Automatic and fast generation of sub-optimal and feasible low-thrust trajectories using a boundary-value pseudo-spectral method

Automatic and fast generation of sub-optimal and feasible low-thrust trajectories using a boundary-value pseudo-spectral method

De Vogeleer, B.J.T.V.

Corral Van Damme, C. (mentor)
Prieto Llanos, T. (mentor)
Noomen, R. (mentor)

GMV

Aerospace Engineering

2008-08-28

Some problems in Astrodynamics, such as the ones posed in the several editions of the Global Trajectory Optimisation Competition, include both a combinatorial and a trajectory optimisation problem. The combinatorial problem consists of finding the sequence of a fixed number of asteroids that will allow to find the optimal trajectory. The trajectory optimisation problem is aimed at finding the optimal rendezvous trajectories connecting the asteroids of the selected sequence. To quickly assess the optimality of the possible sequences it would be interesting to have a fast algorithm that generates a good initial guess. If no limitations on the thrust or constraints on the departure and arrival velocity are considered, this 2-Point Boundary Value Problem is analytically solved by the Lambert Problem. This analytic solution has a ballistic arc in between impulsive manoeuvres and sometimes this trajectory is no good approximation for an optimal low-thrust trajectory. The method developed here, describes the shape of the 3-dimensional trajectory with expansions in power series. These expressions contain a number of unknown coefficients or Degrees of Freedom. Substitution of the Boundary Conditions leads to conditions that guarantee the satisfaction of the Boundary Conditions. The remaining Degrees of Freedom then act as optimisation variables. During the optimisation process the propellant mass is minimised for 8 selected test cases. It is shown that the method works very well for relatively short transfers. This new and fast algorithm provides a trajectory that is close to the optimum one, has a small error in final mass and allows to derive the structure of the optimal thrusting profile.

coltreps
trajectory optimisation
initial guess/estimate
shape based method

http://resolver.tudelft.nl/uuid:0f6174ae-244a-4df3-9680-9e9aa67fcf21

TU Delft, Aerospace Engineering, Astrodynamics and Satellite Systems

Student theses

master thesis

(c) 2008 De Vogeleer, B.J.T.V.