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For the Planetary Defense Conference Exercise 2019, we set out to find ways to obtain the earliest possible characterization of the incoming (fictitious!) asteroid, 2019 PDC. After a partially successful deflection, a 'small' fragment was still bound for impact. The location was only known two weeks before impact - the time left for the evacuation of the larger New York City metropolitan region. With experience in Near-Earth Object (NEO) exploration mission design, solar sail and solar-electric propulsion (SEP) technology for small spacecraft, agile responsive design and integration, and from previous PDC Exercises, the importance of earliest possible information on impact location and energy was obvious. NEO in-situ exploration can provide invaluable information not just for deflection actions but also for planetary science and resource utilization. This is only possible with space missions closely approaching the asteroid. Expecting a solar sail mission flying in the 2020s could be re-directed, a unique feature of solar sailing, we searched for multiple rendezvous missions at initial sail technology characteristic accelerations of =2 years, within

This paper describes a novel method to compute minimum-time solar-sail trajectories starting from a given low-thrust solution. The method is based on the use homotopy and numerical continuation. Homotopy is used to link the low-thrust with the solar-sail optimal control problem. Numerical continuation is used to compute the optimal solar-sail solution, starting from a given low-thrust planar solution, which is normally easy to find. Planar solar sail trajectories are computed by means of the homotopic approach. These solutions are used to compute, in a single shooting approach, three-dimensional solar-sail trajectories, for transfer scenarios involving a small change of the orbital inclination. The proposed homotopic approach is tested against a conventional approach, based on the use of a genetic algorithm. Numerical test cases are performed both on Earth-Mars and Earth-Apophis rendezvous. The results show that the proposed method is advantageous, in terms of accuracy of the solution and computational time.

This report presents a mapping between the elements of highly non-Keplerian orbits and classical orbital elements. Three sets of elements are discussed and mappings are derived in closed, analytical form for both the direct and inverse problem. Advantages and drawbacks of the use of each set of elements are discussed. A sensitivity analysis is performed on all mappings presented. The spacecraft thrust-induced acceleration used to generate families of highly non-Keplerian orbits is extracted from the inverse mapping from the osculating orbital elements. The key signatures of highly non-Keplerian orbits in Keplerian elements tracking data are determined through a set of representative test cases.

The scientific interest in near-Earth asteroids (NEAs) and the classification of some of those as potentially hazardous\ud asteroid for the Earth stipulated the interest in NEA exploration. Close-up observations of these objects will increase\ud drastically our knowledge about the overall NEA population. For this reason, a multiple NEA rendezvous mission through\ud solar sailing is investigated, taking advantage of the propellantless nature of this groundbreaking propulsion technology.\ud Considering a spacecraft based on the DLR/ESA Gossamer technology, this work focuses on the search of possible\ud sequences of NEA encounters. The effectiveness of this approach is demonstrated through a number of fully-optimized\ud trajectories. The results show that it is possible to visit five NEAs within 10 years with near-term solar-sail technology.\ud Moreover, a study on a reduced NEA database demonstrates the reliability of the approach used, showing that 58% of the\ud sequences found with an approximated trajectory model can be converted into real solar-sail trajectories. Lastly, this second\ud study shows the effectiveness of the proposed automatic optimization algorithm, which is able to find solutions for a large\ud number of mission scenarios without any input required from the user.

The scientific interest for near-Earth asteroids (NEAs) as well as the interest in potentially hazardous asteroids from the perspective of planetary defense led the space community to focus on NEA mission studies. A multiple NEA rendezvous mission with close-up observations of several objects can help to improve the characterization of these asteroids. This work explores the design of a solar-sail spacecraft for such a mission, focusing on the search of possible sequences of encounters and the trajectory optimization. This is done in two sequential steps: a sequence search by means of a simplified trajectory model and a set of heuristic rules based on astrodynamics, and a subsequent optimization phase. A shape-based approach for solar sailing has been developed and used for the first phase. The effectiveness of the proposed approach is demonstrated through a fully-optimized multiple NEA rendezvous mission. The results show that it is possible to visit 5 NEAs within 10 years with near-term solar-sail technology.

This paper describes a novel method to solve solar-sail minimum-time-of-flight optimal control problems starting from a low-thrust solution. The method is based on a homotopic continuation. This technique allows to link the low-thrust with the solar-sail acceleration, so that the solar-sail solution can be computed starting from the usually easier low-thrust one by means of a numerical iterative approach. Earth-to-Mars transfers have been studied in order to validate the proposed method. A comparison is presented with a conventional solution approach, based on the use of a genetic algorithm. The results show that the novel technique has advantages, in terms of accuracy of the solution and computational time.

