Orbit Maintenance Research Articles

Orbital and Angular Dynamics Analysis of the Small Satellite SAR Mission INFANTE

INFANTE is an ambitious Portuguese project of a small satellite for Earth observation using synthetic aperture radar and multispectral camera. The mission is a precursor and a technology demonstrator for a constellation for home waters coverage. The satellite will be deployed on a relatively low Earth orbit due to the SAR and power budget requirements. The restrictions on the altitude and the stabilization accuracy are relatively tight. Orbital and angular motion simulation results are reported in the paper. The possibility of the mission implementation using available attitude control and determination low-cost hardware is confirmed. Despite the low orbit altitude, the necessity of the orbit maintenance is questioned due to the specific satellite shape.

Tracking neighboring quasi-satellite orbits around Phobos

We consider the orbital maintenance problem on a quasi-satellite orbit about the Martian moon, Phobos. The orbit is computed using a high-fidelity ephemeris model so that the major sources of disturbances are due to measurement error. Two types of orbit maintenance schemes are considered. The first is based on asymptotically tracking the desired trajectory and the second is based on stabilizing to the manifold of trajectories that share the same Jacobi constant as the reference trajectory. The latter can be done because trajectories with the same Jacobi constant are in the neighborhood of one another. The results show that the trajectory-tracking scheme has lower fuel consumption when tracking must be precise and that the approach of stabilizing to a manifold has better fuel consumption at the expense of tracking.

Orbital Maintenance of a Constellation of CubeSats for Internal Gravity Wave Tomography

The advent of radio occultation (RO) instruments aboard CubeSats leads to the possibility of a mission to sound atmospheric internal gravity waves if such satellites are deployed in close-flying constellation. The satellites in the constellation must have slightly perturbed orbital inclinations in order to spread the RO soundings within clusters in two horizontal dimensions, and consequently the satellites will disperse because they will experience different rates of regression of nodes. This dispersion must be countered by propulsive maneuvering in order to maintain the close formation of the constellation. Here, a theoretical approach to the necessary propulsive maneuvering is presented and simulations using comprehensive orbit propagators are performed to analyze four propulsive systems: two cold gas propulsion systems and two electrospray propulsion systems. Cold gas propulsion permits greater separations in inclination between satellites in a constellation by virtue of the greater thrust they can exert on a spacecraft: cold gas propulsion can permit inclination separations of 1 to 10 $^\circ$ while electrospray limits separations to less than 0.2 $^\circ$ . On the other hand, electrospray propulsion provides much longer mission lifetime by virtue of the greater total thrust it offers: cold gas propulsion expends all of its fuel in maintaining the constellation formation in less than approximately 100 days while electrospray propulsion can maintain formation for greater than 1000 days before expending all of its fuel. Mission lifetime is the most critical consideration for a mission, thus electrospray propulsion is recommended for the constellation-flying of CubeSats, but the accelerations that they offer must be greatly increased to enable spacecraft separations useful for tomography of internal gravity waves. Note that any close-flying constellation involving satellites with slightly perturbed inclinations will experience the same dispersing effect as the constellations described herein and, thus, require the same propulsive maneuvering to maintain formation.

Collision probability of composite cubesats hovering in leader-follower configuration

Analytical expressions are obtained for computing the collision probability of a large Composite CubeSats hovering in the close vicinity of another large Composite CubeSats in a Leader-Follower configuration. The composite is constructed from a large number of Unitary CubeSats arranged in a cuboid volume. The study involves the modeling of the growth of a time-dependent probability density function over a period of time and the effects of that growth on the collision probability. Studies of collision probability as a function of time are performed in terms of the parameters: separation between neighboring orbiters, covariance size (different in three directions) and the size of the two cuboid CubeSat Composites. It was found that certain combinations of parameters resulted in collision probability curves which intersected and others did not. This curve-crossing phenomenon cannot be predicted in advance but must be demonstrated quantitatively by performing detailed computations. This knowledge may be used to advantage in the design of distributed systems and in the orbital maintenance of their configuration. Moreover, the Principle of Scaling is used to obtain collision probabilities using the results obtained from a relatively small number of case studies so as to circumvent the effort to perform copious computer runs when the input parameters are changed.

