Automated multigravity assist trajectory planning with a modified ant colony algorithm

The paper presents an approach to transcribe a multigravity assist trajectory design problem into an integrated planning and scheduling problem. A modified Ant Colony Optimization (ACO) algorithm is then used to generate optimal plans corresponding to optimal sequences of gravity assists and deep space manoeuvers to reach a given destination. The modified Ant Colony Algorithm is based on a hybridization between standard ACO paradigms and a tabu-based heuristic. The scheduling algorithm is integrated into the trajectory model to provide a fast time-allocation of the events along the trajectory. The approach demonstrated to be very effective on a number of real trajectory design problems

Multi-rendezvous Spacecraft Trajectory Optimization with Beam P-ACO

The design of spacecraft trajectories for missions visiting multiple celestial bodies is here framed as a multi-objective bilevel optimization problem. A comparative study is performed to assess the performance of different Beam Search algorithms at tackling the combinatorial problem of finding the ideal sequence of bodies. Special focus is placed on the development of a new hybridization between Beam Search and the Population-based Ant Colony Optimization algorithm. An experimental evaluation shows all algorithms achieving exceptional performance on a hard benchmark problem. It is found that a properly tuned deterministic Beam Search always outperforms the remaining variants. Beam P-ACO, however, demonstrates lower parameter sensitivity, while offering superior worst-case performance. Being an anytime algorithm, it is then found to be the preferable choice for certain practical applications.Comment: Code available at https://github.com/lfsimoes/beam_paco__gtoc

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

System Architecture Optimization Using Hidden Genes Genetic Algorithms with Applications in Space Trajectory Optimization

In this dissertation, the concept of hidden genes genetic algorithms is developed. In system architecture optimization problems, the topology of the solution is unknown and hence, the number of design variables is variable. Hidden genes genetic algorithms are genetic algorithm based methods that are developed to handle such problems by hiding some genes in the chromosomes. The genes in the hidden genes genetic algorithms evolve through selection, mutation, and crossover operations. To determine if a gene is hidden or not, binary tags are assigned to them. The value of the tags determine the status of the genes. Different mechanisms are proposed for the evolution of the tags. Some mechanisms utilize stochastic operations while others are based on deterministic operations. All the proposed mechanisms are tested on mathematical and space trajectory optimization problems. Moreover, Markov chain models of the mechanisms are derived and their convergence is investigated analytically. The results show that the proposed concept are capable to search for the optimal solution by autonomously enabling the algorithms to assign the hidden genes

Artificial neural networks for multiple NEA rendezvous missions with continuous thrust

The interest for near-Earth asteroids for scientific studies and, in particular, for potentially hazardous asteroids requires the space community to perform multiple-asteroid missions with close-up observations. To this end, multiple near-Earth asteroid rendezvous missions can help reduce the cost of the mission. Given the enormous number of asteroids, this work proposes a method based on artificial neural networks (ANNs) to quickly estimate the transfer time and cost between asteroids using low-thrust propulsion. The neural network output is used in a sequence search algorithm based on a tree-search method to identify feasible sequences of asteroids to rendezvous. The rendezvous sequences are optimized by solving an optimal control problem for each leg to verify the feasibility of the transfer. The effectiveness of the presented methodology is assessed through sequences of asteroids of interest optimized using two low-thrust propulsion systems, namely solar electric propulsion and solar sailing. The results show that ANNs are able to estimate the duration and cost of low-thrust transfers with high accuracy in a modest computational time

