The growing population of man-made objects with the build up of mega-constellations and the multiplication of space debris not only increases the potential danger to all space vehicles and in-space infrastructures (including space observatories), but also poses a serious threat to astronomy and dark skies. Monitoring of this population requires precise satellite characterization, which is a challenging task that involves analyzing observational data such as position, velocity, and light curves using optimization methods. In this study, the applications of two optimization procedures are proposed and analyzed to determine the parameters associated with the dynamics of a satellite: one based on the Theory of Functional Connections (TFC) and another one based on the Nelder–Mead heuristic optimization algorithm. The TFC performs linear functional interpolation to embed the constraints of the problem into a functional. We propose to use this functional to analytically embed the observational data of a satellite into its equations of dynamics. After that, any solution will always satisfy the observational data. The second proposed procedure takes advantage of the Nelder–Mead algorithm, that does not require the gradient of the objective function, as alternative solution. The accuracy, efficiency, and dependency on the initial guess of each method is investigated, analyzed, and compared for several dynamical models. These methods can be used to obtain the physical parameters of a satellite from available observational data and for space debris characterization contributing to follow-up monitoring activities in space and astronomical observatories.

The Pampilhosa da Serra Space Observatory (PASO) is located in the center of the continental Portuguese territory, in the heart of a certified Dark Sky destination by the Starlight Foundation (Aldeias do Xisto) and has been an instrumental asset to advance science, education and astrotourism certifications. PASO hosts astronomy and Space Situational Awareness (SSA) activities including a node of the Portuguese Space Surveillance \& Tracking (SST) infrastructure network, such as a space radar currently in test phase using GEM radiotelescope, a double Wide Field of View Telescope system, a EUSST optical sensor telescope. These instruments allow surveillance of satellite and space debris in LEO, MEO and GEO orbits. The WFOV telescope offers spectroscopy capabilities enabling light curve analysis and cosmic sources monitoring. Instruments for Space Weather are being considered for installation to monitor solar activities and expand the range of SSA services.

A formation flying control algorithm using the Lorentz force for Low Earth Orbits to achieve a trajectory with required shape and size is proposed in the paper. The Lorentz force is produced as a result of interaction between the Earth’s magnetic field and an electrically charged spacecraft. Achievement of the required trajectories represents a challenge since the control in three-dimensional space is a scalar value of the satellite’s charge. A Lyapunov-based control algorithm is developed for elimination of the initial relative drift after the launch. It also aims at reaching a required amplitudes for close relative trajectories for in-plane and out-of-plane motion. Due to the absence of full controllability, the algorithm is incapable of correcting all the parameters of the relative trajectory such as in-plane and out-of-plane phase angles. The proposed control allows to converge to the trajectory with required shape and size, though with some oscillating errors in the vicinity of the required trajectory parameters. Numerical simulation of the relative motion is used to study performance of the control algorithm for one case of one controlled satellite and two cases of five controlled satellites forming a nested ellipses and train formations. The convergence time and final trajectory accuracy are evaluated for different control parameters and orbits using Monte Carlo approach.

MAGAL lays the foundations for a future constellation of small satellites carrying radar altimeters aiming to improve the understanding of ocean circulation variability at local, regional, and global scales. All necessary tools will be developed, including a new small, low-power altimeter payload and a miniaturized satellite platform, grounded on the Space 4.0 industry, to be manufactured inseries, minimizing production, operational and launch costs. To implement a collaborative constellation, and better tackle the gaps of large radar altimeter programmes, MAGAL will use a Data Analysis Centre, based on cloud services, for storage and process of data, based on known and improved algorithms, including overlay of layers from multiple sources (e.g. meteorology and opensource data). As a constellation of six satellites, MAGAL increases the density of sea surface topography measurements, enabling more data for altimetry products, when used in synergy with other missions, in coastal areas and over mesoscale features. This results in scientific and commercial information aggregated into a single platform, displayed in various graphical interfaces, allowing overlaid correlations. MAGAL is aligned with the insights from the EU agenda for sustainable development, adding value, alongside the underlying technology development, bringing together the sea's economy and its sustainable growth.

