Global trajectory optimisation: can we prune the solution space when considering deep space manoeuvres?

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.

Search space pruning and global optimization of multiple gravity assist trajectories with deep space manoeuvres

This paper deals with the design of optimal multiple gravity assist trajectories with deep space manoeuvres. A pruning method which considers the sequential nature of the problem is presented. The method locates feasible vectors using local optimization and applies a clustering algorithm to find reduced bounding boxes which can be used in a subsequent optimization step. Since multiple local minima remain within the pruned search space, the use of a global optimization method, such as Differential Evolution, is suggested for finding solutions which are likely to be close to the global optimum. Two case studies are presented.

Search space pruning and global optimisation of Multiple Gravity Assist spacecraft trajectories

We introduce and describe the Multiple Gravity Assist problem, a global optimisation problem that is of great interest in the design of spacecraft and their trajectories. We discuss its formalization and we show, in one particular problem instance, the performance of selected state of the art heuristic global optimisation algorithms. A deterministic search space pruning algorithm is then developed and its polynomial time and space complexity derived. The algorithm is shown to achieve search space reductions of greater than six orders of magnitude, thus reducing significantly the complexity of the subsequent optimisation.

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.

The Solar Stormwatch CME catalogue: results from the first space weather citizen science project

Solar Stormwatch was the first space weather citizen science project, the aim of which was to identify and track coronal mass ejections (CMEs) observed by the Heliospheric Imagers aboard the STEREO satellites. The project has now been running for approximately 4 years, with input from >16000 citizen scientists, resulting in a dataset of >38000 time-elongation profiles of CME trajectories, observed over 18 pre-selected position angles. We present our method for reducing this data set into aCME catalogue. The resulting catalogue consists of 144 CMEs over the period January-2007 to February-2010, of which 110 were observed by STEREO-A and 77 were observed by STEREO-B. For each CME, the time-elongation profiles generated by the citizen scientists are averaged into a consensus profile along each position angle that the event was tracked. We consider this catalogue to be unique, being at present the only citizen science generated CME catalogue, tracking CMEs over an elongation range of 4 degrees out to a maximum of approximately 70 degrees. Using single spacecraft fitting techniques, we estimate the speed, direction, solar source region and latitudinal width of each CME. This shows that, at present, the Solar Stormwatch catalogue (which covers only solar minimum years) contains almost exclusively slow CMEs, with a mean speed of approximately 350 kms−1. The full catalogue is available for public access at www.met.reading.ac.uk/spate/stormwatch. This includes, for each event, the unprocessed time-elongation profiles generated by Solar Stormwatch, the consensus time-elongation profiles and a set of summary plots, as well as the estimated CME properties.