Trajectory design of multi-target missions via graph transcription and dynamic programming.

Missions that can visit multiple orbital targets represent the next cornerstone for space travels, be it for science, exploration or even exploitation. The trajectory design of such missions requires to solve a mixed-integer programming problem, on which the selection of a proper sequence of targets depends upon the quality of the trajectory that links them, where quality usually refers to propellant consumption or mission duration. Two aspects are important when addressing these problems. The first one is to identify optimal solutions with respect to critical mission parameters. Current approaches to solve these problems require computing time that rises with the number of control parameters, as the visiting objects sequence length, as well as rely on a-priori knowledge to define a manageable design space (i.e., departing dates, presence of deep space manoeuvres, etc.). Moreover, the more challenging multi-objective optimization needs to be tackled to ap- propriately inform the mission design with full extent of launch opportunities. The second aspect is that beyond the obvious complexity of such problems formulation, preliminary mission design requires not only to locate the global optimum solutions but, also, to map the ensemble of solutions that leads to feasible transfers. This thesis describes a pipeline to transcribe the mixed-integer space into a discrete graph made by grids of interconnected nodes for missions that visit multiple celestial objects, like planets, asteroids, comets, or a combination thereof, by means of one single space- craft. This allows to exploit optimal substructure of such problems, opening dynamic programming to be conveniently applied. Dynamic programming principles are thus ex- tended to multi-objective optimization of such trajectories and used to explore the tran- scribed graph, guaranteeing Pareto optimality with efficient computational effort. A mod- ified dynamic programming approach is also derived that allows to retain more and diverse solutions in the final set compared to known standard approaches, while guaranteeing global optimality on the transcribed space. Numerous applications are presented where such pipeline is successfully applied. Tra- jectories towards Jupiter and Saturn alongside novel transfers for comet sample return missions are discussed, as well as trajectories that visit multiple asteroids in the main belt. Such scenarios prove robustness and efficiency of proposed approaches in capturing optimal solutions and wide Pareto fronts on search spaces of complex configuration.PhD in Aerospac

A multi-fidelity optimization process for complex multiple gravity assist trajectory design

Multiple-gravity assist (MGA) trajectories exploit successive close passages with Solar System planets to change spacecraft orbital energy. This allows to explore orbital regions that are demanding to reach otherwise. However, to automatically plan an MGA transfer it is necessary to solve a complex mixed integer programming problem, to find the best sequences among all combinations of encountered planets and dates for the spacecraft manoeuvres. MGA problem is characterized by multiple local minimum solutions and an optimizable parameter space of complex configuration.Current approaches to solve MGA problem require computing time that rise steeply with the number of control parameters, such as the length of the MGA sequence. Moreover, the most useful problem to be solved is a multi-objective optimization (generally with v and transfer duration as fitness criteria) since it allows to inform the preliminary mission design with the full extent of launch opportunities. With the present paper, a novel toolbox named ASTRA (Automatic Swing-by TRAjectories) is described to assess the possibility of solving these challenges. ASTRA employs multi-fidelity optimization to construct feasible planetary sequences. It automatically selects planetary encounters and evaluates Lambert’s problem solutions over a grid of transfer times. Discontinuities between incoming and outgoing Lambert arcs are in part compensated by the fly-by of the planet. If required, an additional v manoeuvre is added, representing the defect between incoming and outgoing spacecraft relative velocity with respect to the planet. Once the solutions are obtained, defects are replaced with Deep Space Manoeuvres (DSMs) between two consecutive encounters. Particle Swarm Optimization (PSO) is used to find the optimal location of DSMs. Mission scenarios towards Jupiter are used as test cases to validate and demonstrate the accuracy of ASTRA solutions

Automatic multi-gravity assist trajectory design with modified Tisserand Graphs exploration

