A reduced model for efficient multiple gravity assist trajectory design

Paper number

IAC-09.C1.2.5

Author

Mr. Matteo Ceriotti, University of Glasgow, United Kingdom

Coauthor

Ms. Camilla Colombo, University of Glasgow, United Kingdom

Coauthor

Dr. Massimiliano Vasile, University of Glasgow, United Kingdom

Year

2009

Abstract

Past and present interplanetary missions have made use of multiple gravity assist manoeuvres (MGA) to limit the propellant consumption or to achieve goals otherwise unreachable with present launch capabilities. However, the preliminary design of MGA trajectories is a difficult task, especially when the sequence of bodies to be visited is free and unknown a priori.
Finding an optimal MGA transfer can be formulated as a mixed integer-continuous optimisation problem, where the integer part is the sequence of bodies to be visited, and for each sequence the trajectory is modelled using continuous variables. The number of combinations can grow exponentially with the number of visited bodies, in particular if resonant MGA or repeated visits are considered; this alone would make the problem NP-hard. Furthermore, finding a globally optimal trajectory, even for a single sequence of bodies, is itself a complex optimisation problem, due to the multimodality of the search domain.
Therefore, the exploration of the whole solution space, for a high fidelity trajectory model, would be excessively computational expensive. A low fidelity model would help in reducing the complexity of the search space and speeding up the search for optimal solutions.
This paper presents a technique for efficiently designing first guess solutions for multiple gravity assist trajectories with deep space manoeuvres. A reduced planar model is coupled to an incremental pruning approach that quickly explores the integer-continuous search space and identifies promising sequences of bodies and gravity assists.
The reduced model adopts analytical propagation of the trajectory and the phasing problem is tackled by introducing a tolerance on matching the true anomaly. Deep space and escape manoeuvres are assumed tangential and located at apsides of each orbit. A feasibility criterion based on the total $\Delta$v required to fly a particular trajectory is introduced and used to prune the search space. In particular, for each sequence, a trajectory is incrementally built adding leg by leg, and the feasibility of each added leg is verified by computing the associated $\Delta$v. The incremental pruning approach allows assessing all the possible sequences without the need to evaluate the full trajectory for each one of them. Unfeasible trajectories are in fact discarded while building the tree of possible sequences, thus cutting the computational time.
The assumptions made for the reduced model were verified to assure a good accuracy; in fact, the solutions identified by the pruning technique can be successfully used as fist guess transfers for local optimisation with a high fidelity model of the trajectory.
This approach was tested on a multi-rendezvous asteroid problem, inspired by the 3rd Global Trajectory Optimisation Competition, and the results will be presented.

Abstract document

IAC-09.C1.2.5.pdf

Manuscript document

(absent)