Dynamics and Control of Satellite Formations Invariant under the Zonal Harmonic Perturbation

A satellite formation operating in low-altitude orbits is subject to perturbations associated to the higher-order harmonics of the gravitational field, which cause a degradation of the formation configurations designed based on the unperturbed model of the Hill–Clohessy–Wiltshire equations. To compensate for these effects, periodic reconfiguration maneuvers are necessary, requiring the prior allocation of a propellant mass budget and, eventually, the use of resources from the ground segment, having a non-negligible impact on the complexity and cost of the mission. Using the Hamiltonian formalism and canonical transformations, a model is developed that allows designing configurations for formation flying invariant with respect to the zonal harmonic perturbation. Jn invariant configurations can be characterized, selecting the drift rate (or boundedness condition) and the amplitude of the oscillations, based on four parameters which can be easily converted in position and velocity components for the satellites of the formation. From this model, a guidance strategy is developed to inject a satellite approaching another spacecraft into a bounded relative trajectory about it and the optimal time for the maneuver, minimizing the total ΔV , is identified. The effectiveness of the model and of the guidance strategy is verified on some scenarios of interest for formations operating in a sun-synchronous and a medium-inclination low Earth orbit and a medium-inclination lunar orbit

A Single-Launch Deployment Strategy for Lunar Constellations

Satellite constellations can provide communication and navigation services to support future lunar missions, and are attracting growing interest from both the scientific community and industry. The deployment of satellites in orbital planes that can have significantly different inclinations and right ascension of the ascending node requires dedicated launches and represents a non-trivial issue for lunar constellations, due to the complexity and low accessibility of launches to the Moon. In this work, a strategy to deploy multiple satellites in different orbital planes around the Moon in a single launch is examined. The launch vehicle moves along a conventional lunar escape trajectory, with parameters selected to take advantage of gravity-braking upon encountering the Moon. A maneuver at the periselenium allows the transfer of the spacecraft along a trajectory converging to the equilibrium region about the Earth–Moon libration point L1 , where the satellites are deployed. Providing a small ΔV , each satellite is transferred into a low-energy trajectory with the desired inclination, right ascension of the ascending node, and periselenium radius. A final maneuver, if required, allows the adjustment of the semimajor axis and the eccentricity. The method is verified using numerical integration using high-fidelity orbit propagators. The results indicate that the deployment could be accomplished within one sidereal month with a modest ΔV budget

Design of a Schlieren system for low enthalpy hypersonic flow visualization in GHIBLI facility and development of image processing and quantitative analysis codes with preliminary application to sonic free jet

GHIBLI is a 2 MW arc-jet hypersonic facility located at CIRA premises in Capua (Italy), designed for testing candidate TPS materials for re-entry vehicles. Measured data during cold flow tests, i.e. with arc-heater off, showed the achievement of hypersonic conditions at the nozzle exit. Hence, a Schlieren system has been designed to investigate qualitatively and quantitatively such a low enthalpy flow-jet. The apparatus is a classical Toepler’s double lens one. CFD analyses of the free jet were performed to determine the density gradients. On the basis of these results, the limit of sensitivity of the system was determined and the components of the apparatus were dimensioned. A COBLED extended white light source, along with slits made of high reflecting material were experimented. Schlieren images, projected on opaque screen are acquired by a CMOS monochromatic sensor. An image processing code was developed in MATLAB to obtain contrast and clearness enhancement. Quantitative analysis was approached by developing a density-contrast relation, based on schlieren phase-shift effects, modeled under the wave theory of light, and the CMOS tension-charge characteristics. For this purpose, a code named Density from Contrast was developed in MATLAB to measure the luminous intensity of each pixel of captured images and thus compute the density field