A swarm of ChipSats equipped with miniature magnetorquers is considered, the electromagnetic interaction force is used for relative motion control at extremely short relative distances up to several centimetres. A ChipSat is a satellite printed on 3.5 x 3.5 cm circuit board with a set of sensors, solar panels, onboard computer, and communication system. Assuming the relative motion between each satellite is known, a Lyapunov-based control algorithm is proposed to achieve bounded relative trajectories. A centralized and a decentralized control approaches are implemented. For the centralized approach, a CubeSat is considered as the main satellite after swarm deployment, producing a high value magnetic dipole moment which interacts with the magnetic dipole of the surrounding ChipSats in order to stop relative drift. For the decentralized approach, the ChipSats are linked in interchangeable pairs in order to apply the electromagnetic control force and reduce the relative drift between the satellites to the vicinity of zero. Two different pairing selection methods are proposed in the paper, based on the closest satellite and on the satellite with highest relative drift. Both translational and rotational motion of satellites are considered. The magnetic dipole moments are used for angular velocity damping when orbit control is not required, and a repulsive collision avoidance electromagnetic control is applied when two ChipSats are within dangerously close proximity to each other. The proposed control schemes performance is studied numerically with different algorithm and ChipSats parameters. The influence of these parameters on the swarm separation is obtained using Monte-Carlo simulations.

A decentralized control algorithm for the construction of a tetrahedral configuration using differential lift and drag forces is proposed in this paper. Four 3U CubeSats launched in LEO are considered. Satellite attitude-controlled motion relative to the incoming airflow provides the required differential forces in order to change the relative translational motion. The developed control algorithm allows one to track the relative reference trajectories for the satellites at the vertices of the tetrahedron of the required shape and size. The influence of the initial launch conditions on the controlled tetrahedral motion is studied in this paper.

A mapping technique for the Newtonian attraction potential and the augmented potential, based on polyhedral approximation for the surface of a small celestial body, is proposed and applied to find the local minima of the augmented potential, where one can expect to find the accumulation of loose objects such as stones, sand, or debris.

Nanosatellites in the swarm initially move along arbitrary unbounded relative trajectories according to the launch initial conditions. Control algorithms developed in the paper are aimed to achieve the required spatial distribution of satellites in the along-track direction. The paper considers a swarm of 3U CubeSats in LEO, their form-factor is suitable for the aerodynamic control since the ratio of the satellite maximum to minimum cross-section areas is 3. Each satellite is provided with the information about the relative motion of neighboring satellites inside a specified communication area. The paper develops the corresponding decentralized control algorithms using the differential drag force. The required attitude control for each satellite is implemented by the active magnetic attitude control system. A set of decentralized control strategies is proposed taking into account the communicational constraints. The performance of these strategies is studied numerically. The swarm separation effect is demonstrated and investigated.

Invariant surfaces play a crucial role in the dynamics of mechanical systems separating regions filled with chaotic behavior. Cases where such surfaces can be found are rare enough. Perhaps the most famous of these is the so-called Hess case in the mechanics of a heavy rigid body with a fixed point. We consider here the motion of a non-autonomous mechanical pendulum-like system with one degree of freedom. The conditions of existence for invariant surfaces of such a system corresponding to non-split separatrices are investigated. In the case where an invariant surface exists, combination of regular and chaotic behavior is studied analytically via the Poincaré-Mel’nikov separatrix splitting method, and numerically using the Poincaré maps.

The dynamics of a spacecraft with variable mass distribution is considered, assuming a central Newtonian gravitational field. The equations of spatial attitude motion are derived within the framework of the so-called satellite approximation and examined via a Hamiltonian approach. The centre of mass of the satellite multibody system moves along an elliptic orbit of arbitrary eccentricity. For a prescribed attitude motion, control via the mass redistribution is determined. Various classes of relative equilibria are detected, and the respective control is obtained. The stability of the spacecraft spatial attitude motions is examined in detail.