Interplanetary Trajectory Optimization with Automated Fly-By Sequences

Critical aspects of spacecraft missions, such as component organization, control algorithms, and trajectories, can be optimized using a variety of algorithms or solvers. Each solver has intrinsic strengths and weaknesses when applied to a given optimization problem. One way to mitigate limitations is to combine different solvers in an island model that allows these algorithms to share solutions. The program Spacecraft Trajectory Optimization Suite (STOpS) is an island model suite of heterogeneous and homogeneous Evolutionary Algorithms (EA) that analyze interplanetary trajectories for multiple gravity assist (MGA) missions. One limitation of STOpS and other spacecraft trajectory optimization programs (GMAT and Pygmo/Pagmo) is that they require a defined encounter body sequence to produce a constant length set of design variables. Early phase trajectory design would benefit from the ability to consider problems with an undefined encounter sequence as it would provide a set of diverse trajectories -- some of which might not have been considered during mission planning. The Hybrid Optimal Control Problem (HOCP) and the concept of hidden genes are explored with the most common EA, the Genetic Algorithm (GA), to compare how the methods perform with a Variable Size Design Space (VSDS). Test problems are altered so that the input to the cost function (the object being optimized) contains a set of continuous variables whose length depends on a corresponding set of discrete variables (e.g. the number of planet encounters determines the number of transfer time variables). Initial testing with a scalable problem (Branin\u27s function) indicates that even though the HOCP consistently converges on an optimal solution, the expensive run time (due to algorithm collaboration) would only escalate in an island model system. The hidden gene mechanism only changes how the GA decodes variables, thus it does not impact run time and operates effectively in the island model. A Hidden Gene Genetic Algorithm ( HGGA) is tested with a simplified Mariner 10 (EVM) problem to determine the best parameter settings to use in an island model with the GTOP Cassini 1 (EVVEJS) problem. For an island model with all GAs there is improved performance when the different base algorithm settings are used. Similar to previous work, the model benefits from migration of solutions and using multiple algorithms or islands. For spacecraft trajectory optimization programs that have an unconstrained fly-by sequence, the design variable limits have the largest impact on the results. When the number of potential fly-by sequences is too large it prevents the solver from converging on an optimal solution. This work demonstrates HGGA is effective in the STOpS environment as well as with GTOP problems. Thus the hidden gene mechanism can be extended to other EAs with members containing design variables that function similarly. It is shown that the tuning of the HGGA is dependent on the specific constraints of the spacecraft trajectory problem at hand, thus there is no need to further explore the general capabilities of the algorithm

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

Spacecraft Trajectory Optimization: A review of Models, Objectives, Approaches and Solutions

This article is a survey paper on solving spacecraft trajectory optimization problems. The solving process is decomposed into four key steps of mathematical modeling of the problem, defining the objective functions, development of an approach and obtaining the solution of the problem. Several subcategories for each step have been identified and described. Subsequently, important classifications and their characteristics have been discussed for solving the problems. Finally, a discussion on how to choose an element of each step for a given problem is provided.La Caixa, TIN2016-78365-

Global optimisation of multiple gravity assist trajectories

Multiple gravity assist (MGA) trajectories represent a particular class of space trajectories in which a spacecraft exploits the encounter with one or more celestial bodies to change its velocity vector; they have been essential to reach high Delta-v targets with low propellant consumption. The search for optimal transfer trajectories can be formulated as a mixed combinatorial-continuous global optimisation problem; however, it is known that the problem is difficult to solve, especially if deep space manoeuvres (DSM) are considered. This thesis addresses the automatic design of MGA trajectories through global search techniques, in answer to the requirements of having a large number of mission options in a short time, during the preliminary design phase. Two different approaches are presented. The first is a two-level approach: a number of feasible planetary sequences are initially generated; then, for each one, families of the MGA trajectories are built incrementally. The whole transfer is decomposed into sub-problems of smaller dimension and complexity, and the trajectory is progressively composed by solving one problem after the other. At each incremental step, a stochastic search identifies sets of feasible solutions: this region is preserved, while the rest of the search space is pruned out. The process iterates by adding one planet-to-planet leg at a time and pruning the unfeasible portion of the solution space. Therefore, when another leg is added to the trajectory, only the feasible set for the previous leg is considered and the search space is reduced. It is shown, through comparative tests, how the proposed incremental search performs an effective pruning of the search space, providing families of optimal solutions with a lower computational cost than a non-incremental approach. Known deterministic and stochastic methods are used for the comparison. The algorithm is applied to real MGA case studies, including the ESA missions BepiColombo and Laplace. The second approach performs an integrated search for the planetary sequence and the associated trajectories. The complete design of an MGA trajectory is formulated as an autonomous planning and scheduling problem. The resulting scheduled plan provides the planetary sequence for a MGA trajectory and a good estimation of the optimality of the associated trajectories. For each departure date, a full tree of possible transfers from departure to destination is generated. An algorithm inspired by Ant Colony Optimization (ACO) is devised to explore the space of possible plans. The ants explore the tree from departure to destination, adding one node at a time, using a probability function to select one of the feasible directions. Unlike standard ACO, a taboo-based heuristics prevents ants from re-exploring the same solutions. This approach is applied to the design of optimal transfers to Saturn (inspired by Cassini) and to Mercury, and it demonstrated to be very competitive against known traditional stochastic population-based techniques

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