Earth-Venus Mission Analysis via Weak Capture and Nonlinear Orbit Control

Exploration of Venus is recently driven by the interest of the scientific community in understanding the evolution of Earth-size planets, and is leading the implementation of missions that can benefit from new design techniques and technology. In this work, we investigate the possibility to implement a microsatellite exploration mission to Venus, taking advantage of (i) weak capture, and (ii) nonlinear orbit control. This research considers the case of a microsatellite, equipped with a high-thrust and a low-thrust propulsion system, and placed in a highly elliptical Earth orbit, not specifically designed for the Earth-Venus mission of interest. In particular, to minimize the propellant mass, phase (i) of the mission was designed to inject the microsatellite into a low-energy capture around Venus, at the end of the interplanetary arc. The low-energy capture is designed in the dynamical framework of the circular restricted 3-body problem associated with the Sun-Venus system. Modeling the problem with the use of the Hamiltonian formalism, capture trajectories can be characterized based on their state while transiting in the equilibrium region about the collinear libration point L1. Low-energy capture orbits are identified that require the minimum velocity change to be established. These results are obtained using the General Mission Analysis Tool, which implements planetary ephemeris. After completing the ballistic capture, phase (ii) of the mission starts, and it is aimed at driving the microsatellite toward the operational orbit about Venus. The transfer maneuver is based on the use of low-thrust propulsion and nonlinear orbit control. Convergence toward the desired operational orbit is investigated and is proven analytically using the Lyapunov stability theory, in conjunction with the LaSalle invariance principle, under certain conditions related to the orbit perturbing accelerations and the low-thrust magnitude. The numerical results prove that the mission profile at hand, combining low-energy capture and low-thrust nonlinear orbit control, represents a viable and effective strategy for microsatellite missions to Venus

Ballistic and powered capture of asteroids in the Sun-Earth-Moon system

Space missions aimed at in-situ exploration of near-Earth asteroids have long attracted the interest of both space agencies and private research groups. Several solutions have been proposed in the last decades, all associated by the critical but pivotal phase of asteroid capture. In fact, the dynamics of asteroid trajectories is that of a negligible mass in a multibody environment, resulting from the combined effect of the gravitational potentials of the surrounding celestial bodies, called the primaries. In the Sun-Earth-Moon system here examined, asteroids typically orbit the center of mass of the system, nevertheless it can happen that, under some conditions, the asteroid gets trapped in the gravitational well of the Earth (or the Moon). Such a scenario is called a ballistic capture and corresponds to an opportune energy condition for an exploration mission. Because of the strong gravitational perturbations characterizing multibody environments, ballistic captures have typically limited duration and all the mission operations, including landing, experiments and take-off, shall be performed within this interval of time. The occurrence and duration of an asteroid capture can be in principle controlled by means of a spacecraft capable of docking the asteroid and providing the thrust acceleration necessary to adequately modify its dynamical state, performing a powered capture. In this work, the conditions for both ballistic and powered capture of a near-Earth asteroid are investigated in the dynamical framework of the elliptic restricted 4-body problem. The problem is modeled using the Hamiltonian formalism and canonical transformations. The dynamic equations of motion are first linearized about quasi-equilibrium points, which represent an extension of libration points existing in the circular restricted 3-body problem, and then set to a normal form of the type saddle-center-center, by means of canonical transformations. The resulting mathematical system allows defining the topological location of capture trajectories, and estimating the capture time, thus representing a powerful tool in the design of ballistic asteroid capture. Furthermore, once identified the parameters characterizing capture condition, expressions for the magnitude and direction of low thrust acceleration to be provided for powered capture are inferred. The accuracy of the proposed method is verified by means of numerical simulations on a number of scenarios for possible missions to be performed in the next future

IAA Italian Regional Symposium of Space Debris Observations from Basilicata

Deorbiting of microsatellites using compact electromagnetic actuators for space debris mitigatio

New techniques for space science missions

In the last decades, the growing interest in investigating natural science in the space environment sets new targets, constraints and challenges in space mission design, defining what is nowadays known as space science. The goal of this PhD research is the development of new techniques of mission analysis, which can lead to further development of space science missions using CubeSat technology. Two main objectives have been pursued, related to both solar system exploration and low Earth orbit missions. Due to the low power and thrust available on a CubeSat, low energy trajectories are necessary to allow solar system exploration. These are designed here considering a further constraint on the transfer time, which should be minimized to limit the effects of the hostile space environment on the on-board systems, typically based on components off-the-shelf. According to these issues, the topological properties of the linear dynamics in the circular restricted 3-body problem were investigated to develop a method allowing the design of internal transit and captures, including the possibility to select the osculating orbital elements at capture. Three guidance strategies are proposed, allowing modification on the ultimate behavior of trajectories to match the desired mission requirements, also in the presence of the gravitational perturbations due to a fourth body. These strategies are effective with modest velocity variations (delta-V) and are tailored to be implemented with compact continuous thrusters, compatible with CubeSats. The method was originally developed in the dynamical framework of the spatial circular restricted 3-body problem and later extended to the elliptic restricted 4-body problem. The final chapters are related to low Earth orbit missions, presenting the development of a purely magnetic attitude determination and control systems, suitable for implementation as a backup solution on CubeSats. Attitude control allows detumbling and pointing towards the magnetic field. At the same time, attitude determination is obtained from the only measurements of a three-axis magnetometer and a model of the geomagnetic field, without implementing any sophisticate filtering solution. To enhance the computational efficiency of the system, complex matrix operations are arranged into a form of the Faddeev algorithm, which can be conveniently implemented on the field programmable gate array core of a CubeSat on-board computer using systolic array architecture. The performance and the robustness of the algorithm are evaluated by means of both numerical analyses in Matlab Simulink and hardware-in-the-loop simulations in a Helmholtz cage facility