Motion of a pendulum tethered via a tether to a rotating asteroid of arbitrary shape is considered. Equations of motion are obtained, conditions for the tether to be stretched are investigated. The constraint releasing processes, as well as constrained activations, are also considered.The computer model for dynamics of the tethered space system (TSS) is built considering the mechanical system subject to an unilateral constraint. The model is constructed as a hybrid automata. The corresponding state variables are described as Real type, that provides a possibility to efficiently developed numerical model for transfers from constrained state of mechanical system to its unconstrained state and back. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Approximation of the gravitational field of an irregular celestial body by the gravitational attraction field of four massive points is studied here in the framework of K-means method, known from the theory of pattern recognition. Using this approach, the simplified models for gravitational fields of asteroid (1620) Geographos and comet (67P) Churyumov-Gerasimenko are constructed. For asteroid (1620) Geographos, the proposed model is compared with the previously used one when this asteroid is represented by four cotangent spheres with co-planar centers.

We consider a gravitating system with triangular mass distribution that can be used as approximation of gravitational field for small irregular celestial bodies. In such system, the locations of equilibrium points, that is, the points where the gravitational forces are balanced, are analyzed. The goal is to find the mass distribution which provides equilibrium in a pre-assigned location near the triangular system, and to study the stability of this equilibrium.

The existence, stability and bifurcation analysis is performed for equilibria of a material point in the gravitational field of three homogeneous penetrable balls fixed in absolute frame. The radii of the balls are assumed finite. In the case when the mass distribution admits a symmetry axis, analytic expressions are written out, allowing one to investigate the properties of equilibrium positions located both on the symmetry axis and outside it. The stability of solutions is studied; domains with different instability degree are described.

Problem of motion of a massive particle in a field of attraction of a homogeneous dumb-bell is considered. It is assumed that the dumb-bell comprises two balls intersecting each other. The balls are not assumed being identical. An approximate expression for the Newtonian potential is written down. Relative equilibria of the particle ("libration points") are investigated within the assumption on uniform rotation of the dumb-bell.

This paper addresses the problem of vibrations produced by switched reluctance actuators, focusing on the linear configuration of this type of machines, aiming at its characterization regarding the structural vibrations. The complexity of the mechanical system and the number of parts used put serious restrictions on the effectiveness of analytical approaches. We build the 3D model of the actuator and use finite element method (FEM) to find its natural frequencies. The focus is on frequencies within the range up to nearly 1.2 kHz which is considered relevant, based on preliminary simulations and experiments. Spectral analysis results of audio signals from experimental modal excitation are also shown and discussed. The obtained data support the characterization of the linear actuator regarding the excited modes, its vibration frequencies, and mode shapes, with high potential of excitation due to the regular operation regimes of the machine. The results reveal abundant modes and harmonics and the symmetry characteristics of the actuator, showing that the vibration modes can be excited for different configurations of the actuator. The identification of the most critical modes is of great significance for the actuator’s control strategies. This analysis also provides significant information to adopt solutions to reduce the vibrations at the design.

We consider the problem of in-plane rotations of a space elevator with variable tether length attached to a surface of one of the primaries in a double system. The planet and its moon (or two asteroids) move about their center of mass in unperturbed elliptic Keplerian orbits. We discuss the possibilities to cause a prescribed motion of the system by changing the tether׳s length. Periodic solutions of the equation for the tether length control are studied using the method of small parameter. The stability of these solutions is studied numerically. The analysis shows that there exists a control law that implements tether rotations which are uniform with respect to true anomaly; one can indicate conditions when the above rotations are stable in the first approximation. These results can be used for the development of a planet elevator or a system for payload transportation to and from asteroid surface.