Spacecraft State Research Articles

Controlling Hamiltonian Integral Invariants of Spacecraft Phase Space Distributions

Phase space distributions outline regions of plausible spacecraft states in phase space given some degree of uncertainty. Under Hamiltonian dynamical flow, geometric features of these distributions become time-invariant and are referred to as Hamiltonian integral invariants. The shape and size of the distributions are correlated to our state uncertainty, so these geometric invariants provide unique, analytical insight into problems of uncertainty propagation. When a Hamiltonian system is perturbed by dissipative forces, the geometric features associated with integral invariants are no longer constant. Rather, they change in time, and the insight into problems of uncertainty propagation also changes. This paper explores how the geometric features of phase space distributions can be targeted with orbital and attitude guidance laws. For example, volume-collapsing guidance laws are designed to restrict both the translational and rotational spacecraft state. Alternative representations for regions of uncertainty are also considered via Monte Carlo and covariance matrix analysis. With these alternative representations, the targeted geometric behavior is validated.

Research on High-Precision and Wide-Range Spacecraft Potential Measurement Method Based on Capacitive Voltage Division.

The charging and discharging of satellite surfaces induced by the space plasma environment constitute a primary cause of spacecraft anomalies, particularly in geosynchronous orbits subject to geomagnetic substorms and hot plasma injections from the magnetotail, where satellites are prone to unequal high-potential charging, significantly impacting the safe and reliable operation of spacecraft. Addressing the need for measuring these unequal charge states, a high-precision, wide-range spacecraft potential measurement method based on capacitive voltage division was investigated. This study analyzed the mechanism of potential measurement and the factors contributing to errors during the measurement process, explored optimal design methodologies, and innovatively developed a fundamental charge zeroing method to resolve output drift issues caused by accumulated errors fundamentally. Consequently, a non-contact potential measurement system was developed, featuring a measurement range of up to -15,000 V, a resolution below 15 V, and a nonlinear error of less than 0.1%. This system provides technical support for monitoring the potential state of spacecraft and ensuring their safety and protection.

Optimal low-thrust orbit transfers connecting Gateway with Earth and Moon

Gateway will represent a primary logistic infrastructure in cislunar space. The identification of efficient orbit transfers capable of connecting Earth, Moon, and Gateway paves the way for enabling refurbishment, servicing, and utilization of this orbiting platform. This study is devoted to determining two-way minimum-time low-thrust orbit transfers that connect both Earth and Moon to Gateway. Backward time propagation is proposed as a very convenient option for trajectories that approach and rendezvous with Gateway, and a unified formulation is introduced for minimum-time orbit transfers, using either forward or backward propagation. Two-way transfers between Gateway and a specified low-altitude lunar orbit are first determined, using an indirect heuristic method, which employs the necessary conditions for optimality and a heuristic algorithm. Second, two-way orbit transfers that connect Earth and Gateway are addressed. Because these trajectories exist under the influence of two major attracting bodies, the underlying optimal control problem is formulated as a multi-arc trajectory optimization problem, involving three different representations for the spacecraft state. Multi-arc optimal control problems are associated with several corner conditions to be enforced at the junction time that separates distinct arcs. However, these conditions are shown to be solvable sequentially for the problem at hand, leveraging implicit costate transformation. This implies that the multi-arc problem has a set of unknown quantities with the same size as that of a single-arc optimal control problem, with apparent advantages of a computational nature. The indirect heuristic method is also applied in this second mission scenario. Low-thrust orbit dynamics is propagated in a high-fidelity dynamical framework, with the use of planetary ephemeris and the inclusion of the simultaneous gravitational action of Sun, Earth, and Moon, along the entire transfer paths, in all cases. The numerical results unequivocally prove that the methodology developed in this research is effective for determining two-way minimum-time low-thrust orbit transfers connecting Earth, Moon, and Gateway.