An adaptive groundtrack maintenance scheme for spacecraft with electric propulsion

In this paper, the repeat-groundtrack orbit maintenance problem is addressed for spacecraft driven by electric propulsion. An adaptive solution is proposed, which combines a hysteresis controller and a recursive least squares filter. The controller provides a pulse-width modulated command to the thruster, in compliance with the peculiarities of the electric propulsion technology. The filter takes care of estimating a set of environmental disturbance parameters, from inertial position and velocity measurements. The resulting control scheme is able to compensate for the groundtrack drift due to atmospheric drag, in a fully autonomous manner. A numerical study of a low Earth orbit mission confirms the effectiveness of the proposed method.

A symplectic moving horizon estimation algorithm with its application to the Earth—Moon L2 libration point navigation

Accurate state estimations are perquisites of autonomous navigation and orbit maintenance missions. The extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are the most commonly used method. However, the EKF results in poor estimation performance for systems are with high nonlinearity. As for the UKF, irregular sampling instants are required. In addition, both the EKF and the UKF cannot treat constraints. In this paper, a symplectic moving horizon estimation algorithm, where constraints can be considered, for nonlinear systems are developed. The estimation problem to be solved at each sampling instant is seen as a nonlinear constrained optimal control problem. The original nonlinear problem is transferred into a series of linear-quadratic problems and solved iteratively. A symplectic method based on the variational principle is proposed to solve such linear-quadratic problems, where the solution domain is divided into sub-intervals, and state, costate, and parametric variables are locally interpolated with linear approximation. The optimality conditions result in a linear complementarity problem which can be solved by the Lemke’s method easily. The developed symplectic moving horizon estimation method is applied to the Earth-Moon L2 libration point navigation. And numerical simulations demonstrate that though more time-consuming, the proposed method results in better estimation performance than the EKF and the UKF.

Stationkeeping Analysis for Solar Sailing the Region of Binary Asteroid Systems

Asteroid exploration may largely benefit from solar-sail propulsion that is coupled with satellite miniaturization. There remain, however, several open questions on sail dynamics in the vicinity of small bodies. One such question is the feasibility of solar-sail missions within binary asteroid systems from the perspective of orbit maintenance. Although sail transfer trajectories to small bodies are often discussed, more work is necessary to understand sail stationkeeping dynamics in such environments. This work focuses on solar-sail stationkeeping in the region of binary asteroids within a modified elliptic restricted three-body problem. Quasi-periodic orbits and Kolmogorov–Arnold–Moser theory are employed to construct reference solutions that are naturally bounded and therefore facilitate orbit maintenance. Reference quasi-periodic behaviors may reflect the characteristics of motion within higher-fidelity models more accurately than purely periodic or equilibrium baseline solutions. Then, a turn-and-hold stationkeeping strategy is implemented to offset orbit determination errors, and stationkeeping parameters are investigated. Using the Didymos binary asteroid system as a representative case study, dynamical reference structures for sail trajectories are explored. Additionally, conditions for their controllability are also discussed. Insight from this analysis is applicable to other binary asteroid systems.

Integrated orbit determination and maintenance in Earth-Moon unstable dynamics environment

The hyperbolic instability of collinear libration point orbits dominates the distribution of orbit uncertainty, which is closely related with the unstable manifold of the local orbit. Exploiting the distribution of orbit uncertainty in an unstable orbital environment, an integrated orbit determination and maintenance approach is proposed. X-ray pulsar navigation embedded in the Kalman filtering architecture is adopted to determine the orbit of a spacecraft flying along the Earth-Moon L2 halo orbit. To keep the spacecraft in the vicinity of the nominal trajectory, the newly proposed orbit maintenance approach based on the covariance matrix is proposed to design the orbit maintenance maneuver. The numerical simulations show that the proposed approach has a good performance in orbit determination and maintenance.

