Nicolò Bernardini

In the recent decade, we witnessed a remarkable proliferation of spacecraft orbiting around Earth and venturing farther into our Solar system. As the number of operated spacecraft increases, the complexity of managing multiple missions escalates, along with the associated costs. Deep space missions will require spacecraft to navigate through challenging trajectories with limited and delayed communications. This makes autonomy crucial for ensuring the success of these missions. Convex optimization has emerged as a promising technique for autonomous guidance and navigation algorithms thanks to its computational speed and convergence properties. Only recently convex optimization has been adopted to solve non-linear optimization problems thanks to the introduction of successive convex programming (SCVX) enabling its application to a wide range of astrodynamics problems. In this research, differential algebra techniques are applied to improve the performances of SCVX by introducing a novel state-dependent trust region that enhances the robustness and optimality of SCVX techniques. The application of SCVX is then successfully expanded to operations around small celestial bodies. Furthermore, to improve the targeting of periodic and quasi-periodic orbits a new methodology based on the representation of these trajectories with their Fourier series is introduced. As spacecraft trajectories are susceptible to various sources of errors, the covariance of the state is included in the optimal control problem to obtain covariance robust trajectories that enable the containing of the expansion of the uncertainties. At the same time, differential algebra is applied to include the effects of the measurements in the optimization process. Finally, a novel convex-based autonomous guidance and navigation algorithm based on high-order Taylor expansions is presented. The new guidance and navigation algorithm enables the exploration of different penalty functions for the estimation process. At the same time, using high-order polynomials allows for the improvement of the computational efficiency of the guidance and navigation algorithm.

Spacecraft trajectory optimization is essential for all the different phases of a space mission, from its launch to end-of-life disposal. Due to the increase in the number of satellites and future space missions beyond our planet, increasing the level of autonomy of spacecraft is a key technical challenge. In this context, traditional trajectory optimization methods, like direct and indirect methods are not suited for autonomous or on-board operations due to the lack of guaranteed convergence or the high demand for computational power. Heuristic control laws represent an alternative in terms of computational power and convergence but they usually result in sub-optimal solutions. Successive convex programming (SCVX) enables to extend the application of convex optimization to non-linear optimal control problems. The definition of a good value of the trust region size plays a key role in the convergence of SCVX algorithms, and there is no systematic procedure to define it. This work presents an improved trust region based on the information given by the nonlinearities of the constraints which is unique for each optimization variable. In addition, differential algebra is adopted to automatize the transcription process required for SCVX algorithms. This new technique is first tested on a simple 2D problem as a benchmark of its performance and then applied to solve complex astrodynamics problems while providing a comparison with indirect, direct, and standard SCVX solutions.

PLATOR is a new electrothermal thruster for space logistics applications, developed by the University of Surrey and the University of Leicester. This paper describes the technology behind the development of the thruster and presents a mission scenario where a PLATOR-propelled spacecraft is used to capture and de-orbit the European Space Agency (ESA)'s Envisat satellite. The orbital transfer trajectory is designed using a time-optimal control approach, and the spacecraft's state vector's uncertainties are assessed through a covariance analysis. A navigation analysis is then performed to evaluate the spacecraft's capability to autonomously track its motion during the transfer using GPS measurements. Finally, a target proximity phase is then simulated to demonstrate the spacecraft's capability to rendezvous and dock with Envisat, using the uncertainties obtained from the covariance analysis, showing the potential of the PLATOR thruster for in-orbit servicing and active debris removal applications.

Guidance and navigation algorithms play a crucial role in ensuring a successful spacecraft mission. This work proposes a full guidance and navigation algorithm based on differential algebra successive convex programming technique (SCVX). By leveraging the high-order expansions around the reference trajectory it is possible to enhance the computational efficiency of convex-based guidance and navigation algorithms. The high-order expansion enables to capture of the non-linearities in the estimation and guidance problems without sacrificing the robustness of the algorithms. Monte Carlo analyses are carried out to assess the benefits of recom-puting the guidance from the estimated state with this new high-order approach while being robust to uncertainties and errors.

Despite several missions, the origin of the two Martian moons, Phobos and Deimos, remains an open question. The goal of the next JAXA’s flagship mission Martian Moons eXploration will be to explore the two Martian moons. The satellite will be injected into a quasi-satellite orbit and it will require some station-keeping maneuvers to maintain the satellite on these orbits. Traditional methods for station-keeping around libration points are not applicable for these orbits due to their rapid evolution. In this paper we propose a new approach to perform station-keeping on periodic and quasi-periodic orbits based on convex optimization. Successive convex optimization is used to solve the time free fuel optimal problem to drive the satellite back to a reference trajectory. The latter is updated every GNC (Guidance Navigation and Control) loop by means of an innovative Discrete Fourier Transform approach that exploits the periodicity and quasi-periodicity of quasi-satellite orbits. To assess the robustness of the methodology the control and the references are computed in the autonomous dynamical model while the propagation is performed in the non-autonomous model while adding injection, orbit determination and executions errors. Monte Carlo analysis demonstrate that quasi-satellite orbits can be maintained using less than 6 m/s per month.

Successive convex programming is a promising technique for onboard applications thanks to its speed and guaranteed convergence. Hence it can be an enabler for future missions where spacecraft autonomy plays a key role. The definition of a good value of the trust region plays a vital role in the successful convergence of SCVX algorithms. This work presents an improved trust region algorithm based on a differential algebra technique that relies on the information given by the nonlinearities of the constraints and does not depend on the user for the initialization of the trust region.

Missions around small bodies present many challenges from their design to the operations, due to the highly non-linear and uncertain dynamics, the limited ∆v budget and constraints coming from orbit determination and mission design. Within this context, mathematical tools to enhance the understanding of the dynamics behavior can be proven useful to support the mission design process. Chaos indicators are adopted to reveal patterns of time-dependent dynamical systems and to enable the identification of practical stability regions, which are then exploited to design bounded orbits in the proximity of small bodies. The methodology is applied to study the MMX and Hera missions. In the MMX context, the final goal is to obtain bounded orbits useful for the global surface mapping and gravity potential determination of Phobos. On the other hand, concerning the Hera mission, a qualitative analysis of the natural motion about the Didymos binary asteroid system is carried out to compute bounded orbits convenient for the global characterization of the two asteroids and to investigate potential landing trajectories. Sensitivity analyses via Monte Carlo simulations are performed to prove the robustness of the different bounded orbits.

Understanding the solar corona and its structure, evolution and composition can provide new insights regarding the processes that control the transport of energy throughout the solar atmosphere and out into the heliosphere. However, the visible emission coming from the corona is more than a million times weaker than the emission from the photosphere, implying that direct corona observations are only possible when the disk of the Sun is fully obscured. In this paper we perform a feasibility study of a Sun occultation mission using the Earth as a natural occulter. The challenge is that the occultation zone created by the Earth does not follow a Keplerian trajectory, causing satellites placed in this region to quickly drift away from eclipse conditions. To increase the number of revisits while optimizing the propellant budget, we propose optimal trajectories in the Sun–Earth-Spacecraft circular restricted three body problem that account for scientific and engineering constraints such as limited power budget and mission duration. Chemical propulsion, electric propulsion and solar sailing configurations are compared in terms of performance and mission feasibility, revealing how 24 h of corona observations would be possible every 39 days with as little as 199 m/s of í µí»¥í µí±‰. The feasibility of the solar sail approach is hereby demonstrated, making it a challenging engineering alternative to currently available technologies.

Despite the advantages of very-low altitude retrograde orbits around Phobos, questions remain about the efficacy of conventional station-keeping strategies in preventing spacecraft such as the Martian Moons eXploration from escaping or impacting against the surface of the small irregular moon. This paper introduces new high-fidelity simulations in which the output of a sequential Square-Root Information Filter is combined with recently developed orbit maintenance strategies based on differential algebra and convex optimization methods. The position and velocity vector of the spacecraft are first estimated using range, range-rate, and additional onboard data types such as LIDAR and camera images. This information is later processed to assess the necessity of an orbit maintenance maneuver based on the estimated relative altitude of MMX about Phobos. If a maneuver is deemed necessary, the state of the spacecraft is fed to either a successive convex optimization procedure or a high-order target phase approach capable of providing sub-optimal station-keeping maneuvers. The performance of the two orbit maintenance approaches is assessed via Monte Carlo simulations and compared against work in the literature so as to identify points of strength and weaknesses.