Attitude determination represents a fundamental task for spacecraft. Achieving this task on small satellites, and nanosatellites in particular, is further challenging, because the limited power and computational resources available on-board, together with the low development budget, set strict constraints on the selection of the sensors and the complexity of the algorithms. Attitude determination is obtained here from the only measurements of a three-axis magnetometer and a model of the Geomagnetic field, stored on the on-board computer. First, the angular rates are estimated and processed using a second-order low-pass Butterworth filter, then they are used as an input, along with Geomagnetic field data, to estimate the attitude matrix using an unsymmetrical TRIAD. The computational efficiency is enhanced by arranging complex matrix operations into a form of the Faddeev algorithm, which is implemented using systolic array architecture on the FPGA core of a CubeSat on-board computer. The performance and the robustness of the algorithm are evaluated by means of numerical analyses in MATLAB Simulink, showing pointing and angular rate accuracy below 10° and 0.2°/s. The algorithm implemented on FPGA is verified by Hardware-in-the-loop simulation, confirming the results from numerical analyses and efficiency.

The subject of this work is the implementation and experimental testing of a purely magnetic attitude control strategy, which can provide stabilization after the deployment and pointing of the spacecraft without any attitude information. In particular, the control produces the detumbling of the satellite and leads it to a desired attitude with respect to the direction of the Earth magnetic field, based on the only information provided by a three-axis magnetometer. The system is meant to be used as a backup solution, in case of failure of the primary strategy and is designed considering the constraints set on time of operations, power consumption, and peak electric current for a typical CubeSat mission. The detumbling and pointing algorithms are implemented on the FPGA core of a CubeSat on-board computer and tested by Hardware-in-the-loop simulations. The simulation setup includes a Helmholtz cage, recreating the magnetic environment along the orbit, the on-board computer, a MEMS three-axis magnetometer and Simulink software, on which the attitude dynamics is propagated. Test on the real system can provide useful information to select the parameters of the control, such as the gains, to estimate the limits of the system, the time of operations and prevent failures.

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.

AstroBio CubeSat is a mission funded by the Italian Space Agency aimed at validating novel lab-on-chip technology, that would enable the use of micro- and nanosatellites as autonomous orbiting laboratories for research in astrobiology. This 3U CubeSat is equipped with a passive magnetic attitude control system (PMACS), including permanent magnets and hysteresis strips, which allows for stabilizing the spacecraft with the longitudinal axis in the direction of the geomagnetic field vector. This work presents the process followed for the experimental characterization of the system, performed on the engineering unit of the satellite by using a Helmholtz cage facility and a spherical air-bearing to recreate environmental conditions similar to the ones experienced during the orbital motion. The hysteresis strips are characterized starting from the determination of the hysteresis loop, from which the energy dissipation per cycle and the apparent magnetic permeability are extracted. Tests performed by using the Helmholtz cage and the air-bearing facility allows for further investigating the damping torque produced by the PMACS and validating the abovementioned parameters. Numerical analysis is then used to select the number of permanent magnets which allows for achieving a pointing accuracy within an error of ${10}^{\circ }$ within 24 h from the deployment. The analysis of the flight data supports the results obtained from the experimental test campaigns, confirming the effectiveness of the proposed methods and of the PMACS design.

This papers introduces an analytic method to define multistage launcher trajectories to determine the payload mass that can be inserted in orbits of different semimajor axes and inclinations. This method can evaluate the gravity loss, which is the main term to be subtracted to the Tziolkowski evaluation of the velocity provided by the thrust of a launcher. In the method, the trajectories are dependent on two parameters only: the final flight-path angle ${\gamma }_f$ at the end of the gravity-turn arc of the launcher trajectory and the duration $t_c$ of the coasting arc following the gravity-turn phase. The analytic formulas for the gravity-turn phase, being solutions of differential equations with a singularity, allow us to identify the trajectory with a required final flight-path angle ${\gamma }_f$ in infinite solutions with the same initial vertical launch condition. This can also drive the selection of the parameters of the pitch manoeuvre needed to turn the launcher from the initial vertical arc. For any pair ${\gamma }_f$ and $t_c$, a launcher trajectory is determined. A numerical solver is used to identify the values ${\gamma }_f$ and $t_c$, allowing for the insertion of the payload mass into the required orbit. The analytic method is compared with a numerical code including the drag effect, which is the only effect overlooked in the analytic formulas. The analytical method is proven to predict the payload mass with an error never exceeding the 10% of the actual payload mass, found through numerical propagation.

In this work, we investigate the behavior of low-energy trajectories in the dynamical framework of the spatial elliptic restricted 4-body problem, developed using the Hamiltonian formalism. Introducing canonical transformations, the Hamiltonian function in the neighborhood of the collinear libration point $L_1$ (or $L_2$), can be expressed as a sum of three second order local integrals of motion, which provide a compact topological description of low-energy transits, captures and quasiperiodic libration point orbits, plus higher order terms that represent perturbations. The problem of small denominators is then applied to the order three of the transformed Hamiltonian function, to identify the effects of orbital resonance of the primaries onto quasiperiodic orbits. Stationary solutions for these resonant terms are determined, corresponding to quasiperiodic orbits existing in the presence of orbital resonance. The proposed model is applied to the Jupiter-Europa-Io system, determining quasiperiodic orbits in the surrounding of Jupiter-Europa $L_1$ considering the 2:1 orbital resonance between Europa and Io.