Impulsive maneuver strategy for multi-agent orbital pursuit-evasion game under sparse rewards

To address the subjectivity of dense reward designs for the orbital pursuit-evasion game with multiple optimization objectives, this paper proposes the reinforcement learning method with a hierarchical network structure to guide game strategies under sparse rewards. Initially, to overcome the convergence challenges in the reinforcement learning training process under sparse rewards, a hierarchical network structure is proposed based on the hindsight experience replay. Subsequently, considering the strict constraints imposed by orbital dynamics on spacecraft state space, the reachable domain method is introduced to refine the subgoal space in the hierarchical network, further facilitating the achievement of subgoals. Finally, by adopting the centralized training-layered execution approach, a complete multi-agent reinforcement learning method with the hierarchical network structure is established, enabling networks at each level to learn effectively in parallel within sparse reward environments. Numerical simulations indicate that, under the single-agent reinforcement learning framework, the proposed method exhibits superior stability in the late training stage and enhances exploration efficiency in the early stage by 38.89% to 55.56% to the baseline method. Under the multi-agent reinforcement learning framework, as the relative distance decreases, the subgoals generated by the hierarchical network transition from long-term to short-term, aligning with human behavioral logic.

Gauss Equations for Local Action-Angle Orbital Elements in Cislunar Space

To track orbits in cislunar space, predict where they will naturally move over time, and identify where unbounded trajectories come from, one may consider local action-angle orbital elements—coordinates that relate a spacecraft state to specific trajectories and exist in approximately integrable regions of the Earth–moon circular restricted three-body problem (CR3BP). As local action-angle elements are a semi-analytical analog to two-body orbital elements, the theory is extended to allow for the study of arbitrary perturbations to the dynamics. Namely, we derive Gauss equations for an arbitrary perturbing acceleration—continuous or discrete—to the CR3BP. Examples for continuous thrust and impulsive ΔV are provided in cislunar space, i.e., around Earth–moon L1,2 in the CR3BP. Strategies for instantaneous maneuver design and transfers between quasi-periodic orbits and manifolds are developed.

Distributed control of spacecraft formation under [formula omitted] perturbation in the port-Hamiltonian framework

To control the relative position and relative velocity of spacecraft formation, a time-varying nonlinear relative motion model under J2 perturbation in an elliptical orbit is established in the port-Hamiltonian (PH) framework, and a distributed control law for spacecraft formation is developed using the consensus algorithm for parameter estimation and the passivity-based control (PBC) method based on the state-error interconnection and damping assignment (IDA) technique. First, the influence of J2 perturbation on the potential energy and orbit parameters in the model is considered when the relative motion model is built in the PH frame, and the expression of the relative motion acceleration under J2 perturbation is given. Second, to solve the problem that the state of the chief spacecraft cannot be directly obtained from the deputy spacecraft under distributed communication, a consensus-based parameter estimation method is introduced, the estimated parameter of the chief spacecraft is applied to the relative motion model in the PH frame, and a state error model with the estimated parameters derived from the consistency algorithm is established. Then, after the stability analysis is conducted on the desired PH system containing the estimated parameter values, the desired Hamiltonian energy function with the estimated parameters is designed according to the time-varying errors of the relative equilibrium states of the deputy spacecraft and the errors between deputy spacecraft, and the distributed control law of spacecraft formation is derived based on the state-error IDA-PBC method. Finally, the expected relative motion trajectory designed based on the TH equation is used to simulate a spacecraft formation under J2 perturbation, and the results indicate that the spacecraft can quickly converge to the expected formation under the influence of the control law.

Three-Dimensional Guidance Laws for Spacecraft Propelled by a SWIFT Propulsion System

This paper discusses the optimal control law, in a three-dimensional (3D) heliocentric orbit transfer, of a spacecraft whose primary propulsion system is a Solar Wind Ion Focusing Thruster (SWIFT). A SWIFT is an interesting concept of a propellantless thruster, proposed ten years ago by Gemmer and Mazzoleni, which deflects, collects, and accelerates the charged particles of solar wind to generate thrust in the interplanetary space. To this end, the SWIFT uses a large conical structure made of thin metallic wires, which is positively charged with the aid of an electron gun. In this sense, a SWIFT can be considered as a sort of evolution of the Janhunen’s E-Sail, which also uses a (nominally flat) mesh of electrically charged tethers to deflect the solar wind stream. In the recent literature, the optimal performance of a SWIFT-based vehicle has been studied by assuming a coplanar orbit transfer and a two-dimensional scenario. The mathematical model proposed in this paper extends that result by discussing the optimal guidance laws in the general context of a 3D heliocentric transfer. In this regard, a number of different forms of the spacecraft state vectors are considered. The validity of the obtained optimal control law is tested in a simplified Earth–Venus and Earth–Mars transfer by comparing the simulation results with the literature data in terms of minimum flight time.

