### Browsing by Author "Sanchez Cuartielles, Joan Pau"

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Item Open Access Analytical and semi-analytical approaches to the third-body perturbation in nearly co-orbital regimes(International Astronautical Federation, 2018-10-01) Sanchez Cuartielles, Joan Pau; Colombo, Camilla; Alessi, Elisa MariaShow more Since the beginning of space exploration, close encounters with celestial bodies in the Solar System have been exploited to change the motion of a spacecraft. Gravity assists are such an example; since they take place inside the planet’s sphere of influence, their most used modelling framework is the patched- conics approximation. This, however, simplifies the spacecraft’s motion as to be affected by only one celestial body at a time. Higher accuracy approaches, such as the circular-restricted three-body problem (CR3BP) models a simultaneous attraction of two bodies (primary and secondary: for example, Sun and Earth) and its application domain extends beyond the classical sphere of influence. In between these approaches, perturbation techniques exist to account for the influence of the sec- ondary, well outside the sphere of influence, in addition to the main attractive body. This paper presents two twin formulations for the variation of the spacecraft’s orbital elements due to the third-body effect in the CR3BP, i.e. the regime of distant encounters outside the secondary’s sphere of influence. These are based on the disturbing function of the previously studied Keplerian Map, derived from the Hamiltonian of the CR3BP in a barycentric coordinate system; additionally, they can be used in any kind of system of small gravitational parameter, such as the Sun-Earth one. The first formulation is a partially analytical solution to the Lagrange planetary equations of motion. This strategy unites fully analytical equations for the evolution of the semi-major axis of the motion, which are obtained via a Taylor expansion on the eccentricity, with the use of the Euler method for the remaining unsolvable differential equations. This strategy allows the prediction of the orbital shape, making it potentially useful for fast online computations and application in GNC algorithms. The second formulation is a mapping model for long time propagation, in which the orbital elements are updated at every periapsis and apoapsis to minimise the inherent numerical errors. This strategy is called the EK-PAP (Euler-Keplerian Periapsis to Apoapsis) map. It shows to be several orders of magnitude faster than the CR3BP, remaining accurate for motion durations up to several synodic periods. Particularly, the application to end-of-life disposal strategies is envisioned, in which the EK-PAP map can ensure that the long-term propagation of the disposed spacecraft follows the guidelines for clean space missions.Show more Item Open Access ARTEMIS: A complete mission architecture to bridge the gap between humanity and near-Earth asteroids(International Astronautical Federation, 2018-10-01) Cano, Jorge; Cunill, Jordi; Diaz, Albert Josep; Golemis, Aris; Gupta, Subham; Innes, Daniel; Maiden, David; March, Kieran; Rael, Harvey; Shawe, James; Sierra, Victor; Torrents, Alejandro; Zorzoli Rossi, Elena; Machuca, Pablo; Neves, Rita; Sanchez Cuartielles, Joan PauShow more Asteroid retrieval missions have recently attracted increasing interest from the community and could provide opportunities for scienti c exploration, resource utilisation and even the development of planetary defence strategies. This paper was developed as a result of a 6-month MSc group project, realised by a total of 14 students at Cran eld University pursuing the Astronautics & Space Engineering degree. An overall system design is proposed for a technology demonstrator mission to move a near-Earth asteroid into an easily-accessible location where it could be further explored by future missions. The target nal orbit is a southern halo orbit around the Lagrange point (L2) on the Sun-Earth system. ARTEMIS (Asteroid Retrieval Technology Mission) abides by ESAs constraints for a Large (L) mission call: realised in only one launch with Ariane 64, an operational duration of less than 15 years and a cost at completion of at most e1100M. The proposed mission combines the design of optimal trajectories, employs advanced solar electric propulsion and introduces a be tting level of spacecraft autonomy. The target is the 2006 RH120 asteroid, with an approximate diameter of 6.5 m and mass of roughly 350 tons. To re ne existing data, the ARROW CubeSat mission (Asteroid Reconnaissance to Research Object Worthiness) is to be launched a year prior to the main mission to probe the asteroid via a y-by. ARROW will provide valuable information, such as the asteroids spin rate, rotational axis and better mass estimate, increasing the overall chance of mission success. The main mission will then capture and secure the asteroid using a mechanism of arm-like booms with xenon- lled VectranTM bags. To allow for proper adaptability to the objects shape and mass distribution, as well as preserve the asteroid unaltered, the mechanism is fully contained in fabric that encapsulates the asteroid. The paper concludes that such a mission is conditionally feasible, and summarises the design process resulting in the nal overall mission baseline design. It also examines the practicality of the suggested design for future missions such as space debris removal or its ability to retrieve celestial bodies with variable mass and shape. Proper adaptation of the design could allow for retrieval of similar size or smaller objects. The future implementation of this mission may further the understanding of the origin of the solar system and act as a catalyst to a new celestial body exploitation industry.