Periodic Reporting for period 4 - COMPASS (Control for Orbit Manoeuvring through Perturbations for Application to Space Systems)
Période du rapport: 2021-02-01 au 2022-04-30
Résumé du contexte et des objectifs généraux du projet
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), but it is also strongly influenced by natural external forces due the gravity of the secondary body, i.e. the Moon and the Sun, atmospheric drag, solar radiation pressure and so on. Natural orbit perturbations are responsible for the trajectory divergence from the nominal two-body problem, increasing the requirements for orbit control. In space situation awareness, orbit perturbations 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 treated 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 orbits, 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 is to significantly deepen the insight into the orbital dynamics of spacecraft and 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. As the main objective of COMPASS, different fields of application were investigated with this novel space mission design philosophy: from counteracting disturbances, to exploiting natural and artificial perturbations. Different applications were investigated where (a) a better insight into the natural dynamics may present an advantage, or (b) the proposed perturbation-driven space mission design philosophy can allow new mission concepts, or (c) enhanced uncertainty and set propagation enable new applications in Space. The methodologies developed were applied to a variety of mission concepts and operational software applications for space situation awareness, space debris mitigation, asteroid mitigation missions, Earth-observation missions, and planetocentric and interplanetary space transfers.
The motion of spacecraft in all these applications is governed by the gravity of the primary body (either the Sun or the central planet), but it is also strongly influenced by natural external forces due the gravity of the secondary body, i.e. the Moon and the Sun, atmospheric drag, solar radiation pressure and so on. Natural orbit perturbations are responsible for the trajectory divergence from the nominal two-body problem, increasing the requirements for orbit control. In space situation awareness, orbit perturbations 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 treated 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 orbits, 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 is to significantly deepen the insight into the orbital dynamics of spacecraft and 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. As the main objective of COMPASS, different fields of application were investigated with this novel space mission design philosophy: from counteracting disturbances, to exploiting natural and artificial perturbations. Different applications were investigated where (a) a better insight into the natural dynamics may present an advantage, or (b) the proposed perturbation-driven space mission design philosophy can allow new mission concepts, or (c) enhanced uncertainty and set propagation enable new applications in Space. The methodologies developed were applied to a variety of mission concepts and operational software applications for space situation awareness, space debris mitigation, asteroid mitigation missions, Earth-observation missions, and planetocentric and interplanetary space transfers.
Travail effectué depuis le début du projet jusqu’à la fin de la période considérée dans le rapport et principaux résultats atteints jusqu’à présent
The first objective of COMPASS is to investigate the orbital dynamics for 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). The second objective is to study the dynamics of perturbations in the phase-space of the orbital elements through Hamiltonian dynamics and perturbation methods.
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 semi-analytical tool PlanODyn V1.0 was also extended to include a new formulation of the kick-map for highly perturbed third-body cases and a better model for the luni-solar perturbations by employing an ecliptic formulation which allows deriving a simple phase space method to identify natural re-entry trajectories. The propulsive effect of a solar sail and low-thrust propulsion were included, considering different sail attitudes 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. The mathematical and algorithm development for the semi-analytical tool for orbit propagation in the planetary environment served as bases for the design of the final product PlanODyn V2.0. A software design plan was developed to define the software blocks for perturbation modelling, dynamics modelling, physical modelling and orbit propagation. A new software is now being implemented following this design to: improve computational cost, improve integrability within other tools, improve understanding of the software blocks and allow more flexibility in using the code. The feature for propagating the Jacobian of the dynamics was added together with the computation of the trace of the Jacobian to be used in the computation of the continuity equation.
For the precise modelling of the spacecraft relative motion in the low Earth orbit region a complete orbit propagation framework was set-up and implemented in the SKiLLeD suite. It exploits the relative orbital elements parametrisation and allows achieving propagation results remarkably more accurate than current methodologies in the literature. The relative orbital elements dynamics formulation was also used in the definition of the control for satellite formation flying with 2 or more spacecraft. Moreover, safety constraints in the close proximity operations were included.
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. New formulations of the dynamics were investigated, such as the Kustaanheimo-Stiefel (KS) variable formulation for interplanetary trajectory in presence of fly-bys. This formulation exploits quaternion-like properties within orbit propagation. Moreover, in the continuing effort of better understand the effect of the third-body perturbation and its models (such as the restricted-three body problem, the kick-map for the third body modelling or the third body perturbation with averaging techniques), an analytical method based on the study of the Jacobian of the dynamics was devised to identify planet fly-by occurrence. A criterion based on the eigenvalues of the dynamics function was formulated to define the region where it is convenient to switch the centre of mass for interplanetary integration. For the propagation of interplanetary trajectories, a GPU-based propagation approach was developed and tested. This also led to a successful application to the NVIDIA Academic Hardware Grant Program by a COMPASS team member.
Maps in the space of 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 or samples of a statistical distribution, tools were devised to propagate large sets of initial conditions and their associated probability. The probability density function characterises an uncertain condition or an actual physical distribution of clouds of objects. A density-based approach was implemented in the suite Starling V1.0 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. The tools devised to propagate large sets of initial conditions and their associated probability where then improved and different interpolation techniques were evaluated and validated looking for generalising them to several applications.
