Approximate solutions in space mission design

In this paper, we address multi-objective space mission design problems. From a practical point of view, it is often the case that,during the preliminary phase of the design of a space mission, the solutions that are actually considered are not 'optimal' (in the Pareto sense)but belong to the basin of attraction of optimal ones (i.e. they are nearly optimal). This choice is motivated either by additional requirements that the decision maker has to take into account or, more often, by robustness considerations. For this, we suggest a novel MOEA which is a modification of the well-known NSGA-II algorithm equipped with a recently proposed archiving strategy which aims at storing the set of approximate solutions of a given MOP. Using this algorithm we will examine some space trajectory design problems and demonstrate the benefit of the novel approach

Computing the set of Epsilon-efficient solutions in multiobjective space mission design

In this work, we consider multiobjective space mission design problems. We will start from the need, from a practical point of view, to consider in addition to the (Pareto) optimal solutions also nearly optimal ones. In fact, extending the set of solutions for a given mission to those nearly optimal significantly increases the number of options for the decision maker and gives a measure of the size of the launch windows corresponding to each optimal solution, i.e., a measure of its robustness. Whereas the possible loss of such approximate solutions compared to optimal—and possibly even ‘better’—ones is dispensable. For this, we will examine several typical problems in space trajectory design—a biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfers—and demonstrate the possible benefit of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose

On the detection of nearly optimal solutions in the context of single-objective space mission design problems

When making decisions, having multiple options available for a possible realization of the same project can be advantageous. One way to increase the number of interesting choices is to consider, in addition to the optimal solution x*, also nearly optimal or approximate solutions; these alternative solutions differ from x* and can be in different regions – in the design space – but fulfil certain proximity to its function value f(x*). The scope of this article is the efficient computation and discretization of the set E of e–approximate solutions for scalar optimization problems. To accomplish this task, two strategies to archive and update the data of the search procedure will be suggested and investigated. To make emphasis on data storage efficiency, a way to manage significant and insignificant parameters is also presented. Further on, differential evolution will be used together with the new archivers for the computation of E. Finally, the behaviour of the archiver, as well as the efficiency of the resulting search procedure, will be demonstrated on some academic functions as well as on three models related to space mission design

On the benefit of ∈-efficient solutions in multi objective space mission design

In this work we consider multi-objective space mission design problems. We will show that it makes sense from the practical point of view to consider in addition to the (Pareto) optimal solutions also nearly optimal ones since this increases significantly the number of options for the decision maker, whereas the possible loss of such approximate solutions compared to optimal - and possibly even 'better' - ones is dispensable. For this, we will examine several typical problems in space trajectory design - a bi-impulsive transfer from the Earth to the asteroid Apophis and several low-thrust multi-gravity assist transfers - and demonstrate the possible benefit of the novel approach. Further, we will present an evolutionary multi-objective algorithm which is designed for this purpose

Approximate Trajectories for Thermal Protection System Flight Tests Mission Design

A mission profile for advanced thermal protection system suborbital flight testing is identified. Its main goal is to achieve a constant heat flux at a specific area of the vehicle for a limited amount of time. A tool capable of exploring broad regions of the design space for these missions is developed, aiming at reducing possible design options to an extent manageable by conventional, more accurate, numeric-simulation-based methods. Based on a simplified model of the point mass dynamics, trajectories optimal for thermal protection system testing and compliant with prefixed path constraints are identified. The approximate method is validated comparing the obtained optimal trajectories with numeric-optimized standard solutions on three test cases. Then, to demonstrate the method effectiveness and flexibility, the mission design space is investigated for reasonable ranges of relevant parameters. Results show that increasing the vehicle's ballistic coefficient allows reducing the specific mechanical energy at reentry, and that the maximum admissible dynamic pressure plays a principal role in affecting the attainable testing performances. An illustrative mission design for novel ceramic thermal protection system testing is presented that minimizes in the analyzed design space the specific mechanical energy at the trajectory apoge

Application of dynamical systems theory to a very low energy transfer

We use lobe dynamics in the restricted three-body problem to design orbits with prescribed itineraries with respect to the resonance regions within a Hill’s region. The application we envision is the design of a low energy trajectory to orbit three of Jupiter’s moons using the patched three-body approximation (P3BA). We introduce the “switching region,” the P3BA analogue to the “sphere of influence.” Numerical results are given for the problem of finding the fastest trajectory from an initial region of phase space (escape orbits from moon A) to a target region (orbits captured by moon B) using small controls

On the stability of approximate displaced lunar orbits

In a prior study, a methodology was developed for computing approximate large displaced orbits in the Earth-Moon circular restricted three-body problem (CRTBP) by the Moon-Sail two-body problem. It was found that far from the L(1) and L(2) points, the approximate two-body analysis for large accelerations matches well with the dynamics of displaced orbits in relation to the three-body problem. In the present study, the linear stability characteristics of the families of approximate periodic orbits are investigated

On the stability of displaced two-body lunar orbits

In a prior study, a methodology was developed for computing approximate large displaced orbits in the Earth-Moon circular restricted three-body problem (CRTBP)by the Moon-Sail two-body problem. It was found that far from the L1 and L2 points, the approximate two-body analysis for large accelerations matches well with the dynamics of displaced orbits in relation to the three-body problem. In the present study, the linear stability characteristics of the families of approximate periodic orbits are investigated

Multi-disciplinary shape optimization of an entry capsule integrated with custom neural network approximation and multi-delity approach

This paper describes a new integrated approach for the multi-disciplinary optimization of a entry capsule’s shape. Aerothermodynamics, Flight Mechanics and Thermal Protection System behaviour of a reference spaceship when crossing Martian atmosphere are considered, and several analytical, semi-empirical and numerical models are used. The multi-objective and multi-disciplinary optimization process implemented in Isight software environment allows finding a Pareto front of best shapes. The optimization process is integrated with a set of artificial neural networks, trained and updated by a multi-fidelity evolution control approach, to approximate the objective and constraint functions. Results obtained by means of the integrated approach with neural networks approximators are described and compared to the results obtained by a different optimization process, not using the approximators. The comparison highlights advantages and possible drawbacks of the proposed method, mainly in terms of calls to the true model and precision of the obtained Pareto front