Characterization of Candidate Solutions for X-Ray Pulsar Navigation

X-ray pulsar based navigation (XNAV) can be used to estimate spacecraft state information based on observation of distant pulsars. XNAV system concepts typically require an initial position estimate since there are many candidate positions which may produce the same measurement. If position ambiguity can be resolved, XNAV may enable full state estimation without prior information. This study seeks to efficiently find candidate spacecraft positions and determine how to select pulsars to minimize the number of candidate solutions within a given domain. A numeric scheme for determining candidate positions is developed for an arbitrary number of observed pulsars. Pulsar selection criteria are developed in terms of relative direction, period, and phase accuracy. Results indicate that it is more time efficient to observe additional pulsars rather than improve the accuracy of pulsar measurements. A smaller angular separation and increased period of the observed pulsars reduces the number of candidate solutions within a given domain. Phase measurement accuracy should be improved simultaneously for all pulsars rather than prioritizing a single pulsar. These selection criteria are verified by evaluating the number of candidate solutions for permutations of 34 real pulsars.

Research on Spacecraft Fault Diagnosis and Recovery Architecture

Fault diagnosis and recovery system is designed to monitor on-orbit state of spacecraft and handle exception, which provides spacecraft security and missions succeed. This report studies the design of spacecraft fault diagnosis and recovery system from technology and architecture two respects. Technical system and modules design from top level for spacecraft fault diagnosis and recovery is proposed. And the architecture of comprehensive fault diagnosis system is also proposed, which supports spacecraft to diagnose and recover on-orbit faults.

Acoustic emission diagnostics of a hull structures by a system of integrating fiber-optic sensors for the aircraft and spacecraft safe operation

A variant of aircraft and spacecraft state of hull structures acoustic emission diagnostics method based on a system of distributed fiber-optic sensors is considered. Such systems can be sources of information for a technical means of ensuring safety at aerospace facilities. The Green's function for a single sensor is found, and the features of its operation under the influence of pulsed acoustic emission signals are considered. The capabilities of the sensor system under consideration in estimating the coordinates and parameters of acoustic emission signals are determined. The results of experimental studies demonstrating the possibility of detecting emission signals under conditions of specific interference are reported.

Constrained evolution of Hamiltonian phase space distributions in the presence of natural, non-conservative forces

Confidence regions for spacecraft state can be constructed in phase space which encapsulate some region where there is a likelihood for the state to reside. These regions can be treated as phase space distributions or structures. Structures, such as surfaces or volumes, are constrained to preserve specific properties as they evolve in phase space under Hamiltonian dynamics. Thus, spacecraft uncertainty is then constrained by Hamiltonian flow which can provide insight into state determination. This work examines the modified constraints in the presence of non-conservative forces which relate to both probabilistic and geometric properties of the evolving uncertainty structure. The modified constraints are then derived for a Two-Body and drag environment and are shown to be valid after comparison with alternative methods. Applying the modified constraints, the constrained evolution of the confidence region is then tied to a simple physical explanation for the changing knowledge in our spacecraft state, in the atmospheric drag environment and Poynting–Robertson drag environment.

Modeling the Thermal State of Small Spacecraft: Errors Due to Incorrect Assessment of the Thermal Environment

Modeling the Thermal State of Small Spacecraft: Errors Due to Incorrect Assessment of the Thermal Environment

Autonomous Optical-Only Spacecraft-to-Spacecraft Absolute Tracking and Maneuver Classification in Cislunar Space

Traditional concerns regarding spacecraft state estimation are exacerbated in cislunar space due to highly nonlinear dynamics, limited observational information, and increasingly overloaded Earth-based resources. These challenges motivate research into space-based navigation and observation capabilities that provide opportunities for autonomy. This paper demonstrates that relative optical measurements provide full inertial estimates of an agent and target spacecraft, while simultaneously enabling classification of unknown maneuvers in the cislunar environment. To achieve this objective two subtasks are demonstrated. First, the spacecraft-to-spacecraft absolute tracking method, which estimates the absolute state of two vehicles using relative measurements, is tested for observability and shown to produce consistent filter solutions given optical sensors. Second, maneuver classification is performed by labeling an estimated control profile generated from the optimal control based estimator. Collectively, this sequential methodology enables an agent craft to autonomously navigate itself while observing a target craft and classifying its maneuvers.