Reaching the boundaries of the Solar system has been made possible by Multi-Gravity Assist (MGA) trajectories that reduce the propellant costs by using the gravity of planets to increase or decrease the energy of a spacecraft’s orbit. Designing an optimal MGA trajectory constitutes a mixed-integer non-linear programming (MINLP) problem, which requires a simultaneous combinatorial search of discrete elements (e.g., planets), as well as an optimisation of continuous variables, such as departing date, transfer times, Deep Space Manoeuvres (DSM), etc., in an exponentially increasing search space. An efficient way to tackle MINLP problems is to first transcribe them into a simplified combinatorial-only problem and, a posteriori, re-optimise the continuous design variables for a subset of promising sequences of discrete elements. The transcription of an MGA-MINLP problem into a pure combinatorial one can be efficiently explored via Tisserand Graphs (TG), which employ the Tisserand invariant to map possible flybys as a function of the spacecraft’s velocity relative to a given planet. Intersections between contour lines of different relative velocity and planet indicate that a gravity assist is feasible energy-wise and depict how the spacecraft orbit will be modified if undergoing that specific gravity assist. Hence, contour line intersections become the nodes of a graph, which can be efficiently explored via tree traversal algorithms. However, the information obtained from such a Tisserand exploration does not provide launch window or time of flight, and only yields a rough order of magnitude estimate of . To solve this, a database approach using real ephemerides of celestial objects to correlate initial phase angles of planets with dates and approximation methods to simulate DSMs were implemented. This allows to successfully establish a list of feasible planetary sequences while providing estimations of propellant costs, launch windows and excess velocities. The solutions identified are validated by re-optimising the complete MGA trajectories as sequences of flybys, DSMs and Lambert arcs intersecting the real positions of the planets involved. Mission scenarios to Jupiter and never-explored objects, e.g. Centaurs or low-perihelion asteroids, are used to validate the accuracy of the Tisserand-based first-guess solutions, as well as the capability to find the global optimum solution in limited computational effort

Multiobjective design of gravity-assist trajectories via graph transcription and dynamic programming

Multiple gravity-assist (MGA) trajectory design requires the solution of a mixed-integer programming problem to find the best sequence among all possible combinations of candidate planets and dates for spacecraft maneuvers. Current approaches require computing times rising steeply with the number of control parameters, and they strongly rely on narrow search spaces. Moreover, the challenging multiobjective optimization needs to be tackled to appropriately inform the mission design with full extent of launch opportunities. This paper describes a methodology based upon a trajectory model to transcribe the mixed-integer space into a discrete graph made by grids of interconnected nodes. The model is based on Lambert arc grids obtained for a range of departure dates and flight times between two planets. A Tisserand-based criterion selects planets to pass by. Dynamic programming is extended to multiobjective optimization of MGA trajectories and used to explore the graph, guaranteeing Pareto optimality with only moderate computational effort. Robustness is ensured by evaluating the relationship between graph and mixed-integer spaces. Missions to Jupiter and Saturn alongside challenging comet sample return transfers involving long MGA sequences are discussed. These examples illustrate the robustness and efficiency of the proposed approach in capturing globally optimal solutions and wide Pareto fronts on complex search spaces.Airbus

Modified tisserand map exploration for preliminary multiple gravity assist trajectory design

Multiple-gravity assist (MGA) trajectories are used in interplanetary missions to change the spacecraft orbital energy by exploiting the gravity of celestial bodies. This allows the spacecraft to reach regions in the Solar System that otherwise would be extremely demanding in terms of propellant. However, if a trajectory seeks to benefit from a long MGA sequence, it is necessary to solve a complex mixed integer programming problem in order to find the best swing-by sequence among all combinations of encountered planets and dates for the various spacecraft manoeuvres. Tisserand graphs provide an efficient way to tackle the combinatorial part of the MGA problem, by allowing a simple computation of the effect of different sequences of gravity assists, based only on energy considerations. Typically, the exploration of Tisserand graphs is performed via a comprehensive Tree Search of possible sequences that reach a specific orbital energy and eccentricity (e.g. Langouski et al.). However, this approach is generally directed by heuristic techniques aimed at finding duration limited, low Δv transfers without formal optimization or time constraint. This results in not having information from Tisserand graphs associated to the trajectory shape, namely the planetary phasing and mission durations. This paper presents a more comprehensive strategy involving the solution of the phasing problem to automatically generate viable ballistic planetary sequences. This approach has proven to be effective in representing trajectory shape already from the Tisserand map exploration step. All the solutions identified by the modified Tisserand map exploration are validated by re-optimizing the complete MGA trajectories as sequences of swing-bys, DSMs and Lambert Arc transfers intersecting the real positions of the planets involved. Different mission scenarios towards Jupiter are used as test cases to validate and demonstrate the accuracy of the Tisserand-based first-guess solution

