73 research outputs found

    Global Trajectory Optimisation : Can We Prune the Solution Space When Considering Deep Space Manoeuvres? [Final Report]

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    This document contains a report on the work done under the ESA/Ariadna study 06/4101 on the global optimization of space trajectories with multiple gravity assist (GA) and deep space manoeuvres (DSM). The study was performed by a joint team of scientists from the University of Reading and the University of Glasgow

    Incremental solution of LTMGA transfers transcribed with an advanced shaping approach

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    In the last decade the global optimisation of low-thrust multi-gravity assist transfers (LTMGA) has been tackled with different approaches. Some authors proposed to generate a first guess solution by building a multi-gravity assist transfer with impulsive manoeuvres and then using a direct or an indirect method to transcribe the multi-impulse arcs into low-thrust arcs. Other authors, notably Petropoulos et al. (2002), De Pascale et al. (2006), Wall et al. (2008) and SchĂĽtze et al. (2009), proposed the use of several forms of trajectory shaping to model low-thrust arcs. The disadvantage in all these studies is that the swingbys are powered and therefore suggest the use of high thrust propulsion along with the low thrust propulsion on board the spacecraft. The problem generally resides in the lack of flexibility of the low thrust trajectory models to satisfy a variety of boundary conditions. In this paper, a spherical shaping model is used whereby all encountered types of boundary constraints are satisfied analytically. Furthermore, a special incremental pruning of the search space is performed before employing a global optimiser. The process is conceptually equivalent to the approach proposed by Becerra et al. for the search space pruning of multi-gravity assist trajectories and exploits the decoupling of pairs of transfer arcs. Such decoupling removes the dependency of one arc from all those that are two or more before, and allows for pruning the search space in polynomial time. Numerical examples are presented for LTMGA transfers from Earth to asteroid Apollo and Earth to Jupiter

    Designing optimal low-thrust gravity-assist trajectories using space-pruning and a multi-objective approach

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    A multi-objective problem is addressed consisting of finding optimal low-thrust gravity-assist trajectories for interplanetary and orbital transfers. For this, recently developed pruning techniques for incremental search space reduction - which will be extended for the current situation - in combination with subdivision techniques for the approximation of the entire solution set, the so-called Pareto set, are used. Subdivision techniques are particularly promising for the numerical treatment of these multi-objective design problems since they are characterized (amongst others) by highly disconnected feasible domains, which can easily be handled by these set oriented methods. The complexity of the novel pruning techniques is analysed, and finally the usefulness of the novel approach is demonstrated by showing some numerical results for two realistic cases

    An incremental approach to the solution of global trajectory optimization problems

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    This paper presents an incremental approach to the solution of multiple gravity assist trajectories (MGA) with deep space maneuvers. The whole problem is decomposed in sub-problems that are solved incrementally. The solution of each sub-problem leads to a progressive reduction of the search space. Unlike other similar methods, the search for solutions of each sub-problem is performed through a stochastic approach. The resulting set of disconnected boxes is transformed into a connected collection of boxes through an affine transformation. For MGA problems, the incremental approach increases both the efficiency and reliability of the optimization process. Two relevant examples will illustrate the effectiveness of the proposed method

    Global optimisation of multiple gravity assist trajectories

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    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

    Methods and tools for preliminary low thrust mission analysis

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    The aim of the present thesis is to develop new methods that are useful for a space mission analyst to design low thrust trajectories in the preliminary phases of a mission study, where the focus is more on exploring various concepts than on obtaining one optimal transfer. The tools cover three main axes: generating low thrust trajectories from scratch, improving existing low thrust trajectories and exploring large search spaces related to multiple gravity assist transfers. Stress is put on the computational efficiency of the tools. Transfer arcs are generated with shaped based approaches, which have the advantage of having the ability to reproduce close to optimal transfers satisfying time of flight constraints and varied boundary constraints without the need for propagation. This thesis presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudo-equinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudo-equinoctial elements is analysed. A two-step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudo-equinoctial shaping. The solutions derived from the shaping approach are improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. Theoretical results are given on the validity of the method and a theorem is derived on the criteria of optimality of the results. The shaping approaches and the combination of shaping and linear-quadratic controller are tested on four case studies: a mission to Mars, a mission to asteroid 1989ML, to comet Tempel-1 and to Neptune. The design of low thrust multiple gravity assist trajectories is tackled by an incremental pruning approach. The incremental pruning of reduced search spaces is performed for decoupled pairs of transfer legs, after which regions of the total search space are identified where all acceptable pairs can be linked together. The gravity assists are not powered therefore the trajectory is purely low thrust and the transfer arcs are modelled by shaping functions and improved with the linear quadratic controller. Such an approach can reduce the computational burden of finding a global optimum. Numerical examples are presented for LTMGA transfers from Earth to asteroid Apollo and to Jupiter

    Asteroid belt multiple flyby options for M-Class Missions

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    Addressing many of the fundamental questions in modern planetary science, as well as in ESA’s cosmic vision, requires a comprehensive knowledge of our Solar System’s asteroid belt. This paper investigates potential opportunities for medium-class asteroid belt survey missions in the timeframe of 2029-2030. The study has been developed in support to CASTAway Asteroid Spectroscopic Survey mission proposal, which is to be submitted to the latest ESA’s medium size mission call. CASTAway envisages the launch of a small telescope with relatively straightforward (i.e. high TRL) remote sensing instrumentation to observe asteroids at a long-range (i.e. point source), but also at a short-range, resolving them at ~10 m resolution. This paper presents a challenging multi-objective optimization problem and discusses the feasibility of such a mission concept. A baseline trajectory is presented that meets both ESA’s medium size mission constraints and the science requirements. The trajectory loops through the asteroid belt during 7 years, visiting 10 objects of a wide range of characteristics, providing sufficient survey time to obtain compositional information for 10,000s of objects and the serendipitous discovery of also 10,000s of 10-m class asteroids. The methodology developed has enabled the exploration of the entire design space for a conservative Soyuz-launch performance, and has found a total of 200 different tour opportunities of the asteroid belt; all compliant with ESA’s 5th call for medium size missions

    Evolutionary neurocontrol: A novel method for low-thrust gravity-assist trajectory optimization

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    This article discusses evolutionary neurocontrol, a novel method for low-thrust gravity-assist trajectory optimization

    A hybrid multiagent approach for global trajectory optimization

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    In this paper we consider a global optimization method for space trajectory design problems. The method, which actually aims at finding not only the global minimizer but a whole set of low-lying local minimizers(corresponding to a set of different design options), is based on a domain decomposition technique where each subdomain is evaluated through a procedure based on the evolution of a population of agents. The method is applied to two space trajectory design problems and compared with existing deterministic and stochastic global optimization methods

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

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    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
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