This paper describes the methodology to find and verify the solution to the 8th Global Trajectory Optimization Competition (GTOC) problem, developed by Team 13, GlasgowJena+. We chose a stochastic approach to quickly assess a large number (about 1010) of 3-spacecraft formations. A threshold was used to select promising solutions for further optimization. Our search algorithm (implemented in Java) is based on three C++ algorithms called via Java native interface (JNI). A great deal was given to the verification process, which became a core part of our solution. Our final solution has a performance index of 75.9710kmJ=×, 40 distinct observations, and the sum of the final masses of the three spacecraft is 5846.57 kg.

Near-Earth Asteroids (NEAs) are an extremely valuable resource to study the origin and evolution of the Solar System more in depth. At the same time, they constitute a serious risk for the Earth in the not-so-remote case of an impact. In order to mitigate the hazard of a potential impact with the Earth, several techniques have been studied so far and, for the majority of them, a good knowledge about the chemical and physical composition of the target object is extremely helpful for the success of the mission. A multiple-rendezvous mission with NEAs, with close-up observations, can help the scientific community to improve the overall knowledge about these objects and to support any mitigation strategy. Because of the cost of this kind of mission in terms of Dv, a solar sail spacecraft is proposed in this study, in order to take advantage of the propellantless characteristic of this system. As part of the DLR/ESA Gossamer roadmap, and thus considering the sailcraft based on this technology, the present work is focused on the search of possible sequences of encounters, with priority on Potentially Hazardous Asteroids (PHAs). Because of the huge amount of NEAs, the selection of the candidates for a multiple rendezvous is firstly a combinatorial problem, with more than a billion of possible sequences for only three consecutive encounters. Moreover, an optimization problem should be solved in order to find a feasible solar-sail trajectory for each leg of the sequence. In order to tackle this mixed combinatorial/optimization problem, the strategy used is divided into two main steps: a sequence search by means of heuristic rules and simplified trajectory models, and a subsequent optimization phase. Preliminary results were presented previously by the authors, demonstrating that this kind of mission is promising. In this paper, we aim to find new sequences by introducing a different approach on the sequence search algorithm and by reducing the area-to-mass ratio of the solar sail. A smaller area-to-mass ratio entails either the possibility to carry on more payload or to reduce the sail area, raising the TRL. A grid search over 10 years of launching dates is carried out, resulting in different sequences of objects depending on the departing date. Two sequences are fully studied and optimized. The mission parameters and trajectories of the sequences found are shown and explained.

Physical interaction with small solar system bodies (SSSB) is key for in-situ resource utilization (ISRU). The design of mining missions requires good understanding of SSSB properties, including composition, surface and interior structure, and thermal environment. But as the saying goes "If you've seen one asteroid, you've seen one Asteroid": Although some patterns may begin to appear, a stable and reliable scheme of SSSB classification still has to be evolved. Identified commonalities would enable generic ISRU technology and spacecraft design approaches with a high degree of re-use. Strategic approaches require much broader in-depth characterization of the SSSB populations of interest to the ISRU community. The DLR-ESTEC GOSSAMER Roadmap Science Working Groups identified target-flexible Multiple Near-Earth asteroid (NEA) Rendezvous (MNR) as one of the missions only feasible with solar sail propulsion, showed the ability to access any inclination and a wide range of heliocentric distances as well as continuous operation close to Earth's orbit where low delta-v objects reside.