A density-based method was developed for propagating the density of a set of objects in the space of the orbital elements. Approaches based on the use of the Gaussian Mixture Model, alpha-shape, and a binning method in the orbital elements, using an Extended Karnaugh Map Representation for efficient memory allocation were implemented. Based on this theoretical approach, the operational software Staling V2.0 is being implemented under a project funded by the European Space Agency. A method for planetary impact probability estimation was developed through an improved line sampling method, as advancement with respect to classical Monte Carlo tools. Finally, an extended state transition matrix was introduced for the propagation in time of orbital uncertainties, vastly outperforming numerical methods.
The third objective of COMPASS is to couple the orbit dynamics in the space of averaged elements with global and local optimisation techniques to develop a novel procedure for travelling in the orbital element space through the exploitation of natural and artificial perturbations. Space transfer intrinsically requires the minimisation of the fuel consumption to maximise the mission lifetime and reduce costs. Therefore, the wise exploitation of perturbations will enhance the effects of the manoeuvre as the spacecraft will “surf” along the perturbation maps.
We developed an optimisation model written in the space of orbital elements to target regions in the perturbation maps such that long-term equilibrium or unstable conditions are met. From the mission design point of view, it corresponds to targeting stable orbits or navigating through orbit perturbations to another orbit condition. A branch of research was initiated on the optimal non-linear constrained control problem resolution applied to low-thrust trajectory optimisation. For interplanetary trajectory design an optimisation strategy was introduced for patching the two body-problem flyby design in the three body-problem dynamics.
Finally, for what regards the theoretical developments, a novel technique for low-thrust trajectory design was developed based on Differential Dynamics Programming formulated in the space or orbital elements. The new formulation of this technique in the orbital elements allows the coupling with the semi-analytical tool PlanODyn to consider and take advantage of orbit perturbations directly within the trajectory optimisation process. As an alternative method to exploit orbit perturbations during the optimisation process, the optimal control problem has been applied directly in the phase space of the long-term dynamics considering luni-solar perturbations.
As the main objective of COMPASS, different fields of application were investigated with this novel space mission design philosophy: from counteracting disturbances, to exploiting natural and artificial perturbations. Different fields of application were investigated where (a) a better insight into the natural dynamics may present an advantage, or (b) the proposed perturbation-driven space mission design philosophy can allow new mission concepts, or (c) enhanced uncertainty and set propagation enable new applications in Space. The methodologies developed were applied to a variety of mission concepts and operational software applications to (1) space debris mitigation, (2) distributed missions for Earth-observation missions and large constellations, (3) Planetary defence and protection, (4) interplanetary and planet-centred trajectory design.
Space debris mitigation
To assess the risk of collision in Space against the many space debris objects, a mathematical model was built to represent the population of space debris and their evolution, stemming from a collision or explosion in space, this model considers them a continuous fluid to know their distribution in space and time. The continuum method for density propagation was successfully applied to the modelling of fragmentations in orbit and the computation of the consequent risk on orbiting satellites. Moreover, a preliminary application to the propagation of the overall debris population has been investigated. Within a co-funded PhD project between COMPASS and the European Space Agency (ESA) a software for continuum propagation, Starling V1.0 has been developed. In addition, reverse engineering techniques and semi-analytical techniques are being employed to detect in-orbit fragmentations. The software tool PlanODyn was also used for the characterisation of a fragmentation in space starting from the Two-Line Elements of observed fragments. An extension of the PUZZLE tool, whose first version was developed in a programme by the Italian Space Agency, was developed to characterise fragmentations on a long period of time. The characterisation of a fragmentation is performed with a series of pruning orbital mechanics criteria on the initial large set of candidate fragments, followed by backward propagation and reverse engineering of the NASA break-up model.
Once debris fragments are modelled and characterise, the next step it to avoid dangerous collision in orbit. Optimal techniques for collision avoidance manoeuvre were devised both for impulsive and low-thrust engines exploiting semi-analytical methods and also retrieving short periodic orbit corrections. The aim of the avoidance manoeuvre is to maximise the objects separation at close encounter or to achieve the minimum collision risk. As the effect of the manoeuvre depends on the orbit and model uncertainty and the time to collision, the effect of drag and solar radiation pressure on the position and velocity uncertainty of the spacecraft were analysed, together with its repercussion on collision avoidance operations. Moreover, the use of artificial intelligence in deciding whether and when to perform the manoeuvre was investigated. The theoretical developments lead to the design of the MISS suite for collision avoidance manoeuvre. This will open the way for the COMPASS group to the on-board implementation of collision avoidance manoeuvre in an on-orbit experiment.
Space debris mitigation can be guaranteed also by responsively endling the end-of-life phase of missions, leading them to an Erath re-entry. The analytical theories developed in the first phase of the project were investigated to enhance the design of Earth satellites disposal and to developed perturbation-based orbit maintenance for a geostationary satellite. The improved phase space representation of orbits allowed the definition of natural end-of-life disposals and the interpretation of the orbit evolution of space debris fragments. The use of solar sail for engineering the effect of solar radiation pressure was investigated and methods to passively stabilise its attitude where found. Moreover, the continuum approach implemented in the suite Starling was also applied to compute the casualty risk on ground for space debris, meteoroids, and spacecraft re-entry also including simplified aero-thermodynamics relations and to model meteoroid re-entry. Among the applications it was used to predict the re-entry of inclined orbit geostationary satellites and the INTEGRAL mission.