New techniques for space science missions

Space exploration was born from the space race between the USSR and the USA, when the two superpowers were driven by the idea that the technological progress, required by spaceflight, could lead to military supremacy, contribute to national security and, eventually, symbolize ideological superiority. In such a hectic context, the readiness of the solutions proposed was predominant over their accessibility and affordability, features nowadays crucial, since space related activities expanded to cover a wide variety of areas of scientific research. New techniques are therefore necessary, to solve the old problem of space exploration complying the modern space mission requirements. In the recent years, there has been a growing interest in space missions related to the dynamics of three body systems. In such a framework, special non-Keplerian trajectories exist and it can be taken advantage of them to design low energy transfers between celestial bodies, requiring less propellant than classical transfers and increasing the flexibility of the mission by either allowing extending the launch window or transferring spacecraft to more orbits on a given date. Also, spacecraft operating in proximity of a collinear libration point, such as space stations and telescopes, can be envisioned and they could greatly benefit from being placed in regions characterized by small perturbations. In this work, I present the state of the art of the modern techniques of mission analysis and give a review of some selected missions based on them, with the aim of defining the topics to further investigate during my PhD

Design and development of a full 5-DOF testbed for testing nanosatellites formation flying, rendezvous and proximity operations

In this paper we present the concept design and the progress in the realization of a spacecraft motion simulator currently being developed by the School of Aerospace Engineering at “Sapienza” University of Rome. The facility is aimed at testing and validating guidance, navigation and control algorithms for nanosat formation flying, rendezvous and proximity operations. To simulate the spacecraft motion dynamics in the terrestrial environment the micro-gravity conditions must be recreated adequately. It means that the effect of the gravity force on both the translation and the rotation of the spacecraft simulator must be compensated or minimized. This goal is achieved through the interaction of the facility core subsystems: a 2-DOF air bearing table, reproducing the spacecraft planar translation on the horizontal plane, and a 3-DOF spherical air bearing, reproducing the spacecraft rotational motion around its center of mass. These two subsystems can operate both independently or simultaneously, thus allowing the spacecraft motion dynamics to be simulated up to 5-DOF. The design of the spacecraft motion simulator is presented with focus on the critical aspects of the project. These include the characterization of the air cushion and related effect on the design of the spherical air bearing, the realization of a balancing system necessary for minimizing the gravity torque and the remote control of the facility for calibration and test operations. Preliminary results from numerical simulations and tests are shown and discussed. Open issues are introduced and possible solutions are proposed

Design and Numerical Validation of an Algorithm for the Detumbling and Angular Rate Determination of a CubeSat Using Only Three-Axis Magnetometer Data

A detumbling algorithm is developed to yield three-axis magnetic stabilization of a CubeSat deployed with unknown RAAN, orbit phase angle, inclination, attitude, and angular rate. Data from a three-axis magnetometer are the only input to determine both the control torque and the angular rate of the spacecraft. The algorithm is designed to produce a magnetic dipole moment which is constantly orthogonal to the geomagnetic field vector, independently of both the attitude and the angular rate of the rigid spacecraft. The angular rates are calculated in real time from magnetometer data, and the use of a second-order low-pass filter allows to rapidly reduce the measurement error within ±0.2 deg/sec. Numerical validation of the algorithm is performed, and a variety of feasible scenarios is simulated assuming the CubeSat to operate in low Earth orbit. The robustness of the algorithm, with respect to unknown deployment conditions, different sampling rates, and uncertainties on the moments of inertia of the CubeSat, is verified