Any effort which intends to physically interact with specific asteroids requires understanding at least of the composition and multi-scale structure of the surface layers, sometimes also of the interior. Therefore, it is necessary first to characterize each target object sufficiently by a precursor mission to design the mission which then interacts with the object. In small solar system body (SSSB) science missions, this trend towards landing and sample-return missions is most apparent. It also has led to much interest in MASCOT-like landing modules and instrument carriers. They integrate at the instrument level to their mothership and by their size are compatible even with small interplanetary missions.\ud \ud The DLR-ESTEC GOSSAMER Roadmap NEA Science Working Groups‘ studies identified Multiple NEA Rendezvous (MNR) as one of the space science missions only feasible with solar sail propulsion. The parallel Solar Polar Orbiter (SPO) study showed the ability to access any inclination and a wide range of heliocentric distances. It used a separable payload module conducting the SPO mission after delivery by sail to the proper orbit. The Displaced L1 (DL1), spaceweather early warning mission study, outlined a very lightweight sailcraft operating close to Earth, where all objects of interest to planetary defence must pass.\ud \ud These and many other studies outline the unique capability of solar sails to provide access to all SSSB, at least within the orbit of Jupiter. Since the original MNR study, significant progress has been made to explore the performance envelope of near-term solar sails for multiple NEA rendezvous.\ud \ud However, although it is comparatively easy for solar sails to reach and rendezvous with objects in any inclination and in the complete range of semi-major axis and eccentricity relevant to NEOs and PHOs, it remains notoriously difficult for sailcraft to interact physically with a SSSB target object as e.g. the HAYABUSA missions do.\ud \ud The German Aerospace Center, DLR, recently brought the GOSSAMER solar sail deployment technology to qualification status in the GOSSAMER-1 project and continues the development of closely related technologies for very large deployable membrane-based photovoltaic arrays in the GOSOLAR project, on which we report separately.\ud \ud We expand the philosophy of the GOSSAMER solar sail concept of efficient multiple sub-spacecraft integration to also include landers for one-way in-situ investigations and sample-return missions. These are equally useful for planetary defence scenarios, SSSB science and NEO utilization. We outline the technological concept used to complete such missions and the synergetic integration and operation of sail and lander.\ud \ud We similarly extend the philosophy of MASCOT and use its characteristic features as well as the concept of Constraints-Driven Engineering for a wider range of operations. For example, the MASCOT Mobility hopping mechanism has already been adapted to the specific needs of MASCOT2. Utilizing sensors as well as predictions, those actuators could in a further development be used to implement anti-bouncing control schemes, by counteracting with the lander‘s rotation. Furthermore by introducing sudden jerk into the lander by utilization of the mobility, layers of loose regolith can be swirled up for sampling.

Physical interaction with small solar system bodies (SSSB) is the next step in planetary science, planetary in-situ resource utilization (ISRU), and planetary defense (PD). It requires a broader understanding of the surface properties of the target objects, with particular interest focused on those near Earth. Knowledge of composition, multi-scale surface structure, thermal response, and interior structure is required to design, validate and operate missions addressing these three fields. The current level of understanding is occasionally simplified into the phrase, ”If you’ve seen one asteroid, you’ve seen one asteroid”, meaning that the in-situ characterization of SSSBs has yet to cross the threshold towards a robust and stable scheme of classification. This would enable generic features in spacecraft design, particularly for ISRU and science missions. Currently, it is necessary to characterize any potential target object sufficiently by a dedicated pre-cursor mission to design the mission which then interacts with the object in a complex fashion. To open up strategic approaches, much broader in-depth characterization of potential target objects would be highly desirable. In SSSB science missions, MASCOT-like nano-landers and instrument carriers which integrate at the instrument level to their mothership have met interest. By its size, MASCOT is compatible with small interplanetary missions. The DLR-ESTEC Gossamer Roadmap Science Working Groups‘ studies identified Multiple Near-Earth asteroid (NEA) Rendezvous (MNR) as one of the space science missions only feasible with solar sail propulsion. The Solar Polar Orbiter (SPO) study showed the ability to access any inclination, theDisplaced-L1 (DL1) mission operates close to Earth, where objects of interest to PD and for ISRU reside. Other studies outline the unique capability of solar sails to provide access to all SSSB, at least within the orbit of Jupiter, and significant progress has been made to explore the performance envelope of near-term solar sails for MNR. However, it is difficult for sailcraft to interact physically with a SSSB. We expand and extend the philosophy of the recently qualified DLR Gossamer solar sail deployment technology using efficient multiple sub-spacecraft integration to also include landers for one-way in-situ investigations and sample-return missions by synergetic integration and operation of sail and lander. The MASCOT design concept and its characteristic features have created an ideal counterpart for thisand has already been adapted to the needs of the AIM spacecraft, former part of the NASA-ESA AIDA mission. Designing the combined spacecraft for piggy-back launch accommodation enables low-cost massively parallel access to the NEA population.