Autonomous Guidance Between Quasiperiodic Orbits in Cislunar Space via Deep Reinforcement Learning

This paper investigates the use of reinforcement learning for the fuel-optimal guidance of a spacecraft during a time-free low-thrust transfer between two libration point orbits in the cislunar environment. To this aim, a deep neural network is trained via proximal policy optimization to map any spacecraft state to the optimal control action. A general-purpose reward is used to guide the network toward a fuel-optimal control law, regardless of the specific pair of libration orbits considered and without the use of any ad hoc reward shaping technique. Eventually, the learned control policies are compared with the optimal solutions provided by a direct method in two different mission scenarios, and Monte Carlo simulations are used to assess the policies’ robustness to navigation uncertainties.

Autonomous Decision-Making for Aerobraking via Parallel Randomized Deep Reinforcement Learning

Aerobraking is a process used to slow down and insert a spacecraft into a low orbit around a planet. It is composed of many orbital passages into the complex atmosphere of the planet, which is used for braking. The aerobraking atmospheric passages are challenging because of the high variability of the atmospheric environment. For this reason, autonomous aerobraking planning is essential for safety and mission performance. This paper develops a parallel domain randomized deep reinforcement learning architecture for autonomous decision-making in a stochastic environment, such as aerobraking atmospheric passages. In this context, the architecture is used for planning aerobraking maneuvers to avoid the occurrence of thermal violations during the atmospheric aerobraking passages and target a final low-altitude orbit. The parallel domain randomized deep reinforcement learning architecture is designed to account for large variability of the physical model, as well as uncertain conditions. Also, the parallel approach speeds up the training process for simulation-based applications, and the domain randomization improves resultant policy generalization. To use this architecture, a Markov-Decision process framework is developed for a general aerobraking-type mission. A three-dimensional running reward function, expressed in spacecraft state and action, is designed. This framework is applied to the 2001 Mars Odyssey aerobraking campaign, which is also used to verify the performance of the parallel domain randomized deep reinforcement learning architecture. With respect to the 2001 Mars Odyssey mission flight data and a Numerical Predictor Corrector (NPC)-based state-of-the-art heuristic for autonomous aerobraking, the proposed architecture outperforms the state-of-the-art heuristic algorithm with an average increase of 87.2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> in the cumulative reward and a decrease of 97.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> in the number of thermal violations. Specifically, the proposed architecture is able to predict and avoid thermal violations while requiring fewer computational resources. Furthermore, it yields a decrease of 98.7 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> in the number of thermal violations with respect to the Mars Odyssey mission flight data and requires 13.9 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> fewer orbits, with a comparable aerobraking duration and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta$</tex-math></inline-formula> V budget. Results also show that the proposed architecture can also learn a generalized policy in the presence of strong uncertainties, such as aggressive atmospheric density perturbations, different atmospheric density models, and a different simulator maximum step size and error accuracy. To this end, a generalization analysis is performed using out-of-distribution generalization environments. Results of the generalization analysis show that the architecture can perform safe aerobraking campaigns with only a maximum increase of 2 in the number of thermal violations for cases in which the simulator accurately described the physical model.

Orbit Determination and Thrust Estimation for Noncooperative Target Using Angle-Only Measurement

The classical interactive multimodel (IMM) algorithm has some disadvantages in tracking a noncooperative continuous thrust maneuvering spacecraft, such as poor steady-state accuracy, difficult selection of subfilter parameters, and mismatched model jump. To address the abovementioned problems, a variable-dimensional adaptive IMM strong tracking filtering algorithm (VAIMM-STEKF) is proposed to estimate the spacecraft’s position, velocity, and maneuvering acceleration state. VAIMM-STEKF contains 2 models, model 1 and model 2, which correspond to the tracking of the spacecraft in maneuvering and nonmaneuvering situations. Model 1 estimates the position and velocity of the spacecraft to ensure tracking accuracy when no maneuver occurs. Model 2 is a strong tracking filter with an augmented state. The adaptive IMM algorithm adjusts the fixed Markov transfer matrix in real time according to the model output probability. According to the different states of the spacecraft, the corresponding model interactive fusion method, together with the strong tracking filter, is adopted to ensure fast tracking when the spacecraft state changes. This method can also adapt to continuous thrust maneuvering spacecraft with different orders of magnitude. Simulation results show that the position accuracy of VAIMM-STEKF can be improved by approximately 27% and the speed accuracy can be enhanced by approximately 17% under different levels of maneuvering acceleration compared with those of the IMM algorithm. The convergence speed of VAIMM-STEKF is also better than the IMM algorithm.

