Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - COMPASS (Control for Orbit Manoeuvring through Perturbations for Application to Space Systems)

Teaser

The use of Space is crucial to life on Earth thanks to the services provided by space assets and the development of technologies, science and space exploration. Current and future space activities are enabled by Space transfer that allows reaching and controlling operational...

Summary

The use of Space is crucial to life on Earth thanks to the services provided by space assets and the development of technologies, science and space exploration. Current and future space activities are enabled by Space transfer that allows reaching and controlling operational orbits. Moreover, they are safeguarded by Space situation awareness that mitigates the hazards caused by asteroids or space debris generated from the break-up of abandoned satellites.

The motion of spacecraft in all these applications is governed by the gravity of the primary body (either the Sun or the central planet or Moon), but it is also strongly influenced by natural external forces due the gravity of the Moon and the Sun, atmospheric drag, solar radiation pressure, third body effect and so on. Natural orbit perturbations are responsible for the trajectory divergence from the nominal two-body problem, increasing the requirements for orbit control; whereas, in space situation awareness, they influence the orbit evolution of space debris that could cause hazard to operational spacecraft and near Earth objects that may intersect the Earth. Indeed, in the conventional models for accurate orbit propagation, these external forces are traditionally seen as perturbations that need to be counteracted by orbit manoeuvres, thus increasing fuel requirements.
However, in the COMPASS project we leverage the dynamics of these natural orbit perturbations and external forces in the planetary and interplanetary environment to develop novel techniques for orbit manoeuvring by “surfing” through orbit perturbations. With this approach we see the entire landscape of the dynamics of orbit, so we can design the best way through that landscape; using orbit perturbations as natural features not accelerations we need to fight.

The potential impact of the COMPASS project will be to significantly reduce the current extremely high space mission costs, especially for small satellite missions. This will create new opportunities for space exploration and exploitation, and space debris mitigation.

Work performed

The first objective of COMPASS is to investigate the orbital dynamics in planetary and interplanetary missions in presence of perturbations through numerical, semi-analytical and analytical approaches, considering both natural orbit perturbations and artificial accelerations (i.e., electric low-thrust or impulsive propulsion, solar or drag sailing, or changes of the reflectivity or drag coefficient of the spacecraft). The second objective is to study the dynamics of perturbations in the phase-space of the orbital elements through Hamiltonian dynamics and perturbation methods.
During the first 30 month of the project, the use of semi-analytical techniques for the modelling of orbit perturbations and tools of dynamical systems theory laid the foundation for a new understanding of the long-term orbit dynamics of the spacecraft or orbiting body in a planet-centred environment or in an interplanetary orbit around the Sun, where a model accounting of the forces of all the planets in the Solar System is needed.
A semi-analytical tool for the long-term orbit propagation in a planetary environment was derived and implemented in the PlanODyn suite, which describes all the main conservative orbit perturbations: third-body effects, solar radiation pressure with eclipses, zonal and resonant tesseral harmonics. For the accurate estimation of the effects of atmospheric drag on the orbit, an orbit contraction method in combination with a smooth exponential atmosphere model was developed. The propulsive effect of a solar sail and low-thrust propulsion were included, considering different sail attitude or low-thrust control strategies and constraints due to eclipses. When also the spacecraft or sail attitude is of concern, the dynamics modelling was performed in slow-fast variables and efficient integration schemes for attitude and orbit coupling.
For the precise modelling of the spacecraft relative motion in the low Earth orbit region a semi-analytical framework was also set-up. It exploits the relative orbital elements parametrisation and allows achieving propagation results remarkably more accurate than current methodologies in the literature.
For the long-term orbit propagation in the interplanetary environment symplectic integration methods were implemented and compared to improve the accuracy of numerical orbit propagation in the n-body dynamics of the solar system to be applied to the verification of planetary protection requirements for interplanetary missions. Together with this, an analytical method based on the study of the Jacobian of the dynamics was devised to identify planet fly-by occurrence.
Maps in the space of convenient orbital parameters and spacecraft characteristics were studied both in the planetary and heliocentric environment to characterise the orbit stability (or chaoticity) properties and its long-term evolution. An analytical theory was developed for distant Earth satellites as the theoretical foundation for novel orbital design and manoeuvring. An analytical analysis of the pork-chop plot for interplanetary transfer design was performed and the post-planetary encounter conditions were defined based on the variation of the orbital elements.