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 Autonomous navigation and guidance for CubeSats to flyby near-Earth asteroids(IAF, 2019-10-25) Machuca, Pablo; Sanchez Cuartielles, Joan PauShow more Recent advancements in CubeSat technology unfold new mission ideas and the possibility to lower the cost of space exploration. Exploiting the natural dynamics around the Sun-Earth barycentric Lagrange points, minimal-ΔV trajectories to flyby asteroids appear which are compatible with current CubeSat propulsive capabilities. Ground operations costs for an interplanetary CubeSat, however, still represent a major challenge towards low-cost missions; hence certain levels of autonomy are desirable. Considering the limited allocation of sensors and actuators in CubeSats, and their limited performance, Monte Carlo simulations are implemented to understand the flyby accuracies that can be achieved through autonomous navigation and guidance. Primary sources of error analyzed in this study include: (1) uncertainties in the departure conditions, (2) errors in the propulsive maneuvers, (3) errors in the observations, and (4) uncertainties in the ephemeris of the target asteroid. An autonomous navigation and guidance strategy is proposed and evaluated, employing observations of the Sun, visible planets and of the target asteroid, and two trajectory correction maneuvers along the trajectory. Flyby accuracies below 100 km are found possible if the mission characteristics are suitable in terms of available ΔV, on-board asteroid visibility time, mission duration, and asteroid ephemeris uncertainty before the mission. Ultimately, this study assesses the readiness level of current CubeSat technology to autonomously flyby near-Earth asteroids, with realistic component specifications and modeling of relevant errors and uncertainties. The effect of the different mission factors on the final flyby accuracies is evaluated, and a feasible autonomous navigation and guidance strategy is proposed in the effort to reduce ground operations and overall mission costs.Show more Item Open Access Drop Your Thesis! 2018 results: 4.74 seconds of microgravity conditions to enable future cubesat landings on asteroids(Elsevier, 2020-06-04) Gautier, F.; Sitepu, Elioenai; Le Blay, C.; Kersey, G.; Sanchez Cuartielles, Joan PauShow more Space exploration has seen a growing number of asteroid missions being launched; mostly due to their scientific interest, but also on account of the potential impact threat and prospective valuable resources of their targets. Landing safely on the surface of an asteroid is one of the main technical challenges before obtaining in-situ observations and ground-truth data. Given the asteroid's extremely weak gravitational field, purely ballistic descent trajectories become a suitable option to reach its surface. However, this is still a very risky operation due to the limited knowledge of the object's physical characteristics. Hence, deploying a small lander is often a more conservative option than endangering the mothercraft itself, and thus a simple CubeSat may provide a low cost solution for asteroid exploration. However, for a CubeSat system to be able to safely land on the surface of an asteroid, a sufficient dissipation of energy must naturally occur at touchdown, or else the resultant bouncing may lead to high uncertainties on the final landing location, or even yield an escape trajectory. This paper describes the result of ESA Academy's Drop Your Thesis! 2018 (DYT2018) programme. DYT2018 carried out a microgravity experiment, led by Land3U team from the Astronautics and Space Engineering Course at Cranfield University, to provide additional data on the engineering constraints relevant to land a CubeSat on the surface of an asteroid. The experiment was performed in ZARM's Drop Tower, located in Bremen, during two Drop campaigns in November 2018 and February 2019. A total of 7 drops were completed, each providing 4.74 s of microgravity under vacuum environment. The experiment measured the coefficient of restitution of a 1U mock-up, equipped with a 4-kg mass, touching down on the simulated asteroid surface with an average velocity of 150 mm/s. Three successful drops measured a coefficient of restitution of 0.26 ± 0.03Show 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 A framework for optical features selection and management for camera-only autonomous navigation in the proximity to small celestial objects(2021-08) Di Fraia, Marco Z; Chemak, L; Sanchez Cuartielles, Joan PauShow more Small celestial bodies such as asteroids and comets are abundantly present in the Solar System, yet their surfaces remain largely unexplored. Achieving regular access to these surfaces would have a major impact on capabilities such as planetary defence and in situ resource utilisation and lead to significant scientific insights. However, missions close to small celestial objects remain challenging in at least two aspects: technically, due to weak gravity fields, complex operational environments and latency from long communication times, and commercially, with the applications still being few and cost-ineffective. A potential solution to reducing development and operational costs and obtaining robust, scalable operations, could be using small, camera-only spacecraft with an elevated degree of autonomy. Enabling a camera-based autonomy requires building appropriate computer vision pipelines. All computer vision pipelines start with the detection of features - salient patterns within the scene. This thesis presents multiple methods and tools enabling the appropriate selection and management of different features for autonomous navigation in proximity to asteroids. To that end, relevant contributions developed during this work consist of: The development of a software toolbox for prototyping and testing optical navigation technologies through a parametrisable synthetic 3D visual environment; An analysis of the response of feature detectors to internal factors (e.g., feature model) and external factors (e.g., illumination). This response, once known, can be used for designing the system or to obtain situational awareness An assessment of the response of template matching methods when the template (model) does not perfectly match the observed target (asteroid, with illumination). Through the above contributions, it was shown that considering environmental cues and the perception model helps in achieving robust camera-only navigation processes. This capability could lead to small satellites autonomously exploring hundreds or thousands of small celestial objects or be employed on more powerful spacecraft for redundancy.Show more Item Open Access Gauss’ variational equations for low-thrust optimal control problems in low-energy regimes(International Astronautical Federation, 2018-10-05) Neves, Rita; Sanchez Cuartielles, Joan PauShow more With the pursuit of increasingly innovative and complex space missions, the focus of the space industry has been turning towards electric propulsion systems. Due to their high specific impulse - about ten times that of a chemical engine - they provide large savings in propellant mass, decreasing the overall cost of the mission. This proves to be essential for small low cost missions, such as interplanetary CubeSats, and more ambitious endeavours such as asteroid retrieval or crewed missions to Mars. Designing a low-thrust trajectory is a more complex task than doing so for a high-thrust one, since computing the thrust sequence that minimizes the fuel spent requires a search over a huge and complex design space. Setting up the optimal control problem generally requires a good first-guess solution, a fine tuning of the parameters involved, and the definition of feasible bounds for the trajectory. In order to converge to a solution, the problem settings are simplified as much as possible. This includes the dynamical framework used, which often may not be sensitive enough to describe the low-energy trajectory regime necessary for some of the mission examples mentioned above. This abstract proposes a new set of equations of motion to solve the optimal control problem. These are derived from the disturbing function of the previously studied Keplerian Map, formulated from the Hamiltonian of the CR3BP. Its motion corresponds to the propagation of Gauss’s planetary equations with both the disturbing potential of the CR3BP, and the accelerations of the electric engine. The novelty of this formulation is that it describes a third-body motion in terms of the orbital elements that define the osculating orbit of the spacecraft, in a barycentric coordinate system. This is advantageous in several respects: first, low-thrust sub-optimal control laws can be easily generated and explored to find a first guess solution near global optima. Second, bounds for the optimal control problem, as well as the boundary values, can be easily defined, which allows for a much faster convergence. This dynamical framework is accurate until very close to the sphere of influence of the perturbing body, and thus can be efficiently used to target low-energy hyperbolic invariant manifold structures associated with periodic orbits near it. The paper presents the methodology as well as a full retrieval trajectory for asteroid 2018 AV2, a small co-orbital asteroid that could be retrieved during its next Earth encounter in 2037.Show more Item Open Access Multi-fidelity modelling of low-energy trajectories for space mission design.(2019-03) Neves, Rita; Sanchez Cuartielles, Joan Pau; Hobbs, Stephen E.Show more The proposal of increasingly complex and innovative space endeavours poses growing demands for mission designers. In order to meet the established requirements and constraints while maintaining a low fuel cost, the use of low-energy trajectories is particularly interesting. These paths in space allow spacecraft to change orbits and move with little to no fuel, but they are computed using motion models of a higher fidelity than the commonly used two-body problem. For this purpose, perturbation methods that explore the third-body effect are especially attractive, since they can accurately convey the system dynamics of a three-body configuration with a lower computational cost, by employing mapping techniques or exploring analytical approximations. The focus of this work is to broaden the knowledge of low-energy trajectories by developing new mathematical tools to assist in mission design applications. In particular, novel models of motion based on the third-body effect are conceived and classified by the forces they account for (conservative or non-conservative). The necessary numerical tools to complement the trajectory design are developed: this includes differential correction methods and targeting schemes, which take advantage of the Jacobian matrices derived from the presented models to generate full low-thrust control laws. One application of this analysis focuses on the trajectory design for missions to near- Earth asteroids. Two different projects are explored: one is based on the preliminary design of separate rendezvous and capture missions to the invariant manifolds of libration point L₂. This is achieved by studying two specific, recently discovered bodies and determining dates, fuel cost and final control history for each trajectory. The other covers a larger study on asteroid capture missions, where several asteroids are regarded as potential targets. The candidates are considered using a multi-fidelity design framework. Its purpose is to filter through the trajectory options using models of motion of increasing accuracy, so that a final refined, low-thrust solution is obtained. The trajectory design hinges on harnessing Earth’s gravity by exploiting encounters outside its sphere of influence, the named Earth-resonant encounters. An additional application explored in this investigation is the search and computation of periodic orbits for different planetary systems, following the current interest for missions involving distant retrograde and prograde orbits. In summary, this thesis presents four novel methods to model the third-body perturbation, distinct in their suitability for applications from real-time computations to long-term orbital predictions. These, together with the additionally developed tools for trajectory design, are applied in two asteroid mission cases. The developed Earth-resonant encounters allow for a very large increase in retrievable mass with respect to the state-of-the-art, namely for the cases of six near-Earth asteroids presented.Show 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 Towards drop your thesis 2018: 4.7 seconds of microgravity conditions to enable future CubeSat landings on asteroids(International Astronautical Federation, 2018-10-05) Sanchez Cuartielles, Joan Pau; Sitepu, Elioenai; Le Blay, Carole; Kersey, George; Ogborne, Stuart; Durrani, Daniyal Ahmad; Zanotti Fragonara, Luca; Gautier, Florian; Kingston, JenniferShow more An increasing number of interplanetary missions are aiming at visiting asteroids and other small bodies, since these may provide clues to understand the formation and evolution of our Solar System. CubeSats allow a low-cost solution to land on these objects, as opposed to risking a much more expensive mothership. The weak gravitational field on these small bodies may also enable the possibility of simply dropping a CubeSat from afar (i.e. ballistic landing). However, ballistic landing of an unpowered spacecraft may be feasible solely within certain asteroid locations, and only if sufficient energy can be dissipated at touchdown. If such conditions are not met, the spacecraft will rebound off the surface. It is likely that the necessary energy dissipation may already occur naturally due to energy loss expected through the deformation of the regolith during touchdown. Indeed, previous low-velocity impact experiments in microgravity seem to indicate that this is exactly the case. However, data from past asteroid touchdowns, Hayabusa and Philae, indicate the contrary. This paper describes the development of an experiment which aims to bridge the aforementioned disagreement between mission data and microgravity experiment; to understand the behaviour of CubeSat landing on asteroids. The experiment will also test a novel damping system made by origami paper that should increase the dissipated energy at touchdown. The experiment will take place at the ZARM Drop Tower in Bremen in November 2018. With the constraint of 5 drops, the experiment will measure the coefficient of restitution during an available time window of 4.74 seconds of microgravity conditions. A 1UCubeSat mock-up will be used to represent a future asteroid lander. In order to mimic the landing of actual missions, the mock-up will have a mass of about 4 kg and it will be given a velocity of 15 cm/s with minimal rotation. This will be achieved by an automated spring-based release mechanism. An asteroid simulant, ESA03-A KM Bentonite Granules will be used to replicate an asteroid mechanical properties at the surface. This paper reviews the final design and the engineering challenges of the experiment.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