Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints

Low-thrust interplanetary space missions are highly complex and there can be many locally optimal solutions. While several techniques exist to search for globally optimal solutions to low-thrust trajectory design problems, they are typically limited to unconstrained trajectories. The operational design community in turn has largely avoided using such techniques and has primarily focused on accurate constrained local optimization combined with grid searches and intuitive design processes at the expense of efficient exploration of the global design space. This work is an attempt to bridge the gap between the global optimization and operational design communities by presenting a mathematical framework for global optimization of low-thrust trajectories subject to complex constraints including the targeting of planetary landing sites, a solar range constraint to simplify the thermal design of the spacecraft, and a real-world multi-thruster electric propulsion system that must switch thrusters on and off as available power changes over the course of a mission

Analytical control laws for interplanetary solar sail trajectories with constraints

An indirect method is used to obtain an analytical control law for a spacecraft with a low-thrust propulsion system which is constituted by a solar sail coupled with a solar electric thruster. Constraints on the control inputs for such as the system need to be taken into account for the design of a control law to avoid reducing control performance, even though the solar electric thruster is employed as an auxiliary system capable of increasing the thrust magnitude of the sailcraft. The aim of this paper is to derive an analytical control law for a system with input constraints. A barrier function is used to analytically obtain a control law without a computationally expensive iterative algorithm. Therefore, using the analytic method presented, a transfer orbit can be readily calculated with an onboard computer. Pontryagin's maximum principle is also used to obtain an optimal control law to compare with the proposed control law. The proposed control law is demonstrated as suitable for an example transfer problem between circular and coplanar orbits

Analysis of interplanetary solar sail trajectories with attitude dynamics

We present a new approach to the problem of optimal control of solar sails for low-thrust trajectory optimization. The objective was to find the required control torque magnitudes in order to steer a solar sail in interplanetary space. A new steering strategy, controlling the solar sail with generic torques applied about the spacecraft body axes, is integrated into the existing low-thrust trajectory optimization software InTrance. This software combines artificial neural networks and evolutionary algorithms to find steering strategies close to the global optimum without an initial guess. Furthermore, we implement a three rotational degree-of-freedom rigid-body attitude dynamics model to represent the solar sail in space. Two interplanetary transfers to Mars and Neptune are chosen to represent typical future solar sail mission scenarios. The results found with the new steering strategy are compared to the existing reference trajectories without attitude dynamics. The resulting control torques required to accomplish the missions are investigated, as they pose the primary requirements to a real on-board attitude control system

Multiple NEA Rendezvous Mission: Solar Sailing Options

The scientific interest in near-Earth asteroids (NEAs) and the classification of some of those as potentially hazardous asteroid for the Earth stipulated the interest in NEA exploration. Close-up observations of these objects will increase drastically our knowledge about the overall NEA population. For this reason, a multiple NEA rendezvous mission through solar sailing is investigated, taking advantage of the propellantless nature of this groundbreaking propulsion technology. Considering a spacecraft based on the DLR/ESA Gossamer technology, this work focuses on the search of possible sequences of NEA encounters. The effectiveness of this approach is demonstrated through a number of fully-optimized trajectories. The results show that it is possible to visit five NEAs within 10 years with near-term solar-sail technology. Moreover, a study on a reduced NEA database demonstrates the reliability of the approach used, showing that 58% of the sequences found with an approximated trajectory model can be converted into real solar-sail trajectories. Lastly, this second study shows the effectiveness of the proposed automatic optimization algorithm, which is able to find solutions for a large number of mission scenarios without any input required from the user

Extension of finite perturbative elements for multi-revolution, low-thrust propulsion transfer optimisation

This paper presents an extension of the analytical solution for perturbed Keplerian motion of a spacecraft under the effect of a low-thrust action (Zuiani et al., Acta Astronautica, 2011). The new formulation will include the possibility for treating two different thrusting modes, i.e. with a fixed thrust direction either in a rotating or in an inertial frame. Moreover the contribution of the J2 effect is also included in the analytical formulae. It will be shown that this approach allows for the fast computation of long, many revolution spirals while maintaining adequate accuracy, and it is able to include the combined actions of different perturbations. The proposed approach will also be applied to the case of a spacecraft with a low-thrust engine, which is injected into a Geostationary Transfer Orbit and will subsequently use its on-board propulsion to transfer to a final circular orbit around the Earth. The completion of the whole transfer might require several spirals and this makes the use of a full numerical propagation prohibitive on a sequential machine. In the proposed method, the thrusting pattern, duration and start of each thrusting arc, is defined through a parameterised function. The spiral is then propagated with the above-mentioned analytical approximation. A direct optimisation approach is then used to optimise these control parameters in order to minimise the propellant cost of the transfer, given a fixed transfer time and a set of boundary conditions

Direct transcription of low-thrust trajectories with finite trajectory elements

This paper presents a novel approach to the design of Low-Thrust trajectories, based on a first order approximated analytical solution of Gauss planetary equations. This analytical solution is shown to have a better accuracy than a second-order explicit numerical integrator and at a lower computational cost. Hence, it can be employed for the fast propagation of perturbed Keplerian motion when moderate accuracy is required. The analytical solution was integrated in a direct transcription method based on a decomposition of the trajectory into direct finite perturbative elements (DFPET). DFPET were applied to the solution of two-point boundary transfer problems. Furthermore the paper presents an example of the use of DFPET for the solution of a multiobjective trajectory optimisation problem in which both the total ∆V and transfer time are minimized with respect to departure and arrival dates. Two transfer problems were used as test cases: a direct transfer from Earth to Mars and a spiral from a low Earth orbit to the International Space Station

Incremental solution of LTMGA transfers transcribed with an advanced shaping approach

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 Schütze 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

A Global Optimisation Toolbox for Massively Parallel Engineering Optimisation

A software platform for global optimisation, called PaGMO, has been developed within the Advanced Concepts Team (ACT) at the European Space Agency, and was recently released as an open-source project. PaGMO is built to tackle high-dimensional global optimisation problems, and it has been successfully used to find solutions to real-life engineering problems among which the preliminary design of interplanetary spacecraft trajectories - both chemical (including multiple flybys and deep-space maneuvers) and low-thrust (limited, at the moment, to single phase trajectories), the inverse design of nano-structured radiators and the design of non-reactive controllers for planetary rovers. Featuring an arsenal of global and local optimisation algorithms (including genetic algorithms, differential evolution, simulated annealing, particle swarm optimisation, compass search, improved harmony search, and various interfaces to libraries for local optimisation such as SNOPT, IPOPT, GSL and NLopt), PaGMO is at its core a C++ library which employs an object-oriented architecture providing a clean and easily-extensible optimisation framework. Adoption of multi-threaded programming ensures the efficient exploitation of modern multi-core architectures and allows for a straightforward implementation of the island model paradigm, in which multiple populations of candidate solutions asynchronously exchange information in order to speed-up and improve the optimisation process. In addition to the C++ interface, PaGMO's capabilities are exposed to the high-level language Python, so that it is possible to easily use PaGMO in an interactive session and take advantage of the numerous scientific Python libraries available.Comment: To be presented at 'ICATT 2010: International Conference on Astrodynamics Tools and Techniques

OEXP Analysis Tools Workshop

This publication summarizes the software needs and available analysis tools presented at the OEXP Analysis Tools Workshop held at the NASA Langley Research Center, Hampton, Virginia on June 21 to 22, 1988. The objective of the workshop was to identify available spacecraft system (and subsystem) analysis and engineering design tools, and mission planning and analysis software that could be used for various NASA Office of Exploration (code Z) studies, specifically lunar and Mars missions

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution