Nicola Baresi

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.

Heteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic Delta V expenditure. However, methods of detecting them can be limited, typically relying on human-in-the-loop or computationally intensive processes. In this paper we present a rapid and fully systematic method of detecting heteroclinic connections between quasi-periodic invariant tori by exploiting topological invariants found in knot theory. The approach is applied to the Earth-Moon, Sun-Earth, and Jupiter-Ganymede circular restricted three-body problems to demonstrate the robustness of this method in detecting heteroclinic connections between various quasi-periodic orbit families in restricted astrodynamical problems.

Upcoming missions towards remote planetary moons will fly in chaotic dynamical environments that are significantly perturbed by the oblateness of the host planet. Such a dominant perturbation is often neglected when designing spacecraft trajectories in planetary moon systems. This paper introduces a new time-periodic set of equations of motion that is based on the analytical solution of the zonal equatorial problem and better describes the dynamical evolution of a spacecraft subject to the gravitational attraction of a moon and its oblate host planet. Such a system, hereby referred to as the Zonal Hill Problem, remains populated by resonant periodic orbits and families of two-dimensional quasi-periodic invariant tori that are calculated by means of numerical continuation procedures. The resulting periodic and quasi-periodic trajectories are investigated for the trajectory design of future planetary moons explorers.

The Near-Earth Asteroid Characterization and Observation (NEACO) mission is a concept study proposing to explore the fast-rotating asteroid (469219) 2016 HO3, one of Earth's few quasi-satellites. In this study, a SmallSat spacecraft performs a scientific investigation that characterizes the asteroid at a sufficient degree to enable future, more in-depth missions. The 166 kg NEACO spacecraft uses a low-thrust, solar electric propulsion system to reach HO3 within 22 months from launch. Its instrument suite consists of two optical cameras, two spectrometers, an altimeter, and a low-velocity impactor. Upon arrival at HO3, NEACO uses pulsed plasma thrusters to hover at varying altitudes to enable lit surface mapping, shape modeling, and surface spectroscopy. The spacecraft will then perform several flybys to estimate the asteroid's mass. Finally, NEACO releases a low-velocity impactor during very low-altitude hovering to validate the existence of regolith and estimate the magnitude of surface cohesion. The science operations are completed within 8 months and the total mission is completed in less than 3 years. The NEACO mission concept integrates novel small-body analyses and proximity operation techniques with high-technology-readiness-level spacecraft components to achieve its science objectives within a reasonable mission timeline.

The surface of the Martian moon Phobos exhibits two distinct geologic units, red and blue, characterized by their spectral slopes. The provenance of these units is uncertain yet crucial to understanding the origin of the Martian moon and its interaction with the space environment. Here we present a combination of dynamical analyses and numerical simulations of particle dynamics to show that periodic variations in dynamic slopes, driven by orbital eccentricity, can cause surface grain motion. For regions with steep slopes that vary substantially over one Phobos orbit, the surface is excavated at a faster rate than the space weathering timescale. Our model predicts that this new mechanism is most effective in regions that coincide with blue units. Therefore, space weathering is the likely driver of the dichotomy on the moon's surface, reddening blue units that represent pristine endogenic material.

The dynamical environment on and about the Martian moon Phobos is explored. This planetary moon provides a unique dynamical environment in the solar system, being subject to extreme tidal forces and having a characteristically non-spherical shape. Further, it is not in a fully circular orbit, meaning that it has librations that arise from its eccentricity, contributing to a periodic forcing environment. Thus, to plan and implement missions in the vicinity of and on Phobos will require these considerations be taken into account. In this paper the latest published models of the Phobos shape and dynamics are used to characterize its dynamical environment in close proximity orbit about the body, for motion across its surface and for controlled hovering motion in its vicinity. It is found that surface motion is subject to a number of "speed limits" that can cause a moving vehicle to leave the surface and to possibly escape the moon and enter orbit about Mars. In terms of orbital stability, the existence of libration orbit families are characterized down to the surface using an exact potential, and the known stable QSO orbits are shown to be associated with families of stable quasi-periodic orbits. (C) 2018 COSPAR. Published by Elsevier Ltd. All rights reserved.

Quasi-periodic invariant tori are of great interest in astrodynamics because of their capability to further expand the design space of satellite missions. However, there is no general consent on what is the best methodology for computing these dynamical structures. This paper compares the performance of four different approaches available in the literature. The first two methods compute invariant tori of flows by solving a system of partial differential equations via either central differences or Fourier techniques. In contrast, the other two strategies calculate invariant curves of maps via shooting algorithms: one using surfaces of section, and one using a stroboscopic map. All of the numerical procedures are tested in the co-rotating frame of the Earth as well as in the planar circular restricted three-body problem. The results of our numerical simulations show which of the reviewed procedures should be preferred for future studies of astrodynamics systems.

The Asteroid Impact & Deflection Assessment (AIDA) mission is planning to visit the Didymos binary system in 2022 in order to perform the first demonstration ever of the kinetic impact technique. Binary asteroids are an ideal target for this since the deflection of the secondary body can be accurately measured by a satellite orbiting in the system. However, these binaries offer an extremely rich dynamical environment whose accurate investigation through analytical approaches is challenging at best and requires a significant number of restrictive assumptions. For this reason, a numerical investigation of the dynamical environment in the vicinity of the Didymos system is offered in this paper. After computing various families of periodic orbits, their robustness is assessed in a high-fidelity environment consisting of the perturbed restricted full three-body problem. The results of this study suggest that several nominally stable trajectories, including the triangular libration points, should not be considered as safe as a state vector perturbation may cause the spacecraft to drift from the nominal orbit and possibly impact one of the primary bodies within a few days. Nonetheless, there exist two safe solutions, namely terminator and interior retrograde orbits. The first one is adequate for observation purposes of the entire system and for communications. The second one is more suitable to perform close investigations of the primary body.

The relative motion about 4179 Toutatis is studied in order to investigate the feasibility of formation flying as an alternative concept for future asteroid exploration missions. In particular, the existence of quasi-frozen orbits about slowly rotating bodies allows us to compute families of periodic orbits in the body-fixed frame of the asteroid. Since these periodic orbits are of the center×center type, quasi-periodic invariant tori are calculated via fully numerical procedures and used to initialize spacecraft formations about the central body. Numerical simulations show that the resulting in-plane and out-of-plane relative trajectories remain bounded over long time spans; i.e., more than 30 days.
•We consider two spacecraft flying in a formation about the asteroid 4179 Toutatis.•We derive first order conditions that minimize the drift between the satellites.•We find a full family of stable periodic orbits about the target asteroid.•We compute quasi-periodic invariant tori and use them to initialize the formation.•Numerical simulations prove that the satellites stay bounded for long time spans.