DNN is proposed to identify the inertia matrix in the presence of complex measurement noise using the DNN with optimized structure. The attitude dynamics of combined spacecraft are firstly derived, and the identification problem considering complex measurement noise is described. Based on the dynamics model, the construction process of DNN for accurately identifying the inertia matrix is proposed. A structure optimization strategy of DNN is then designed to optimize the structure of DNN for increasing computing efficiency. This strategy provides a whole set of solutions including the structure selection of the initial DNN, the redundant neurons pruning process, and the end-of-optimization condition. By combining the proposed construction process of DNN, the structure of the DNN is finally optimized by iterating the structured pruning and retraining step. The performance of the proposed DNN with optimized network structure is verified on a testing set with complex measurement noise. The results show that the proposed approach can accurately identify the inertia matrix of combined spacecraft, and meanwhile greatly improve the computing efficiency of DNN.

Homogeneous Finite-Time Pose Tracking of Leader–Following Spacecraft Formation Using a Twistor-Based Model

For integrated pose control of six-degree-of-freedom (6-DOF) leader–following spacecraft formations, the coupled relative pose between two spacecraft is described by a unified model in the framework of twistors, based on which a finite-time control law is devised for the 6-DOF dynamic system. Firstly, some necessary coordinate frames are defined, and then, relative 6-DOF dynamics of the follower spacecraft with respect to the desired frame are modeled by using twistors. Secondly, an integrated pose controller is designed for the 6-DOF formation that takes full advantage of homogeneous theory to guarantee finite-time stability. Finally, numerical simulations are carried out to validate the effectiveness of the proposed controller. Developing integrated 6-DOF formation control law based on twistors is more straightforward than conventional methods, and the finite-time algorithm achieves stronger robustness than asymptotic ones.

Bounding nonlinear stretching about spacecraft trajectories using tensor eigenpairs

Local linearization is often used to enable analytical methods in spacecraft dynamics, navigation, and control. However, the linear approximation becomes inaccurate at large distances from the linearization point and/or when the underlying dynamical system is strongly nonlinear. As a result, linearization-based methods like the finite time Lyapunov exponent (FTLE) can underestimate stretching in phase space. Alternatively, this paper presents a semianalytical method to quantify nonlinear stretching: the eigenpairs of higher-order tensors are used to bound the maximum stretching of a state deviation over time. The tenors in question are derived from the Taylor series expansion of a nonlinear solution flow about a reference trajectory, i.e., the state transition tensor (STT) expansion. It is well known that the eigenvalues of the Cauchy–Green tensor (CGT) bound the stretching of state deviations over time for a linear system, and the largest eigenvalue can be related to the FTLE. This paper will present higher-order, nonlinear analogs to the CGT and the FTLE to more accurately bound nonlinear stretching for applications in guidance, navigation, and control.

Current status and prospects of adaptive PID control in spacecraft attitude control

Spacecraft attitude control is a precise aspect that requires accurate operation. Adaptive PID control, in this case, could be a promising approach for improving the performance. In order to provide a better comprehension about the adaptive PID control in spacecraft attitude control, This paper will mainly discuss the aspect in current solutions, challenges, and future directions through providing and interpreting the scientific and reliable essays in this area. Several kinds of classic adaptive PID control will be introduced in the paper for their feasibility and applicability. Then, paper will discuss several kinds of limitations faced by traditional adaptive PID control in reality such as the complexity of spacecraft dynamics. To overcome these limitations, this paper will also discuss a couple of machine learning based adaptive PID control proposed by researchers such as fuzzy logic systems. These adaptive schemes can adjust the controller parameters through advanced algorithms to ameliorate the control performance of the spacecraft.

A method for direct in-space thrust estimation from low-acceleration orbital maneuvers

This paper presents a method for performing direct in-space thrust estimation for low-acceleration propulsion systems using measurements of the spacecraft’s position taken during an orbital maneuver. The method is based on the ensemble Kalman update which does not require linearization of the spacecraft dynamics nor does it require Gaussian distributions for parameter uncertainties and measurement noise, allowing for a more general approach to thrust estimation. In addition, modeling error, such as that caused by the truncation of a spherical-harmonics representation of the Earth’s gravitational field, can be explicitly accounted for by representing the error with Gaussian processes. Simulated experiments show that uncertainty in the propulsive acceleration magnitude on the order of 0.1 mum/s^2 (1sigma) can be achieved at an orbit altitude of approximately 410 km with temporally-sparse measurements even in the presence of uncertain atmospheric drag, and Monte Carlo analysis demonstrates the consistency of the inference results. Trends in the estimate of the propulsive acceleration with the true acceleration value are explored empirically and theoretically in order to allow for generalization of the results. The outcome of this work is a systematic approach to direct in-space thrust estimation that can support the final steps of development for future in-space electric propulsion systems or the calibration of a thruster during a mission.

Optimizing the Location of the Piezoelectric Actuator and Analyzing Its Effect on the Dynamics of Asymmetric Flexible Spacecraft

To address the challenge of optimizing the placement of actuators on an asymmetric spacecraft continuum system, this paper develops a rigid–flexible electromechanical coupling dynamic model that integrates the interactions among rigidity, flexibility, and electromechanical coupling effects. The model is constructed using ordinary differential equations and partial differential equations (ODE–PDEs) and considers the effects of the installation position and physical characteristics (mass and stiffness) of the piezoelectric (PZT) actuator on an asymmetric flexible spacecraft continuum system. The proposed model aims to accurately capture the complex interactions among the rigid body, flexible appendages, and PZT actuators. Based on the developed model, the installation location of the actuators is optimized using a genetic algorithm with a hybrid optimization criterion. In the numerical simulations, the proposed optimization algorithm is employed to determine the optimal installation position for the actuators. Then, the influence of the actuator’s physical characteristics and installation position on the dynamic properties of the spacecraft and the performance of the control system is investigated. The numerical simulation results demonstrate that the optimization algorithm can effectively identify the appropriate actuator installation location for the desired application. Utilizing the actuator with the optimized position allows for effective vibration suppression while consuming less energy.

Simple Mathematical Models for the Dynamics Of Spacecraft With Deployed Solar Panels

Most present day spacecrafts have large interconnected deployed solar panels having very low natural frequencies. The control torque applied to maneuver the spacecraft sets up transient oscillations in the spacecraft. The present work studies the nature of these interactions. The spacecraft in orbit can be modeled as a free rigid mass with flexible elements attached to it. It is shown that the oscillations of the spacecraft body are characterized by the dynamic characteristics of the flexible panel even if the mass and mass moment of inertia of the body is signifcantly higher than that of the flexible panels. A simple model consisting of an Euler-Bernoulli beam attached to a mass can represents such a system. The infuence of various parameters of the Euler-Bernoulli beam and the rigid element on the disturbances caused in the rigid element are investigated. The characteristics are determined for a step and also for a torque input. The responses are obtained in terms of nondimensionalised quantities. It is demonstrated that using the simple model developed the responses of spacecraft body can be easily obtained.