Deterministic and stochastic exploration of long asteroid fly-by sequences exploiting tree-graph and optimal substructure properties

In the past, space trajectory design was limited to the optimal design of transfers to single destinations. However, a somewhat more daring approach is today making the space community to consider missions that visit, with one single spacecraft, a multitude of celestial objects; such as asteroid tour mission proposals CASTAway or MANTIS, which both proposed to visit 10 or more asteroids in a quick succession of asteroid fly-bys. The design of these so-called asteroid tours is complicated by the fact that the sequence of asteroids is not known a priori, but is the objective of the optimisation itself. This leads to a complex mixed-integer non-linear programming (MINLP) problem, on which the decision variables assume both continuous and discrete values. Beyond the obvious complexity of such problem formulation, preliminary mission design requires not only to locate the global optimum solution but, also, to map the ensemble of solutions that leads to feasible transfers. This paper analyses the complexity of such search space, which can be efficiently modelled as a tree-graph of interconnected Lambert arc solutions between two consecutive asteroids. This allows to exploit the optimal substructure of the problem and enables complete tree traverse explorations for limited asteroid catalogues. Nevertheless, the search space quickly grows in complexity for larger catalogues, featuring a labyrinthine multi-modal structure and extreme non-linearities. This underlying complexity ultimately renders common stochastic heuristics, such as Ant Colony Optimization, rather inefficient. Mostly, due to the fact that the metaheuristic processes are not able to gather any real understanding, or knowledge, such that it can efficiently guide the search. Instead, an astrodynamics-lead heuristic based on the distance between spacecraft and asteroid at the asteroid’s MOID-point crossing epoch, enables an efficient pruning of the asteroid catalogue. Then, deterministic processes based on dynamic programming and beam search can be efficiently applied, providing solutions to both the global optimum and the constraint satisfaction problems

An automatic process for sample return missions based on dynamic programming optimization

This work describes a methodology to design sample return missions and rendezvous trajectories options towards cometary objects. These are visited through a succession of fly-bys with Solar System planets, on an overall Multiple Gravity Assist (MGA) transfer. The method is based upon dynamic programming in conjunction to a specific MGA trajectory optimization model to investigate sample return mission scenarios. The model implemented is based on evaluation of grids of transfers between successive planets. The grid is obtained with Lambert arc transfer for a range of departure dates at one planet and range of time of flight to the next planet. For each successive planet in the sequence, discontinuities between incoming and outgoing Lambert arcs arise, which are in part compensated by the fly-by of the planet and, if required, an additional Δv maneuver is added on the given leg of a planet-to-planet transfer. The solutions identified are validated by re-optimizing the complete MGA trajectories as sequences of swing-bys, Deep Space Maneuvers and Lambert arcs transfers. A procedure for discontinuities removal using position constraints is also presented. Mission scenarios towards Saturn are used to validate the accuracy of proposed methods. Trajectory design for novel sample return options and rendezvous are explored for objects among Jupiter Family Comets (JFCs), as well as for never explored targets and orbital regions, as highly inclined Centaurs objects

Efficiency of tree-search like heuristics to solve complex mixed-integer programming problems applied to the design of optimal space trajectories