Meta-heuristic methods for optimization of truss structures with vibration frequency constraints

Vibration frequencies are important and easily attainable parameters, which can be used to observe the dynamic behavior of a structural system. In many cases, it is beneficial to place some restrictions on the natural frequencies of a structure for different purposes. As a well-known example, it is advantageous to constrain the vibration frequencies of a structural system so as to prevent resonance in response to external excitation. Another application is in space structures, which are supposed to operate in zero gravity conditions; constraining natural frequencies is crucial in order to control the dynamic response to different sources of vibration like orbit maintenance maneuvers. Attempting to optimize a weight- or cost-related objective function of a structure, while placing lower and/or upper bounds on its vibration frequencies, gives rise to the well-known problem of structural optimization with frequency constraints. This paper reviews different meta-heuristic optimization techniques utilized to address different examples of the problem.

Historical-orbital-data-based method for monitoring the operational status of satellites in low Earth orbit

A method is developed for monitoring the operational status of satellites in low Earth orbit (LEO) based on their historical two-line element (TLE) data. In this method, whether the satellite still has the maneuverability to maintain the orbital altitude is used as the criteria for judging the operational status, the whole judgment process includes two steps. The first step is to design a specialized algorithm to detect orbit maintenance maneuvers from the satellite's TLE time-history. The algorithm uses abnormal data segments of the TLE derived semi-major axis time series to identify the orbit maintenance maneuver, and various measures are taken to eliminate the noise interference and to ensure the detection accuracy. The second step is to use the detected maneuvering history to determine the current operational status of the satellite. In this step, the statistical technique is used to get the temporal regularity of the satellite to implement orbit maintenance maneuvers and the allowable range of the natural variation of the semi-major axis, so then the criteria for determining the satellite operational status is developed. Analysis of typical LEO satellites indicates that this method can accurately determine the current operational status of the satellite and provide an approximate estimation interval of the satellite retiring time, which is of practical value.

Semi-analytical acquisition algorithm for repeat-groundtrack orbit maintenance

In this paper, the orbit acquisition and maintenance strategies for the repeat-groundtrack orbit are investigated to maintain the ground track of the satellite within a certain range. Two kinds of orbital dynamics models are introduced to calculate the on-orbit state of satellite. One is the orbital propagation model which is of high fidelity and can approximately express the forces acting on the satellite. The other is the design model which is of low fidelity and utilized by the semi-analytical acquisition algorithm to yield the reference repeatgroundtrack orbit. Combining the differential correction and analytical expressions, the results computed by the semi-analytical acquisition algorithm are of relatively high precision compared with the genetic algorithm. At the same time, the computational burden of the semi-analytical acquisition algorithm is far less than the genetic algorithm. Based on the reference orbit, two orbit maintenance strategies which are designed for chemical and electric engines are put forward to correct the orbit in order to make the ground track of satellite shift in a certain range. The application to the Chinese-French Oceanic Satellite mission has well validated the feasibility of these two strategies. Simulation results have shown that the strategy designed for chemical engine can keep the ground track displacement within 200 m, while all the orbit points can possess sub-meter repeat distance through adopting the strategy designed for the electric engine, which satisfies the requirements of the Chinese-French Oceanic Satellite mission.

Lunar orbit dynamics and maneuvers for Lunisat missions

Lunisat represents a next-generation microsatellite aimed at orbiting the Moon, and equipped with dispensers for the release of nanosatellites. This research is focused on the orbital dynamics of both the main microsatellite and the nanosatellites after release. Due to the irregular concentrations of mass in the Moon, low altitude, near-circular lunar orbits are affected by a considerable number of harmonics of the Moon gravitational field. Nonsingular equinoctial orbit elements are employed for orbit propagations, in conjunction with numerical averaging, which is a numerical technique that allows substantial computational improvements. The dynamical model considers a large number of harmonics of the lunar gravitational field, as well as the Earth and Sun perturbing influence as third bodies. Low-altitude lunar satellites turn out to impact the lunar surface after a few weeks or months. In case of an unsatisfactory lifetime, two simple orbit maintenance strategies are evaluated, together with the related propellant budget. Nanosatellites will be released from Lunisat by means of springs. The orbit of each nanosatellite depends on the release conditions, i.e. the relative velocity magnitude and direction. This work investigates the nanosatellite lifetimes as functions of these conditions. Lastly, minimum-time low-thrust transfers for reducing the orbit altitude are investigated, both for nanosatellite release and for the conclusive phase of the Lunisat mission, which finally terminates with the impact on the lunar surface.

