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.
ASJC Scopus subject areas
- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics