### Browsing by Author "Bellome, Andrea"

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Item Open Access Application of nanosatellites for lunar missions(IEEE, 2021-06-07) Bellome, Andrea; Nakhaee-Zadeh, Aydin; Zaragoza Prous, Guillermo; Leng, Louis; Coyle, Matthew; D'Souza, Sharon; Mummigatti, Suchetan; Serfontein, ZariaShow more 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.Show more Item Open Access Automatic multi-gravity assist trajectory design with modified Tisserand Graphs exploration(International Astronautical Federation (IAF), 2022-09-22) Afsa, Hadrien; Bellome, Andrea; Sanchez Cuartielles, Joan Pau; Kemble, StephenShow more 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.Show more Item Open Access An automatic process for sample return missions based on dynamic programming optimization(AIAA, 2021-12-29) Bellome, Andrea; Sanchez, Joan-Pau; Rico Álvarez, Jose Ignacio; Afsa, Hadrien; Kemble, Stephen; Felicetti, LeonardShow more 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.Show more Item Open Access Design of a pipeline for satellite-aided capture at the giant planets of the solar system(IEEE, 2024-05-13) Garny, Hugo; Bellome, Andrea; Felicetti, LeonardShow more For orbiters aiming at the outer planets of our solar system, most of the ∆V cost is associated with the final insertion at the targeted planet. An efficient way of reducing this cost is using flybys of the moons of the planet to reduce the energy of the orbit at arrival, called satellite-aided capture. Designing a full transfer from the Earth to an outer planet, including multiple gravity assists and satellite-aided capture raises important issues that must be addressed. One of them is the multiple control parameters that are required to compute such a trajectory. These parameters must be varied over a large array of values to guarantee that all possibilities are covered with enough precision, ensuring that the final trajectory is the best possible. Current approaches on satellite-aided capture mainly focus on designing trajectories inside the sphere of influence of the targeted planet, with no or minimal focus on linking it to the interplanetary trajectory. However, it remains to create a full pipeline to compute a transfer trajectory from the Earth to an outer planet of the solar system using multiple gravity assists and satellite-aided capture. This paper will focus on creating such a pipeline for orbiters targeting Jupiter, Saturn, Uranus, and Neptune. First, different multiple gravity assists sequences are computed, allowing to make a choice based on transfer time and ∆V cost. This is obtained with a multi-objective dynamic programming exploration, allowing to capture optimal Pareto fronts of ∆V and time of flight in limited computational effort. This transfer sets initial conditions of the satellite-aided capture. Multiple capture sequences are computed around these initial conditions allowing to choose the one minimizing the insertion ∆V . Finally, the last branch of the interplanetary transfer is modified to meet the updated initial conditions of the interplanetary transfer. To compute the satellite-aided capture, the branches between the moons of the sequences are simulated using Lambert arcs. The flybys are approximated as discrete events and are computed to meet the conditions set by the previous and following branches. This pipeline is capable of reproducing scenarios of previous missions to Jupiter and Saturn, ensuring proper functioning of the code. It can also be used to design new trajectories for orbiter at Uranus and Neptune, which have only been visited by Voyager 2 during flybys.Show more Item Open Access Deterministic and stochastic exploration of long asteroid fly-by sequences exploiting tree-graph and optimal substructure properties(International Astronautical Federation (IAF), 2022-09-22) Sanchez, Joan-Pau; Bellome, Andrea; Carrillo, Maria; Del Ser, J.Show more 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.Show more Item Open Access Diversity-based heuristic search for multiple-asteroid tours(IEEE, 2024-05-13) Grabowski, Jan; Bellome, Andrea; Felicetti, LeonardShow more An asteroid tour is a sequence of asteroid flybys performed by a spacecraft in a single mission. Visiting different types of asteroids would be of a great scientific return, but planning such type of mission is highly complex. This is because the combinatorial problem of selecting sequences of asteroids is coupled with optimal control problem of finding viable trajectories in terms of transfer times and manoeuvre locations. The combinatorial problem can be tackled with heuristic algorithms that explore the search space to find optimized flyby sequences of asteroids. This paper proposes a search strategy to increase the diversity of the set of flyby sequences found from the resolution of the optimization problem. The goal is to find a tree exploration method that will improve the quality of the solutions by increasing the number of targets encountered and eliminating duplicated sequences while preserving the average ∆v cost. A diversity measure for a set of solutions is defined based on the ∆v cost of the transfer and the nature of the asteroids in the sequences. A variant of the Beam Search (BS) algorithm, referred to as Diversity Search (DS), is tested. Unlike BS, the DS algorithm eliminates duplicated sequences from the final set of solutions. New asteroid tours are found, allowing to reach targets with a higher inclination or eccentricity, but the average ∆v of a flyby sequence is higher than solutions found with BS. A hybrid search strategy using BS and DS is explored. The goal is to reduce the search space with respect to two criteria: ∆v and diversity score. By pruning the search space according to ∆v first, the hybrid search algorithm is able to generate a diverse set of asteroid tours while preserving the total ∆v of the solutions. Compared to DS, less new asteroids are encountered in the solutions but the average ∆v remains similar to results obtained with BS.Show more Item Open Access Efficiency of tree-search like heuristics to solve complex mixed-integer programming problems applied to the design of optimal space trajectories(IAF, 2021-10-25) Bellome, Andrea; Carrillo, Maria; Sanchez Cuartielles, Joan Pau; Del Ser, J.; Kemble, Stephen; Felicetti, LeonardShow more 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.Show more Item Open Access Icarus: In-situ monitoring of the surface degradation on a near-sun asteroid(Elsevier, 2021-05-21) Lehtinen, Tuomas; Granvik, Mikael; Bellome, Andrea; Sánchez, Joan-PauShow more Icarus is a mission concept designed to record the activity of an asteroid during a close encounter with the Sun. The primary science goal of the mission is to unravel the nontrivial mechanism(s) that destroy asteroids on orbits with small perihelion distances. Understanding the destruction mechanism(s) allows us to constrain the bulk composition and interior structure of asteroids in general. The Icarus mission does not only aim to achieve its science goals but also functions as a technical demonstration of what a low-cost space mission can do. The proposed space segment will include a single spacecraft capable of surviving and operating in the harsh environment near the Sun. The spacecraft design relies on the heritage of missions such as Rosetta, MESSENGER, Parker Solar Probe, BepiColombo, and Solar Orbiter. The spacecraft will rendezvous with an asteroid during its perihelion passage and records the changes taking place on the asteroid’s surface. The primary scientific payload has to be capable of imaging the asteroid’s surface in high resolution using visual and near-infrared channels as well as collecting and analyzing particles that are ejected from the asteroid. The payload bay also allows for additional payloads relating to, for example, solar research. The Icarus spacecraft and the planned payloads have high technology readiness levels and the mission is aimed to fit the programmatic and cost constraints of the F1 mission (Comet Interceptor) by the European Space Agency. Considering the challenging nature of the Icarus trajectory and the fact that the next F-class mission opportunity (F2) is yet to be announced, we conclude that Icarus is feasible as an F-class mission when certain constraints such as a suitable launch configuration are met. A larger mission class, such as the M class by the European Space Agency, would be feasible in all circumstances.Show more Item Embargo Modified dynamic programming for asteroids belt exploration(Elsevier, 2023-12-09) Bellome, Andrea; Sanchez, Joan Pau; García Mateas, José Carlos; Felicetti, Leonard; Kemble, StephenShow more In the past, space trajectory optimisation was limited to the design of space transfers to single destinations. More recent mission concepts however present the challenge to target multiple destinations; be it for science, exploration or even exploitation. This paper focuses on space trajectories that aim to visit multiple main-belt asteroids with one single spacecraft. The trajectory design of these missions is complicated by the fact that the asteroid sequence is not known a priori, but it is the objective of the optimisation problem. Usually, these problems are tackled as global optimisation problems under the formulation of Mixed-Integer Non-Linear Programming, on which the design 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 problem. The paper describes a multi-fidelity design pipeline that enables a consistent exploration of all feasible asteroid tours with a given set of mission boundary conditions (e.g., launch window, mission duration, Δv). The consistency of the exploration is ensured by a deterministic search scheme which retains the n-best paths at each stage of a dynamic programming process. Bellman’s principle of optimality is made applicable by transcribing the search space into a series of discretized events defined by asteroid index and fly-by epoch, as well as ensuring optimal substructure property with the choice of transfer model and design variables. The method is deployed to explore asteroid tour opportunities visiting 10 or more main belt objects and mission boundary conditions compatible with medium or discovery class missions. 79 million such trajectories are found with launch date in 2037.Show more Item Open Access Modified tisserand map exploration for preliminary multiple gravity assist trajectory design(IAFASTRO, 2020-10-14) Bellome, Andrea; Cuartielles, Joan-Pau Sanchez; Felicetti, Leonard; Kemble, StephenShow more 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 solutionsShow more Item Open Access A multi-fidelity optimization process for complex multiple gravity assist trajectory design(ICATT, 2021-06-25) Bellome, Andrea; Sanchez Cuartielles, Joan Pau; Kemble, Stephen; Felicetti, LeonardShow more 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.Show more Item Open Access Multiobjective design of gravity-assist trajectories via graph transcription and dynamic programming(AIAA, 2023-04-02) Bellome, Andrea; Sanchez Cuartielles, Joan Pau; Felicetti, Leonard; Kemble, StephenShow more 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.Show more Item Open Access Optimal time-fixed impulsive non-Keplerian orbit to orbit transfer algorithm based on primer vector theory(Elsevier, 2023-06-06) Bucchioni, Giordana; Gemignani, Gabriele; Lombardi, Francesco; Bellome, Andrea; Leitão, João Pedro Fernandes; Lizy-Destrez, Stèphanie; Innocenti, MarioShow more The work applies a systematic method to compute an optimal transfer trajectory between two non-Keplerian halo orbits in the Circular Restricted Three-body formulation of the Earth–Moon dynamics. The paper exploits the knowledge of the natural non-linear dynamics and the primer vector theory applied to the Circular Restricted Three Body Problem to design optimal multi-impulsive Halo-to-Halo transfers with fixed and limited Time of flight, from every point of the departure orbit to every point of the arrival orbit with an optimal number of impulses. The used method is constituted by three systematic steps with the goal of facilitating the mission design process and the on-board autonomous guidance implementation of future missions in highly non-linear dynamics.Show more Item Open Access Team theAntipodes: solution methodology for GTOC11(Elsevier, 2022-09-13) Armellin, Roberto; Beauregard, Laurent; Bellome, Andrea; Bernardini, Nicolo; Fossa, Alberto; Fu, Xiaoyu; Holt, Harry; Parigini, Cristina; Pirovano, Laura; Wijayatunga, MinduliShow more This paper presents the solution approach developed by the team “theAntipodes” for the 11th Global Trajectory Optimization Competition (GTOC11). The approach consists of four main blocks: (1) mothership chain generation, (2) rendezvous table generation, (3) the dispatcher, and (4) the refinement. Blocks 1 and 3 are purely combinatorial optimization problems that select the asteroids to visit and allocate them to the Dyson ring stations. The rendezvous table generation involves interpolating time-optimal transfers to find all transfer opportunities between selected asteroids and the ring stations. The dispatcher uses the data stored in the table and allocates the asteroids to the Dyson ring stations in an optimal fashion. The refinement ensures each rendezvous trajectory meets the problem accuracy constraints, and introduces deep-space maneuvers to the mothership transfers. We provide the details of our solution that, with a score of 5992, was worth 3rd place.Show more Item Open Access Trajectory design of multi-target missions via graph transcription and dynamic programming.(Cranfield University, 2022-12) Bellome, Andrea; Sanchez Cuartielles, Joan Pau; Felicetti, Leonard; Kemble, StephenShow more 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.Show more