Passive debris mitigation is not enough to guarantee the long-term sustainability of the space debris environment; thus Active Debris Removal (ADR) has to actively remove debris target in orbit. Effort was dedicated to develop a space debris index and an index to select target debris objects to be removed from orbit to aid the definition of space debris policies. The Relative Orbital Element (ROE) analytical framework developed within COMPASS paves the way to a straightforward enhancement of ROE-based guidance navigation and control algorithms. An analytical precise line-of-sight modelling was developed to support angles-only navigation applications, a key technology for rendezvous to non-cooperative targets in space. Relative motion dynamics have been applied to the design of ADR missions, in particular the far-to-close range rendezvous including collision avoidance constraints. Plume impingement technique were proposed to control the random tumbling of the object to be captured. These techniques were applied in the framework of an ESA project to deliver the Sunrise ADR service for large constellations.
One of the most important spin-off of the COMPASS project within space debris mitigation is the e.Cube mission concept, a CubeSat mission to validate in space all the models developed within the COMPASS project within the space situation awareness field. The e.Cube mission concept, proposed within a framework of the Italian Space Agency (ASI) aims to (1) validate with an in-orbit experiment the sub-millimetre debris particle, (2) study the uncertainties during re-entry for improving re-entry predictions by means of a distributed set of sensors within the spacecraft and (3) perform a series of CAM against some synthetic object directly in orbit. The e.Cube mission has passed the first round of evaluation by ASI and will be most probably funded for phase A in autumn 2022 (Link: https://www.asi.it/2022/03/cubesat-lasi-al-lavoro-per-il-futuro-del-settore/(s’ouvre dans une nouvelle fenêtre)).
The COMPASS team has strengthened research collaborations on space debris with the European Space Agency and the Italian Space Agency. Noteworthy, within the space debris filed the COMPASS team has contributed to the Inter Agency Space Debris Coordination Committee Working Group 2 (being part of the Italian delegation) on modelling by defining the action task for the definition of a proxy for computing the
overall capacity of space and define a debris index. In this framework some preliminary research work was performed to review the use of carrying capacity concept in application other than the space field and to compare with a very simple 1D debris model some definition of the space capacity available in the literature. As a result of the extensive work on space debris mitigation, the COMPASS team and Politecnico di Milano is now one of the refence institutions for space debris modelling and space sustainability studies.
Distributed missions for Earth-observation and large constellations
Within the rising space economy, Space assets at the services they provide are now fundamental to our daily live. The COMPASS project devoted effort to develop a framework for the quantitative assessment of the socio-economic benefit of space missions to the humankind trying to map the mission outcome to the United Nations Global development goals. In the field of Earth-based missions for Earth Observation, advanced formation flying techniques were applied to the design of a rigid formation of three or more satellites. The formation flying design framework developed within COMPASS found its most relevant application in the ESA mission study for the Formation Flying Large Aperture Synthesis mission for remote sensing.
Space is getting crowded also due to the recent announced plans on the deployment in orbit of large constellation of small satellites. Mission involving large constellations have been tacked, devising new techniques for the optimisation of the constellation under several design criteria. We have performed the optimisation and design of satellite large constellations considering all the phases of their mission, from the orbit raising, till the mission end-of-life, with the consideration of self-induced collision among satellite within the constellation. The new method for low-thrust trajectory design based on semi-analytical techniques and refinement with Differential Dynamics Programming were applied to the design of orbit raising of large constellation missions and the mission architecture for an ADR service for large constellation was studied.
In the case of the Global Navigation Satellite System, its performance was evaluated via the G-CAT tool, in both nominal and failure modes through coverage analysis.
The task on constellation design has also focused on space sustainability challenges. In particular, we defined aa model for the brightness of a satellite to be used for minimising the light pollution by large constellation satellites. The brightness model was validated with observations of the OneWeb satellites, performed by the GAL Hassin, astronomic park in Isnello.
Planetary defence and protection
In the framework of space situation awareness of asteroid impact threats, we performed the mission analysis of potential threat scenarios by using the kinetic impactor strategy to deflect potentially hazardous asteroids. This was done in the framework of a collaboration with the Italian Space Agency and an on-going discussion with the United Nation-mandated Space Mission Planning Advisory Group to which COMPASS is actively contributing as part of the Italian delegation. To increase the technology readiness level of this deflection technique, COMPASS focused the research on the characterisation of close encounters between the asteroid and the Earth to achieve an optimal deflection design for planetary protection in presence of close encounters. The mission design of a kinetic impactor mission was then performed exploiting intermediate fly-bys and tacking both the direct hit scenario and a resonant-hit scenario. Moreover, a new technology for asteroid deflection based on the electro-magnetic interaction between the spacecraft and the asteroid was devised. The design of the optimal deflection manoeuvre for near-Earth objects was performed using the b-plane representation and considering gravity assists during the asteroid interception phase to improve the arrival conditions. In the field of asteroid deflection missions, we have also extended the NASA break-up model, originally developed for space debris, to model the distribution of fragments when a kinetic impactor satellite hits the asteroid.
