Abstract
Minimum-fuel, impulsive, time-fixed solutions are obtained for the problem
of orbital rendezvous and interception with interior path constraints. Transfers
between coplanar circular orbits in an inverse-square gravitational field
are considered, subject to a circular path constraint representing a minimum
or maximum permissible orbital radius. Primer vector theory is extended
to incorporate path constraints, and the optimal number of impulses along
with their times and positions are determined. The existence of constraint
boundary arcs is investigated as well as the optimality of a class of singular
arc solutions. A bifurcation phenomenon is discovered in a maximum-radius
solution as the transfer time is increased. To illustrate the complexities
introduced by path constraints, an analysis is made of optimal rendezvous
in field-free space subject to a minimum radius constraint.