Alessandro Zavoli

Indirect Optimization of Satellite Deployment into a Highly Elliptic Orbit

The analysis of the optimal strategies for the deployment of a spacecraft into a highly elliptic orbit is carried out by means of an indirect optimization procedure, which is based on the theory of optimal control. The orbit peculiarities require that several perturbations are taken into account: an 8 × 8 model of the Earth potential is adopted and gravitational perturbations from Moon and Sun together with solar radiation pressure are considered. A procedure to guarantee convergence and define the optimal switching structure is outlined. Results concerning missions with up to 4.5 revolutions around the Earth are given, and significant features of this kind of deployment are highlighted.

Indirect Optimization of Finite-Thrust Cooperative Rendezvous

A time-constrained finite-thrust rendezvous between two cooperating spacecraft is investigated in detail in this paper. To ensure high numerical accuracy, the optimization is carried out by means of an indirect method that exploits an “a priori” subdivision of the trajectory into burn and coast arcs, whose time lengths become additional unknown parameters. Issues related to simultaneous presence of two switching control structures, one for each maneuvering spacecraft, are analyzed. A peculiar approach, which relies on the adoption of a different timescale for each spacecraft, is proposed; the introduction of multiple decision vectors allows for an easy management of the switching control structures for missions involving two or more maneuvering spacecraft. As an example, a coplanar rendezvous is thoroughly analyzed; necessary conditions for optimality are comprehensively derived for both target/chaser and cooperative maneuvers. Numerical results are provided and solutions are discussed.

Deployment of a Two-Spacecraft Formation into a Highly Elliptic Orbit with Collision Avoidance

The finite-thrust deployment of a two-satellite formation into a highly elliptic orbit is optimized by means of an indirect approach, which is based on the theory of optimal control. Earth oblateness and gravitational perturbations from Moon and Sun are considered. The optimization procedure provides the engine switching times and the thrust direction during each burn in order to transfer the satellites to the same prescribed final orbit with assigned distance between them at the apogee passage; the total final mass is maximized. A minimum-distance constraint is introduced when required to avoid collision risk. Different deployment strategies are analyzed; in particular, the classical chaser-target approach is compared to cooperative deployment. Necessary conditions for optimality are derived and numerical results presented

Preliminary Capture Trajectory Design for Europa Tomography Probe

The objective of this work is the preliminary design of a low- transfer from an initial elliptical orbit around Jupiter into a final circular orbit around the moon Europa. This type of trajectory represents an excellent opportunity for a low-cost mission to Europa, accomplished through a small orbiter, as in the proposed Europa Tomography Probe mission, a European contribution to NASA’s Europa Multiple-Flyby Mission (or Europa Clipper). The mission strategy is based on the leveraging concept, and the use of resonant orbits to exploit multiple gravity-assist from the moon. Possible sequences of resonant orbits are selected with the help of the Tisserand graph. Suitable trajectories are provided by an optimization code based on the parallel running of several differential evolution algorithms. Different solutions are finally compared in terms of propellant consumption and flight time.