The COMPASS team have contributed to the UN-mandated Space Mission Planning Advisory Group by organising the first SMPAG hypothetical threat exercise to focus on the inter-agency procedure to organise a coordinated response to the threat. The objectives are (1) to define the tasks required for a SMPAG coordinated response to the Exercise NEO threat, (2) to define which entity/ies would be responsible for these tasks and (3) to identify the procedures internally to each SMPAG member to propose a response to the SMPAG.
Finally, some focus was also given to scientific missions to asteroids; in this aspect the dynamics of dust at asteroids has been modelled using a perturbed three body problem and using perturbation techniques and the relative dynamics approach has been applied to mission for the definition of the gravity field at asteroids.
Interplanetary and planet-centred trajectory design
To enhance the interplanetary trajectory design and select the planets for fly-by manoeuvre a design strategy was derived for “surfing” among planets. This, however, need to be compliant to planetary protection requirements, so that man-made objects do not contaminate other planets. We have devised new methods for verifying, through orbit propagation and uncertainty modelling, that these requirements are satisfied. The planetary protection verification analysis tool devised in COMPASS was applied to the ESA-NASA JUICE mission through a collaboration with the European Space Agency. We also investigated the end-of-life disposal design for spacecraft at libration points orbits to give a physical interpretation of their probability of return to Earth. The work on planetary protection and the collaboration with the European Space Agency gave the opportunity to extend the applicability of uncertainty propagation techniques from planetary protection applications to robust trajectory design applications where an additional step is the definition of the control action and the selection of flyby planets.
In the field of interplanetary missions, the COMPASS project contributed to the application of the fly-by map to the NASA CLIPPER mission. The techniques for long-term orbit propagation were applied to the planetary protection analysis of ESA missions within two confounded PhD programmes between COMPASS and ESA that lead to the development of an improved version of the SNAPPshot software and on robust trajectory design techniques accounting for generic evolving uncertainties. Current work is devoted to devise a completely new formulation based on Kustaanheimo-Stiefel variables to improve efficiency and insight into the dynamics for robust mission design. For interplanetary trajectory design we devised a method for the identification of the feasible flyby trajectories using the pork-chop plot analysis and the Syzygy function, traditionally used in astronomy. A collaboration with NASA JPL was initiated in this topic.
The philosophy of surfing through orbit perturbation was principally applied to space transfer design. Indeed, we designed of end-of-life disposal of INTEGRAL and XMM spacecraft with perturbation enhanced control algorithm. The effect of perturbations was also considered for the computation of frozen orbits for Moon exploration with orbit maintenance through an electrospray thruster for CubeSat. We performed low-thrust trajectory design for a novel de-orbiting strategy by using low-thrust and passive de-orbiting sails, reducing the fuel consumption compared with the conventional de-orbiting method that aims at lowering the perigee altitude. In this respect, the attitude stability of pyramidal-shaped helio-stable sails close to a sun-pointing direction was studied for application to end-of-life passive and semi-controlled deorbiting.
Dissemination
For dissemination activities and engaging with policy makers several interactive games were developed using the COMPASS algorithms as backend and creating graphical interfaces and Virtual Reality applications. Different COMPASS games were developed to (1) show the impact of space activities to humankind and their contribution to the UN Sustainable development goals, (2) raise awareness about the space debris problem and the ring of artificial non-operational objects we are creating around the Earth, (3) show the orbit and ground coverage of Earth-orbiting satellites and large constellations, (4) design interplanetary missions and missions to deflect asteroids. All the dissemination activities are reported in the report and the website section dedication to dissemination and outreach. Remarkably, the COMPASS project was invited to represent the European Research Council at the European Research and Innovation Days, Brussels, 24-26 Sept. 2019. (Website: https://erc.europa.eu/event/european-research-and-innovation-days(s’ouvre dans une nouvelle fenêtre)). The European Research and Innovation Days is the first annual policy event of the European Commission, bringing together stakeholders to debate and shape the future research and innovation landscape. The COMPASS project was presented as an example of ERC projects. (Website: https://erc.europa.eu/projects-figures/stories/making-space-safer-place-satellites-and-spacecraft(s’ouvre dans une nouvelle fenêtre) ERC Website: https://erc.europa.eu/erc-participants-event-2019-research-innovation-days(s’ouvre dans une nouvelle fenêtre)).
