Quadratic-based computation of four-impulse
rendezvous near circular orbit,
to appear in Journal of Guidance, Control, and Dynamics
Thomas E. Carter (Eastern Connecticut State University)
and Sergio A. Alvarez (Worcester Polytechnic Institute)
Abstract
Spacecraft rendezvous problems have recently gained new importance
with the proliferation of communications satellites and the ongoing
work on the international space station. As space traffic increases,
the economics of maneuvers required for activities such as maintenance
and repair will become increasingly significant. This provides
renewed impetus for theoretical work leading to efficient computation
of optimal rendezvous maneuvers. In the present paper we build upon
a classical paper of Prussing to develop a new computational procedure
for four-impulse rendezvous using linearized equations of motion near
a circular orbit. Our approach is based on an analysis of the primer
vector equations (adjoint dynamics). The problem of determining if
given terminal states allow a four-impulse rendezvous is reduced
to the solution of a simple system of nonlinear equations.