As many of the foreseen applications require handling distributions, representing either uncertainties in the initial orbit conditions or in the physical model or to propagate several physical objects of samples of a distribution, tools were devised to propagate large sets of initial conditions and their associated probability, which characterise an uncertain condition or a physical distribution of clouds of objects. A density-based approach was implemented for the simulation and prediction of atmospheric re-entries and evolution of cloud of debris fragments in orbit. Notably, this methodology can be adapted to the propagation of distributed object densities but also to probability distributions for uncertainty propagation. A method for planetary impact probability estimation

Final results

The COMPASS project bridges over the disciplines of orbital dynamics, dynamical systems theory, optimisation and space mission design by developing novel techniques for orbit manoeuvring by “surfing” through orbit perturbations.
The use of analytical theories, numerical simulation through semi-analytical techniques and high-fidelity dynamics and tools of dynamical systems theory allowed the understanding of the long-term evolution of space objects. With respect to classical astrodynamics the COMPASS methodology aimed at engineering the natural effects through optimisation to obtain useful space applications such as satellite end-of-life disposal and orbit raising and to enhance the conventional techniques for modelling the relative motion. Indeed, the ambition of COMPASS is to radically change the current space mission design philosophy: from counteracting disturbances, to exploiting natural and artificial perturbations. The devised techniques for orbit manoeuvring through perturbations can be enhance the use for small satellites working in a constellation to achieve unique mission goals. This will increase the services that spacecraft can offer to our daily lives, such as the monitoring of our planets, weather forecast, global positioning and navigation, global internet, telecommunications.
Moreover, in the field of trajectory optimisation, a Keplerian-elements-based differential dynamic programming algorithm is being developed so that the dynamics can be modelled with variational equations and using orbital elements as state representation. As a first guess trajectory design a blended error-correction steering law was developed for orbit raising and de-orbiting of coplanar satellites. For the design of interplanetary trajectories including gravity assist manoeuvres, a preliminary selection of the minimum solutions is performed using the analysis of the pork-chop plot and the analytical evaluation of the variation of the orbital elements induced by a fly-by. The Syzygy function, traditionally used in astronomy, was here applied to the identification of feasible flyby solutions.

Statistical, numerical and semi-analytical methods have been used for modelling uncertainties and applied to several space applications.
(1) Minimum collision probability criteria and time-based state transition matrices have been used for the design of collision avoidance manoeuvres (CAMs). Methods for the analytic design of CAMs are very recent and promising as they can be applied to space traffic management. Moreover, the uncertainty growth has been introduced in the sensitivity analysis of lead time for impulsive CAMs.
(2) In the framework of density-based propagation applied to space debris propagation, fragment propagation and re-entry prediction, the method proposed in the past was extended up to six dimensions of the phase space, demonstrating its applicability in orbital state propagation. Notably, this methodology can be adapted to the propagation of distributed object densities but also to probability distributions for uncertainty propagation
(3) In the application of uncertainty modelling for planetary protection analysis, a multi-event procedure was developed for the verification of planetary protection requirements starting from an initial uncertainty distribution as an alternative to the Monte Carlo method for the estimation of the probability of impact between the propagated body and a celestial body, based on the recognition of the time windows where close approaches with planets occur and repeated line-sampling applications.

Different techniques for mission design have been devised. For example, for future missions using many satellites working as a constellation, the constellation geometry has been optimised considering multiple cost drivers over the entire mission lifetime. A novel de-orbiting strategy has been developed in which the low-thrust propulsion and de-orbiting sails are used for the active and passive disposal phase

Website & more info

More info: http://www.compass.polimi.it/.