In the past, space trajectory optimization was limited to optimal design of transfers to single destinations, where optimality refers to minimum propellant consumption or transfer time. New technologies, and a more daring approach to space, are today making the space community consider missions that target multiple destinations. In the present paper, we focus on missions that aim to visit multiple asteroids within a single launch. The trajectory design of these missions is complicated by the fact that the asteroid sequences are not known a priori but are the objective of the optimization itself. Usually, these problems are formulated as global optimization (GO) problems, under the formulation of mixed-integer non-linear programming (MINLP), on which the decision variables assume both continuous and discrete values. However, beyond the aim of finding the global optimum, mission designers are usually interested in providing a wide range of mission design options reflecting the multi-modality of the problems at hand. In this sense, a Constraint Satisfaction Problem (CSP) formulation is also relevant. In this manuscript, we focus on these two needs (i.e. tackling both the GO and the CSP) for the asteroid tour problem. First, a tree-search algorithm based upon the Bellman’s principle of optimality is described using dynamic programming approach to address the feasibility of solving the GO problem. This results in an efficient and scalable procedure to obtain global optimum solutions within large datasets of asteroids. Secondly, tree-search strategies like Beam Search and Ant Colony Optimization with back-tracking are tested over the CSP formulations. Results reveal that BS handles better the multi-modality of the search space when compared to ACO, as this latter solver has a bias towards elite solutions, which eventually hinders the diversity needed to efficiently cope with CSP over graphs

Application of nanosatellites for lunar missions

Two major themes for the space sector in recent years have been the resurgence of missions to the Moon, facilitating the expansion of human presence into the Solar System, and the rapid growth in CubeSat launches. Lunar missions will play an important role in sustainable space exploration, as discussed in the Global Exploration Roadmap. The Roadmap outlines the next steps for the current and next generation of explorers and reaffirms the interest of 14 space agencies to return to the Moon. Over the past decade, a more daring approach to space innovation and the proliferation of low-cost small satellites have invited commercialization and, subsequently, have accelerated the development of miniaturized technologies and substantially reduced the costs associated with CubeSats. In this context, CubeSats are increasingly being considered as platforms for pioneering missions beyond low-Earth orbit. This paper describes a 3U nanosatellite mission to the Moon, designed as part of the UKSEDS Satellite Design Competition, capable of capturing and analysing details of the lunar environment. To achieve the primary mission objectives, a camera and an infrared spectrometer have been included to relay information about historic lunar landmarks to Earth. The design was developed to be integrated with Open Cosmos' OpenKit and reviewed by experts in the field from SSPI. The paper includes a detailed assessment of the current state of miniaturized instruments and the quality of scientific return which can be achieved by a lunar CubeSat mission. This concludes in an overall feasibility study of lunar CubeSats, a discussion of the current limitations and challenges associated with CubeSat technologies and a framework for future missions

Aprendizajes y prácticas educativas en las actuales condiciones de época: COVID-19

“Esta obra colectiva es el resultado de una convocatoria a docentes, investigadores y profesionales del campo pedagógico a visibilizar procesos investigativos y prácticas educativas situadas en el marco de COVI-19. La misma se inscribe en el trabajo llevado a cabo por el equipo de Investigación responsable del Proyecto “Sentidos y significados acerca de aprender en las actuales condiciones de época: un estudio con docentes y estudiantes de la educación secundarias en la ciudad de Córdoba” de la Facultad de Filosofía y Humanidades. Universidad Nacional de Córdoba. El momento excepcional que estamos atravesando, pero que también nos atraviesa, ha modificado la percepción temporal a punto tal que habitamos un tiempo acelerado y angustiante que nos exige la producción de conocimiento provisorio. La presente publicación surge como un espacio para detenernos a documentar lo que nos acontece y, a su vez, como oportunidad para atesorar y resguardar las experiencias educativas que hemos construido, inventado y reinventando en este contexto. En ella encontrarán pluralidad de voces acerca de enseñar y aprender durante la pandemia. Este texto es una pausa para reflexionar sobre el hacer y las prácticas educativas por venir”.Fil: Beltramino, Lucia (comp.). Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Escuela de Archivología; Argentina