Generalised multi-impulsive manoeuvres for optimum spacecraft rendezvous in near-circular orbit

Abstract

This work describes the design of an impulsive manoeuvres' planner meant for onboard autonomous optimum formation flying reconfigurations in near-circular orbit. The whole variation of the relative orbit is stepwise achieved through intermediate configurations, so that passive safety and delta-v consumption minimisation are pursued. The description of the relative motion is accomplished in terms of relative orbital elements and the reconfiguration plan takes into account mean effects due to the Earth oblateness coefficient and differential drag. Manoeuvres consist of sets of triple tangential impulses and a single out-of-plane burn to establish each intermediate configuration. They are scheduled in time intervals compliant with the user-defined permissible time control windows.

Model of $$J_2$$ J 2 perturbed satellite relative motion with time-varying differential drag

“…In Leonard et al (1989), a Cartesian approach is used and the differential drag is modeled by a constant acceleration (i.e., A = B = 0) thus achieving a model not able to capture the possible linear in time variation of the relative eccentricity vector. In Gaias et al (2013) the constant differential drag is simply reproduced through a variation of the relative semi-major axis linearly in time. Subsequently, this effect determines a quadratic in time behavior of the relative mean longitude due to the relationship between δa and δu within the relative motion dynamics.…”

“…The relative state expressed by the ROE set is augmented by three constant additional parameters, characterized by a straightforward geometrical interpretation. The first additional parameter is the time derivative of the relative semi-major axis, as already suggested in Gaias et al (2013). The remaining two are the time derivatives respectively of the x and y components of the relative eccentricity vector, firstly introduced by this work.…”

Formation establishment and reconfiguration using differential elements in J2-perturbed orbits

“…They assume a circular or near-circular reference orbit [1][2][3][4]6,9,10,[13][14][15][16] 3. They assume a set of impulse times and do not solve for the optimal ones [15][16][17][18][19][20][21]. 4.…”

“…The discrete formulation is analytically solvable with the use of differential orbital elements as state variables. Similar discrete solvable formu lations have been used by Breger and How [17], Roth [19], Saunders [16], Anderson and Schaub [20], and Gaias et al [21], where the problem is broken up into many segments and the overall fuel cost is minimized, but these methods typically allow more impulses than necessary and do not find the true optimal times.…”

“…[21] include differen tial drag in the analytical model, which is a primary consid eration in low Earth orbit. However, it is extremely difficult to model this perturbation accurately for general spacecraft formations because of its dependence on the attitude and shape of both spacecraft and problems with modeling at mospheric density and surface interactions.…”