Two-impulse transfer between coplanar elliptic orbits using along-track thrust

Abstract

The two-body two-impulse orbit transfer problem between two coplanar elliptic orbits using only along-track thrust is studied in this paper. Both impulse vectors are constrained to be on the along-track directions at the impulse points. First, the relationship between transfer angle and final true anomaly is derived. For a given final true anomaly, the range of the transfer angle is obtained for different cases. Then, the transfer angle is solved by the secant method in its feasible range. With the transfer angle and the transfer semilatus rectum, the velocity vectors of the transfer orbit at impulse points are obtained. Two impulse points and the corresponding impulse magnitudes for a 180 • transfer are also analyzed. Finally, the minimum-energy and minimum-transit-time solutions are obtained by optimizing the final true anomaly. Numerical tests demonstrate the effectiveness of the proposed method for two-impulse along-track orbit transfers. The results show that the minimum-energy transfer with two along-track impulses is close to the "true" minimum-energy transfer with two free-direction impulses.

Optimal control of rapid cooperative spacecraft rendezvous with multiple specific-direction thrusts

“…For the impulse orbital-transfer problem, Zhang et al. 8 studied the two-body two-impulse orbit-transfer problem between two coplanar elliptic orbits using only along-track thrust, finding that the minimum-energy solution with two along-track impulses approaches the “true” optimal transfer with two free-direction impulses. In addition, Iorfida et al.…”

“…The control of multiple thrusters as studied by Zhang et al. 8 is thus essentially the control of a single thruster. It greatly reduces the difficulty of calculation.…”

An evolutionary discretized Lambert approach for optimal long-range rendezvous considering impulse limit

“…Besides the impulse magnitude constraint, impulse direction is also sometimes considered as another kind of constraint in the literature. It can be the tangential impulse [16], along-track impulse [17] or continuous-thrust transfer with specific control magnitude and direction constraints [18]. Regarding the initial and final condition, the problems can be categorized as point to point, point to orbit and orbit to orbit maneuvers.…”