Moreover, the PI of the COMPASS project was selected to participate to the World Economic Forum (WEF) Young Scientists programme at the Annual Meeting of the New Champions 1-3 Jul. 2019, Dalian, People's Republic of China (Website: https://www.weforum.org/events/annual-meeting-of-the-new-champions-2019(s’ouvre dans une nouvelle fenêtre)) as part of the ERC delegation composed of some ERC scientist and Jean-Pierre Bourguignon. The PI was a contributor to the agenda with a blog on “Europe is designing satellites that 'surf' their way past space debris” (Website: https://www.weforum.org/agenda/authors/camilla-colombo(s’ouvre dans une nouvelle fenêtre) World Economic Forum news: https://www.weforum.org/press/2019/06/unveiled-the-brightest-young-scientific-minds-in-the-world(s’ouvre dans une nouvelle fenêtre) and ERC news: https://erc.europa.eu/event/erc-summer-davos-leadership-40-succeeding-new-era-globalization(s’ouvre dans une nouvelle fenêtre))
More info on the research project can be also found on the project webpage: www.compass.polimi.it
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 semi-analytical tool PlanODyn V1.0 was also extended to include a new formulation of the kick-map for highly perturbed third-body cases and a better model for the luni-solar perturbations by employing an ecliptic formulation which allows deriving a simple phase space method to identify natural re-entry trajectories. The propulsive effect of a solar sail and low-thrust propulsion were included, considering different sail attitudes 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. The mathematical and algorithm development for the semi-analytical tool for orbit propagation in the planetary environment served as bases for the design of the final product PlanODyn V2.0. A software design plan was developed to define the software blocks for perturbation modelling, dynamics modelling, physical modelling and orbit propagation. A new software is now being implemented following this design to: improve computational cost, improve integrability within other tools, improve understanding of the software blocks and allow more flexibility in using the code. The feature for propagating the Jacobian of the dynamics was added together with the computation of the trace of the Jacobian to be used in the computation of the continuity equation.
For the precise modelling of the spacecraft relative motion in the low Earth orbit region a complete orbit propagation framework was set-up and implemented in the SKiLLeD suite. It exploits the relative orbital elements parametrisation and allows achieving propagation results remarkably more accurate than current methodologies in the literature. The relative orbital elements dynamics formulation was also used in the definition of the control for satellite formation flying with 2 or more spacecraft. Moreover, safety constraints in the close proximity operations were included.
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. New formulations of the dynamics were investigated, such as the Kustaanheimo-Stiefel (KS) variable formulation for interplanetary trajectory in presence of fly-bys. This formulation exploits quaternion-like properties within orbit propagation. Moreover, in the continuing effort of better understand the effect of the third-body perturbation and its models (such as the restricted-three body problem, the kick-map for the third body modelling or the third body perturbation with averaging techniques), an analytical method based on the study of the Jacobian of the dynamics was devised to identify planet fly-by occurrence. A criterion based on the eigenvalues of the dynamics function was formulated to define the region where it is convenient to switch the centre of mass for interplanetary integration. For the propagation of interplanetary trajectories, a GPU-based propagation approach was developed and tested. This also led to a successful application to the NVIDIA Academic Hardware Grant Program by a COMPASS team member.
Maps in the space of 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 or samples of a statistical distribution, tools were devised to propagate large sets of initial conditions and their associated probability. The probability density function characterises an uncertain condition or an actual physical distribution of clouds of objects. A density-based approach was implemented in the suite Starling V1.0 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. The tools devised to propagate large sets of initial conditions and their associated probability where then improved and different interpolation techniques were evaluated and validated looking for generalising them to several applications.
A density-based method was developed for propagating the density of a set of objects in the space of the orbital elements. Approaches based on the use of the Gaussian Mixture Model, alpha-shape, and a binning method in the orbital elements, using an Extended Karnaugh Map Representation for efficient memory allocation were implemented. Based on this theoretical approach, the operational software Staling V2.0 is being implemented under a project funded by the European Space Agency. A method for planetary impact probability estimation was developed through an improved line sampling method, as advancement with respect to classical Monte Carlo tools. Finally, an extended state transition matrix was introduced for the propagation in time of orbital uncertainties, vastly outperforming numerical methods.
The third objective of COMPASS is to couple the orbit dynamics in the space of averaged elements with global and local optimisation techniques to develop a novel procedure for travelling in the orbital element space through the exploitation of natural and artificial perturbations. Space transfer intrinsically requires the minimisation of the fuel consumption to maximise the mission lifetime and reduce costs. Therefore, the wise exploitation of perturbations will enhance the effects of the manoeuvre as the spacecraft will “surf” along the perturbation maps.
We developed an optimisation model written in the space of orbital elements to target regions in the perturbation maps such that long-term equilibrium or unstable conditions are met. From the mission design point of view, it corresponds to targeting stable orbits or navigating through orbit perturbations to another orbit condition. A branch of research was initiated on the optimal non-linear constrained control problem resolution applied to low-thrust trajectory optimisation. For interplanetary trajectory design an optimisation strategy was introduced for patching the two body-problem flyby design in the three body-problem dynamics.
Finally, for what regards the theoretical developments, a novel technique for low-thrust trajectory design was developed based on Differential Dynamics Programming formulated in the space or orbital elements. The new formulation of this technique in the orbital elements allows the coupling with the semi-analytical tool PlanODyn to consider and take advantage of orbit perturbations directly within the trajectory optimisation process. As an alternative method to exploit orbit perturbations during the optimisation process, the optimal control problem has been applied directly in the phase space of the long-term dynamics considering luni-solar perturbations.