Precise Autonomous Orbit Maintenance of a Low Earth Orbit Satellite

AbstractIn this paper, the problem of precise autonomous orbit maintenance of a satellite using output feedback and quadratic optimal regulators in a low Earth orbit is investigated. Autonomous on-...

Drift Counteraction and Control of Downsized and Underactuated Systems: What MPC Has to Offer?

Motivated by practical applications, the paper highlights MPC formulations suitable for counteracting system drift and the effects of large measured disturbances/set-point changes, and for overcoming limitations of underactuation. For drift counteraction, where the objective is to maximize the time or yield until the system trajectory exits a prescribed set, defined by system safety constraints, operating limits and/or efficiency requirements, MPC, based on mixed integer or conventional linear programming, can lead to effective solutions for higher order systems than possible with dynamic programming and value iterations based methods. Such solutions can have broad applicability including for fuel optimal Geostationary Orbit (GEO) station keeping, spacecraft Low Earth Orbit (LEO) maintenance, underactuated spacecraft attitude control, hybrid electric propulsion energy management, glider flight management, and the development of driving policies for adaptive cruise control and autonomous driving. The paper also highlights the capability of MPC to achieve non-smooth local stabilization of underactuated systems that can be exploited for attitude control of underactuated spacecraft with reaction wheel failures. Related results for systems that cannot be globally stabilized by continuous feedback are also mentioned. Finally, opportunities to handle large load and set-point changes with reference governors are discussed.

A deployable mechanism concept for the collection of small-to-medium-size space debris

Current efforts in active debris removal strategies and mission planning focus on removing the largest, most massive debris. It can be argued, however, that small untrackable debris, specifically those smaller than 5 cm in size, also pose a serious threat. In this work, we propose and analyze a mission to sweep the most crowded Low Earth Orbit with a large cupola device to remove small-to-medium-size debris. The cupola consists of a deployable mechanism expanding more than 25 times its storage size to extend a membrane covering its surface. The membrane is sufficiently stiff to capture most small debris and to slow down the medium-size objects, thus accelerating their fall. An overview of the design of a belt-driven rigid-link mechanism proposed to support the collecting cupola surface is presented, based on our previous work. Because of its large size, the cupola will be subject to significant aerodynamic drag; thus, orbit maintenance analysis is carried out using the DTM-2013 atmospheric density model and it predicts feasible requirements. While in operation, the device will also be subject to numerous hyper-velocity impacts which may significantly perturb its orientation from the desired attitude for debris collection. Thus, another important feature of the proposed debris removal device is a distributed array of flywheels mounted on the cupola for reorienting and stabilizing its attitude during the mission. Analysis using a stochastic modeling framework for hyper-velocity impacts demonstrates that three-axes attitude stabilization is achievable with the flywheels array. MASTER-2009 software is employed to provide relevant data for all debris related estimates, including the debris fluxes for the baseline mission design and for assessment of its expected performance. Space debris removal is a high priority for ensuring sustainability of space and continual launch and operation of man-made space assets. This manuscript presents the first analysis of a small-to-medium size debris removal mission, albeit finding it to not be economically viable at the present time.

Design of communication relay mission for supporting lunar-farside soft landing

ChangE-IV will be the first soft-landing and rover mission on the lunar farside. The relay satellite, which is located near the Earth-Moon L2 point for relay communication, is the key to the landing mission. Based on an analysis of the characteristics of the task and the technical difficulties associated with the relay satellite system, the overall design scheme of the relay communication mission is proposed in terms of trajectory design and communication system design among other aspects. First, according to the complex dynamic environment, a mission orbit that serves as an uninterrupted communication link is presented. A short-duration and low-energy transfer trajectory with lunar flyby is discussed. Orbital correction and a low-cost control strategy for orbit maintenance in the Earth-Moon L2 point region are provided. Second, considering the existing technical constraints, the requirement of relay communication in different stages and the design schemes of frequency division and redundant relay communication system are introduced. Finally, based on the trajectory design index and the performance of the communication system, the overall design scheme of the relay communication mission is proposed. This mission will provide the technical support and reference required for the ChangE-IV mission.