Spacecraft hitch detection and health evaluation based on Multivariable Time Series

In this paper, unsupervised method is studied to solve the problem that it is difficult for spacecraft to obtain tagged hitch data. Firstly, the incremental cross-correlation filtered attribute selection algorithm (ICF) is used to complete the selection of feature subsets of spacecraft multivariate time series (MTS);Then the unsupervised learning model of LSTM-SAE is trained on a large number of normal data; Finally, a complete hitch monitoring and health evaluation system is established and verified on the data of three fault degrees. The feature space of normal data is constructed, and the health state of spacecraft is measured by the reconstruction error of faulted data and the distance of feature space. It solves the problem of predicting and avoiding catastrophic failures of spacecraft under the conditions of lack of prior knowledge, unbalanced data distribution and incomplete failure modes.

A Novel Visual-Based Terrain Relative Navigation System for Planetary Applications Based on Mask R-CNN and Projective Invariants

In the framework of autonomous spacecraft navigation, this manuscript proposes a novel vision-based terrain relative navigation (TRN) system called FederNet. The developed system exploits a pattern of observed craters to perform an absolute position measurement. The obtained measurements are thus integrated into a navigation filter to estimate the spacecraft state in terms of position and velocity. Recovering crater locations from elevation imagery is not an easy task since sensors can generate images with vastly different appearances and qualities. Hence, several problems have been faced. First, the crater detection problem from elevation images, second, the crater matching problem with known craters, the spacecraft position estimation problem from retrieved matches, and its integration with a navigation filter. The first problem was countered with the robust approach of deep learning. Then, a crater matching algorithm based on geometric descriptors was developed to solve the pattern recognition problem. Finally, a position estimation algorithm was integrated with an Extended Kalman Filter, built with a Keplerian propagator. This key choice highlights the performance achieved by the developed system that could benefit from more accurate propagators. FederNet system has been validated with an experimental analysis on real elevation images. Results showed that FederNet is capable to cruise with a navigation accuracy below 400 meters when a sufficient number of well-distributed craters is available for matching. FederNet capabilities can be further improved with higher resolution data and a data fusion integration with other sensor measurements, such as the lunar GPS, nowadays under investigation by many researchers.

Deep reinforcement learning for rendezvous guidance with enhanced angles-only observability

This research studies the application of reinforcement learning in spacecraft angles-only rendezvous guidance in the presence of multiple constraints and uncertainties. To apply a standard reinforcement learning framework, a stochastic optimal control problem is constructed as a time-discrete Markov decision process, and the observability of angles-only navigation is included in the construction of a reward function. A proximal policy optimization algorithm is used to train a deep neural network (DNN) to map observations of spacecraft state to an optimal control strategy. The trained guidance control network provides a robust nominal orbit and the corresponding closed-loop guidance law, which has the potential to improve the performance of closed-loop navigation, guidance and control. Numerical simulation results are given for an example of far-rendezvous approach guidance. The influence of different weights of the observability term in the reward function on the optimal control strategy is studied. The robustness of the obtained closed-loop control law is evaluated and verified through Monte Carlo simulations in disturbed scenarios.

Distributed Prescribed-Time Attitude Coordination for Multiple Spacecraft With Actuator Saturation Under Directed Graph

This article studies the distributed prescribed-time coordination problem for the attitude system of multiple spacecraft subject to actuator saturation under the communication topology containing a directed spanning tree. The prescribed-time coordination requires that every spacecraft in a formation reaches an agreement state in a preset time. This preset time is set by the user and independent of any other control parameters and the initial state of spacecraft. To achieve this goal, we first design a distributed prescribed-time observer for every follower spacecraft to estimate the state of leader spacecraft. Next, a prescribed-time attitude control law is proposed by utilizing the estimated state of the leader spacecraft. In the proposed control law, an adaptive compensation law is used to compensate the input saturation. Furthermore, the prescribed-time stability of multispacecraft system subject to input saturation under the proposed scheme is analyzed in theory and simulation. The simulation results show the high reliability and effectiveness of the scheme.