As the main objective of COMPASS, different fields of application were investigated with this novel space mission design philosophy: from counteracting disturbances, to exploiting natural and artificial perturbations. Different fields of application were investigated where (a) a better insight into the natural dynamics may present an advantage, or (b) the proposed perturbation-driven space mission design philosophy can allow new mission concepts, or (c) enhanced uncertainty and set propagation enable new applications in Space. The methodologies developed were applied to a variety of mission concepts and operational software applications to (1) space debris mitigation, (2) distributed missions for Earth-observation missions and large constellations, (3) Planetary defence and protection, (4) interplanetary and planet-centred trajectory design.
Space debris mitigation
To assess the risk of collision in Space against the many space debris objects, a mathematical model was built to represent the population of space debris and their evolution, stemming from a collision or explosion in space, this model considers them a continuous fluid to know their distribution in space and time. The continuum method for density propagation was successfully applied to the modelling of fragmentations in orbit and the computation of the consequent risk on orbiting satellites. Moreover, a preliminary application to the propagation of the overall debris population has been investigated. Within a co-funded PhD project between COMPASS and the European Space Agency (ESA) a software for continuum propagation, Starling V1.0 has been developed. In addition, reverse engineering techniques and semi-analytical techniques are being employed to detect in-orbit fragmentations. The software tool PlanODyn was also used for the characterisation of a fragmentation in space starting from the Two-Line Elements of observed fragments. An extension of the PUZZLE tool, whose first version was developed in a programme by the Italian Space Agency, was developed to characterise fragmentations on a long period of time. The characterisation of a fragmentation is performed with a series of pruning orbital mechanics criteria on the initial large set of candidate fragments, followed by backward propagation and reverse engineering of the NASA break-up model.
Once debris fragments are modelled and characterise, the next step it to avoid dangerous collision in orbit. Optimal techniques for collision avoidance manoeuvre were devised both for impulsive and low-thrust engines exploiting semi-analytical methods and also retrieving short periodic orbit corrections. The aim of the avoidance manoeuvre is to maximise the objects separation at close encounter or to achieve the minimum collision risk. As the effect of the manoeuvre depends on the orbit and model uncertainty and the time to collision, the effect of drag and solar radiation pressure on the position and velocity uncertainty of the spacecraft were analysed, together with its repercussion on collision avoidance operations. Moreover, the use of artificial intelligence in deciding whether and when to perform the manoeuvre was investigated. The theoretical developments lead to the design of the MISS suite for collision avoidance manoeuvre. This will open the way for the COMPASS group to the on-board implementation of collision avoidance manoeuvre in an on-orbit experiment.
Space debris mitigation can be guaranteed also by responsively endling the end-of-life phase of missions, leading them to an Erath re-entry. The analytical theories developed in the first phase of the project were investigated to enhance the design of Earth satellites disposal and to developed perturbation-based orbit maintenance for a geostationary satellite. The improved phase space representation of orbits allowed the definition of natural end-of-life disposals and the interpretation of the orbit evolution of space debris fragments. The use of solar sail for engineering the effect of solar radiation pressure was investigated and methods to passively stabilise its attitude where found. Moreover, the continuum approach implemented in the suite Starling was also applied to compute the casualty risk on ground for space debris, meteoroids, and spacecraft re-entry also including simplified aero-thermodynamics relations and to model meteoroid re-entry. Among the applications it was used to predict the re-entry of inclined orbit geostationary satellites and the INTEGRAL mission.
Passive debris mitigation is not enough to guarantee the long-term sustainability of the space debris environment; thus Active Debris Removal (ADR) has to actively remove debris target in orbit. Effort was dedicated to develop a space debris index and an index to select target debris objects to be removed from orbit to aid the definition of space debris policies. The Relative Orbital Element (ROE) analytical framework developed within COMPASS paves the way to a straightforward enhancement of ROE-based guidance navigation and control algorithms. An analytical precise line-of-sight modelling was developed to support angles-only navigation applications, a key technology for rendezvous to non-cooperative targets in space. Relative motion dynamics have been applied to the design of ADR missions, in particular the far-to-close range rendezvous including collision avoidance constraints. Plume impingement technique were proposed to control the random tumbling of the object to be captured. These techniques were applied in the framework of an ESA project to deliver the Sunrise ADR service for large constellations.
One of the most important spin-off of the COMPASS project within space debris mitigation is the e.Cube mission concept, a CubeSat mission to validate in space all the models developed within the COMPASS project within the space situation awareness field. The e.Cube mission concept, proposed within a framework of the Italian Space Agency (ASI) aims to (1) validate with an in-orbit experiment the sub-millimetre debris particle, (2) study the uncertainties during re-entry for improving re-entry predictions by means of a distributed set of sensors within the spacecraft and (3) perform a series of CAM against some synthetic object directly in orbit. The e.Cube mission has passed the first round of evaluation by ASI and will be most probably funded for phase A in autumn 2022 (Link: https://www.asi.it/2022/03/cubesat-lasi-al-lavoro-per-il-futuro-del-settore/(s’ouvre dans une nouvelle fenêtre)).
The COMPASS team has strengthened research collaborations on space debris with the European Space Agency and the Italian Space Agency. Noteworthy, within the space debris filed the COMPASS team has contributed to the Inter Agency Space Debris Coordination Committee Working Group 2 (being part of the Italian delegation) on modelling by defining the action task for the definition of a proxy for computing the
overall capacity of space and define a debris index. In this framework some preliminary research work was performed to review the use of carrying capacity concept in application other than the space field and to compare with a very simple 1D debris model some definition of the space capacity available in the literature. As a result of the extensive work on space debris mitigation, the COMPASS team and Politecnico di Milano is now one of the refence institutions for space debris modelling and space sustainability studies.