Single-Switch Quasi-Resonant DC–DC Converter for a Pulsed Plasma Thruster of Satellites

Due to its low mass and medium impulse bit, the pulsed plasma thruster (PPT) is a suitable electric propulsion system for orbit maintenance and attitude control for nanosatellites. The PPT uses an igniter circuit to produce an arc in vacuum for plasma generation. In this paper, a new quasi-resonant converter topology is proposed for the PPT igniter. It consists of a resonant tank, a step-up transformer, and a Cockcroft–Walton voltage multiplier circuit. While other resonant converters require a switch bridge, the proposed approach uses only a single switch. This prevents the possible short-circuit of the same leg in a switch bridge caused by the noise interference or single event effect in space. Moreover, the switching control is realized without a dead time which simplifies the implementation. Both simulation and experimental results have validated that the proposed topology operates in a quasi-resonant state to realize zero-current switching. It reduces the switching noise, voltage spike, and switch's conduction loss. Moreover, the proposed topology also has a better boost capability than some of the existing resonant converters.

High-precision repeat-groundtrack orbit design and maintenance for Earth observation missions

The focus of this paper is the design and station keeping of repeat-groundtrack orbits for Sun-synchronous satellites. A method to compute the semimajor axis of the orbit is presented together with a station-keeping strategy to compensate for the perturbation due to the atmospheric drag. The results show that the nodal period converges gradually with the increase of the order used in the zonal perturbations up to $$J_{15}$$ . A differential correction algorithm is performed to obtain the nominal semimajor axis of the reference orbit from the inputs of the desired nodal period, eccentricity, inclination and argument of perigee. To keep the satellite in the proximity of the repeat-groundtrack condition, a practical orbit maintenance strategy is proposed in the presence of errors in the orbital measurements and control, as well as in the estimation of the semimajor axis decay rate. The performance of the maintenance strategy is assessed via the Monte Carlo simulation and the validation in a high fidelity model. Numerical simulations substantiate the validity of proposed mean-elements-based orbit maintenance strategy for repeat-groundtrack orbits.

Orbit Control of Fly-around Satellite with Highly Eccentric Orbit Using Solar Radiation Pressure

The method of controlling highly eccentric accompanying flight orbit using the solar wing is proposed in this paper. The formation is maintained by controlling the orbit of the accompanying satellite (follower). The accompanying satellite rotates around its inertial principal axis with a constant angular velocity. The control on the accompanying satellite is divided into the in-plane control and out-of-plane control. The in-plane control is superior to the out-of-plane control. The out-of-plane control force is applied when the in-plane error is eliminated or the in-plane control force can not be supplied due to some geometrical factors. By the sliding mode control method, the magnitude and direction of the control force required by the in-plane orbit control are calculated. Then accordingly, the expression of the solar wing orientation with respect to the satellite body in the control process is derived, so that by adjusting the orientation of the solar wing, the required control force can be obtained. Finally, the verification on this method is performed by numerical simulations, including the orbit adjustment, error elimination, and the orbit maintenance. It is shown that this method can keep the error less than 5 m, and it is feasible for the space formation flight.

微小重力環境下における接触制御のための運動推定システムの構築

Recently, according to the progress of space development, space debris such as used satellites or parts of rockets are rapidly increasing in orbit. Therefore, system to maintain the satellite orbit condition is important for safe and sustainable space utilization. Orbital Maintenance System (OMS) is a concept of satellite system to maintain orbit condition by serving inspection, repair, and removal of failed satellites. Because OMS is expected to control non-cooperative space debris, analysis and control of contact dynamics with non-cooperative target are one of the key technologies to realize OMS. Especially, it is essentially important to establish technologies to capture rotating objects under microgravity condition because many space debris are generally tumbling in orbit. This paper proposes an estimation method of rotational motion using depth image sensor. Effectiveness of the method is qualified using a floating and rotating robot in two-dimensional micro-gravity condition.