Optimization and guidance of very low-thrust transfers to geostationary orbit

Paper number

IAC-06-C1.4.01

Author

Mr. Jesus Gil-Fernandez, GMV S.A., Spain

Coauthor

Mr. Lorenzo Tarabini, GMV S.A., Spain

Coauthor

Mrs. Mariella Graziano, GMV S.A., Spain

Coauthor

Mr. Miguel Angelo Molina, GMV S.A., Spain

Year

2006

Abstract

Within the industry it is currently of interest to find the minimum-time transfer of an electrically propelled spacecraft to a desired position in the geostationary (GEO) belt. A new hybrid direct/indirect optimization algorithm has been developed to compute the optimal transfer from the launch conditions to the final orbit. In order to perform a rendezvous with a desired GEO satellite, the problem of the phasing must also be addressed, i.e. the arrival at the final orbit must be at the geographic longitude of the client.

The thrust-to-gravity ratio of the considered electric propulsion scenario is so small that several hundreds of revolutions are required to perform the large change in orbital elements and achieve the final orbit. These very long propagations cause that some methods are not applicable due to ill-conditioning of the numerical problem. Therefore, a numerically stable technique is mandatory to solve the problem. In addition, the optimization algorithm must be robust in the sense of providing feasible solutions even before the final convergence to optimal solution and of having low sensitivity to the initial guess. Finally, the computational time is desired to be as fast as possible.

The minimum-time solution imposes continuous thrust along the transfer. Under the assumption of constant thrust level and specific impulse, the only control variables are the angles defining the thrust direction, pitch in the orbital plane and yaw in the out-of-plane direction.

To fulfill all the abovementioned requirements, GMV developed a blending optimization technique using a hybrid direct/indirect algorithm. The fast evolution problem is solved by means of optimal control formulation. The secular or mean trajectory is optimized with a direct method in which a set of nodes defines the trajectory whose coordinates are the optimization variables. The inclusion of certain path constraints in the secular trajectory such as fixed secular apogee altitude is straightforward. This hybrid optimization avoids the numerical instability, decreases the computational time, reduces the sensitivity to the initial guess and provides a feasible transfer at every optimization step.

One possible guidance algorithm is to maintain the nodes of the secular trajectory, save the last one for the phasing problem, and to compute the optimal control for the present revolution considering the real secular trajectory to be followed from the actual position to reach the next node. That is to control the secular trajectory around the optimal one. The deterministic perturbations (third bodies, non-spherical gravity potential and solar radiation pressure), not included in the optimization, are included in simulations to test the guidance algorithm. The simulations could be used to derive bounds on the stochastic perturbations from the navigation and actuators.

Application to transfers from Ariane5 geo-synchronous transfer orbit (GTO) to GEO is presented and two types of trajectories are analyzed, sub-synchronous, secular apogee constrained below GEO altitude, and super-synchronous, free apogee altitude. The flight time with free final longitude is 195.56 days in the super-synchronous transfer and 210.97 days in the super-synchronous one. Two different final GEO locations are presented (90ºE and 90ºW) to prove the phasing algorithm, which increase the flight time in less than half a day. Eventually, the compensation of the deterministic perturbations by the guidance strategy leads to an increase of the transfer time of less than half a day.

Abstract document

IAC-06-C1.4.01.pdf

Manuscript document

IAC-06-C1.4.01.pdf (🔒 authorized access only).

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