Distributed missions for Earth-observation and large constellations
Within the rising space economy, Space assets at the services they provide are now fundamental to our daily live. The COMPASS project devoted effort to develop a framework for the quantitative assessment of the socio-economic benefit of space missions to the humankind trying to map the mission outcome to the United Nations Global development goals. In the field of Earth-based missions for Earth Observation, advanced formation flying techniques were applied to the design of a rigid formation of three or more satellites. The formation flying design framework developed within COMPASS found its most relevant application in the ESA mission study for the Formation Flying Large Aperture Synthesis mission for remote sensing.
Space is getting crowded also due to the recent announced plans on the deployment in orbit of large constellation of small satellites. Mission involving large constellations have been tacked, devising new techniques for the optimisation of the constellation under several design criteria. We have performed the optimisation and design of satellite large constellations considering all the phases of their mission, from the orbit raising, till the mission end-of-life, with the consideration of self-induced collision among satellite within the constellation. The new method for low-thrust trajectory design based on semi-analytical techniques and refinement with Differential Dynamics Programming were applied to the design of orbit raising of large constellation missions and the mission architecture for an ADR service for large constellation was studied.
In the case of the Global Navigation Satellite System, its performance was evaluated via the G-CAT tool, in both nominal and failure modes through coverage analysis.
The task on constellation design has also focused on space sustainability challenges. In particular, we defined aa model for the brightness of a satellite to be used for minimising the light pollution by large constellation satellites. The brightness model was validated with observations of the OneWeb satellites, performed by the GAL Hassin, astronomic park in Isnello.
Planetary defence and protection
In the framework of space situation awareness of asteroid impact threats, we performed the mission analysis of potential threat scenarios by using the kinetic impactor strategy to deflect potentially hazardous asteroids. This was done in the framework of a collaboration with the Italian Space Agency and an on-going discussion with the United Nation-mandated Space Mission Planning Advisory Group to which COMPASS is actively contributing as part of the Italian delegation. To increase the technology readiness level of this deflection technique, COMPASS focused the research on the characterisation of close encounters between the asteroid and the Earth to achieve an optimal deflection design for planetary protection in presence of close encounters. The mission design of a kinetic impactor mission was then performed exploiting intermediate fly-bys and tacking both the direct hit scenario and a resonant-hit scenario. Moreover, a new technology for asteroid deflection based on the electro-magnetic interaction between the spacecraft and the asteroid was devised. The design of the optimal deflection manoeuvre for near-Earth objects was performed using the b-plane representation and considering gravity assists during the asteroid interception phase to improve the arrival conditions. In the field of asteroid deflection missions, we have also extended the NASA break-up model, originally developed for space debris, to model the distribution of fragments when a kinetic impactor satellite hits the asteroid.
The COMPASS team have contributed to the UN-mandated Space Mission Planning Advisory Group by organising the first SMPAG hypothetical threat exercise to focus on the inter-agency procedure to organise a coordinated response to the threat. The objectives are (1) to define the tasks required for a SMPAG coordinated response to the Exercise NEO threat, (2) to define which entity/ies would be responsible for these tasks and (3) to identify the procedures internally to each SMPAG member to propose a response to the SMPAG.
Finally, some focus was also given to scientific missions to asteroids; in this aspect the dynamics of dust at asteroids has been modelled using a perturbed three body problem and using perturbation techniques and the relative dynamics approach has been applied to mission for the definition of the gravity field at asteroids.
Interplanetary and planet-centred trajectory design
To enhance the interplanetary trajectory design and select the planets for fly-by manoeuvre a design strategy was derived for “surfing” among planets. This, however, need to be compliant to planetary protection requirements, so that man-made objects do not contaminate other planets. We have devised new methods for verifying, through orbit propagation and uncertainty modelling, that these requirements are satisfied. The planetary protection verification analysis tool devised in COMPASS was applied to the ESA-NASA JUICE mission through a collaboration with the European Space Agency. We also investigated the end-of-life disposal design for spacecraft at libration points orbits to give a physical interpretation of their probability of return to Earth. The work on planetary protection and the collaboration with the European Space Agency gave the opportunity to extend the applicability of uncertainty propagation techniques from planetary protection applications to robust trajectory design applications where an additional step is the definition of the control action and the selection of flyby planets.
In the field of interplanetary missions, the COMPASS project contributed to the application of the fly-by map to the NASA CLIPPER mission. The techniques for long-term orbit propagation were applied to the planetary protection analysis of ESA missions within two confounded PhD programmes between COMPASS and ESA that lead to the development of an improved version of the SNAPPshot software and on robust trajectory design techniques accounting for generic evolving uncertainties. Current work is devoted to devise a completely new formulation based on Kustaanheimo-Stiefel variables to improve efficiency and insight into the dynamics for robust mission design. For interplanetary trajectory design we devised a method for the identification of the feasible flyby trajectories using the pork-chop plot analysis and the Syzygy function, traditionally used in astronomy. A collaboration with NASA JPL was initiated in this topic.