Physical interaction with small solar system bodies (SSSB) is the next step in planetary science, planetary in-situ resource utilization (ISRU), and planetary defense (PD). It requires a broader understanding of the surface properties of the target objects, with particular interest focused on those near Earth. Knowledge of composition, multi-scale surface structure, thermal response, and interior structure is required to design, validate and operate missions addressing these three fields. The current level of understanding is occasionally simplified into the phrase, "If you've seen one asteroid, you've seen one Asteroid", meaning that the in-situ characterization of SSSBs has yet to cross the threshold towards a robust and stable scheme of classification. This would enable generic features in spacecraft design, particularly for ISRU and science missions. Currently, it is necessary to characterize any potential target object sufficiently by a dedicated pre-cursor mission to design the mission which then interacts with the object in a complex fashion. To open up strategic approaches, much broader in-depth characterization of potential target objects would be highly desirable. In SSSB science missions, MASCOT-like nano-landers and instrument carriers which integrate at the instrument level to their mothership have met interest. By its size, MASCOT is compatible with small interplanetary missions. The DLR-ESTEC Gossamer Roadmap Science Working Groups' studies identified Multiple Near-Earth asteroid (NEA) Rendezvous (MNR) as one of the space science missions only feasible with solar sail propulsion. The Solar Polar Orbiter (SPO) study showed the ability to access any inclination and a wide range of heliocentric distances, with a separable payload module delivered by sail to the proper orbit. The Displaced-L1 (DL1) spaceweather early warning mission study sailcraft operates close to Earth, where all objects of interest to PD must pass and low delta-v objects for ISRU reside. Other studies outline the unique capability of solar sails to provide access to all SSSB, at least within the orbit of Jupiter, and significant progress has been made to explore the performance envelope of near-term solar sails for MNR. However, it is difficult for sailcraft to interact physically with a SSSB. We expand and extend the philosophy of the recently qualified DLR Gossamer solar sail deployment technology using efficient multiple sub-spacecraft integration to also include landers for one-way in-situ investigations and sample-return missions by synergetic integration and operation of sail and lander. The MASCOT design concept and its characteristic features have created an ideal counterpart for this. For example, the MASCOT Mobility hopping mechanism and its power supply concept have already been adapted to the specific needs of MASCOT2 which was to be carried on the AIM spacecraft of ESA as part of the NASA-ESA AIDA mission to binary NEA Didymos. The methods used or developed in the realization of MASCOT such as Concurrent Engineering, Constraints-Driven Engineering and Concurrent Assembly Integration and Verification enable responsive missions based on now available as well as near-term technologies. Designing the combined spacecraft for piggy-back launch accommodation enables low-cost massively parallel access to the NEA population.

The exploration of small solar system bodies started with fast fly-bys of opportunity on the sidelines of missions to the planets. The tiny new worlds seen turned out to be so intriguing and different from all else(and each other) that dedicated sample-return and in-situ analysis missions were developed and launched. Through these, highly efficient low-thrust propulsion expanded from commercial use into mainstream and flagship science missions, there in combination with gravity assists. In parallel, the growth of small spacecraft solutions accelerated in numbers as well as individual spacecraft capabilities. The on-going missions OSIRIS-REx (NASA) or Hayabusa2 (JAXA) with its landers MINERVA-II and MASCOT, and the upcoming NEA scout mission are examples of this synergy of trends. The continuation of these and other related developments towards a propellant-less and highly efficient class of spacecraft for solar system exploration emerges in the form of small spacecraft solar sails designed for carefree handling and equipped with carried landers and application modules. These address the needs of all asteroid user communities– planetary science, planetary defence, and in-situ resource utilization – as well as other fields of solar system science and applications such as space weather warning and solar observations. Already the DLR-ESTEC GOSSAMER Roadmap for Solar Sailing initiated studies of missions uniquely feasible with solar sails such as Displaced L1 (DL1) space weather advance warning and monitoring and Solar Polar Orbiter(SPO) delivery, which demonstrate the capabilities of near-term solar sails to reach any kind of orbit in the inner solar system. This enables Multiple Near-Earth Asteroid (NEA) rendezvous missions (MNR),from Earth-coorbital to extremely inclined and even retrograde target orbits. For these mission types using separable payloads, design concepts can be derived from the separable Boom Sail Deployment Units characteristic of DLR GOSSAMER solar sail technology, nanolanders like MASCOT, or microlanders like the JAXA-DLR Jupiter Trojan Asteroid Lander for the OKEANOS mission which can shuttle from the sail to the targets visited and enable multiple NEA sample-return missions. These nanospacecraft scale components are an ideal match creating solar sails in micro-spacecraft format whose launch configurations are compatible with secondary payload platforms such as ESPA and ASAP. The DLR GOSSAMER solar sail technology builds on the experience gained in the development of deployable membrane structures leading up to the successful ground deployment test of a (20 m) solar sail at DLR Cologne in 1999 and in the 20 years since.