The philosophy of surfing through orbit perturbation was principally applied to space transfer design. Indeed, we designed of end-of-life disposal of INTEGRAL and XMM spacecraft with perturbation enhanced control algorithm. The effect of perturbations was also considered for the computation of frozen orbits for Moon exploration with orbit maintenance through an electrospray thruster for CubeSat. We performed low-thrust trajectory design for a novel de-orbiting strategy by using low-thrust and passive de-orbiting sails, reducing the fuel consumption compared with the conventional de-orbiting method that aims at lowering the perigee altitude. In this respect, the attitude stability of pyramidal-shaped helio-stable sails close to a sun-pointing direction was studied for application to end-of-life passive and semi-controlled deorbiting.
Dissemination
For dissemination activities and engaging with policy makers several interactive games were developed using the COMPASS algorithms as backend and creating graphical interfaces and Virtual Reality applications. Different COMPASS games were developed to (1) show the impact of space activities to humankind and their contribution to the UN Sustainable development goals, (2) raise awareness about the space debris problem and the ring of artificial non-operational objects we are creating around the Earth, (3) show the orbit and ground coverage of Earth-orbiting satellites and large constellations, (4) design interplanetary missions and missions to deflect asteroids. All the dissemination activities are reported in the report and the website section dedication to dissemination and outreach. Remarkably, the COMPASS project was invited to represent the European Research Council at the European Research and Innovation Days, Brussels, 24-26 Sept. 2019. (Website: https://erc.europa.eu/event/european-research-and-innovation-days(s’ouvre dans une nouvelle fenêtre)). The European Research and Innovation Days is the first annual policy event of the European Commission, bringing together stakeholders to debate and shape the future research and innovation landscape. The COMPASS project was presented as an example of ERC projects. (Website: https://erc.europa.eu/projects-figures/stories/making-space-safer-place-satellites-and-spacecraft(s’ouvre dans une nouvelle fenêtre) ERC Website: https://erc.europa.eu/erc-participants-event-2019-research-innovation-days(s’ouvre dans une nouvelle fenêtre)).
Moreover, the PI of the COMPASS project was selected to participate to the World Economic Forum (WEF) Young Scientists programme at the Annual Meeting of the New Champions 1-3 Jul. 2019, Dalian, People's Republic of China (Website: https://www.weforum.org/events/annual-meeting-of-the-new-champions-2019(s’ouvre dans une nouvelle fenêtre)) as part of the ERC delegation composed of some ERC scientist and Jean-Pierre Bourguignon. The PI was a contributor to the agenda with a blog on “Europe is designing satellites that 'surf' their way past space debris” (Website: https://www.weforum.org/agenda/authors/camilla-colombo(s’ouvre dans une nouvelle fenêtre) World Economic Forum news: https://www.weforum.org/press/2019/06/unveiled-the-brightest-young-scientific-minds-in-the-world(s’ouvre dans une nouvelle fenêtre) and ERC news: https://erc.europa.eu/event/erc-summer-davos-leadership-40-succeeding-new-era-globalization(s’ouvre dans une nouvelle fenêtre))
More info on the research project can be also found on the project webpage: www.compass.polimi.it
Progrès au-delà de l’état des connaissances et impact potentiel prévu (y compris l’impact socio-économique et les conséquences sociétales plus larges du projet jusqu’à présent)
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 phases, respectively. Scheduling the timing to start orbit raising and de-orbiting operation for the satellites was demonstrated to be a fundamental factor to avoid the self-induced collision at the mission design stage.
As space activities are boosting, it will be needed in the near future, to regulate the traffic in space. To this aim we are using the developed tools to devise a mean for “rating” satellites and missions based on their impact on the environment and the benefit they provide to human activities and life on Earth, to drive the development of space toward sustainability. This was represented also via a graphic interactive COMPASS game used for dissemination.
Finally, despite orbit and attitude coupled systems are known to have two different time scales, the usual approach is to separate the motions by assuming a generalised shape of the spacecraft (e.g. cannonball). In COMPASS the procedure to use slow-fast dynamical systems theory has been developed for a large family of spacecraft by reducing the problem to close to Hamiltonian and using perturbation theory to study small oscillations close to the sun-pointing direction for a helio-stable sail.
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 phases, respectively. Scheduling the timing to start orbit raising and de-orbiting operation for the satellites was demonstrated to be a fundamental factor to avoid the self-induced collision at the mission design stage.
As space activities are boosting, it will be needed in the near future, to regulate the traffic in space. To this aim we are using the developed tools to devise a mean for “rating” satellites and missions based on their impact on the environment and the benefit they provide to human activities and life on Earth, to drive the development of space toward sustainability. This was represented also via a graphic interactive COMPASS game used for dissemination.
Finally, despite orbit and attitude coupled systems are known to have two different time scales, the usual approach is to separate the motions by assuming a generalised shape of the spacecraft (e.g. cannonball). In COMPASS the procedure to use slow-fast dynamical systems theory has been developed for a large family of spacecraft by reducing the problem to close to Hamiltonian and using perturbation theory to study small oscillations close to the sun-pointing direction for a helio-stable sail.