93-141
Optimal Power-Limited Rendezvous For Linearized Equations Of Motion
Thomas E. Carter*
Abstract
The structure of the solution of the fixed-time optimal power-limited rendezvous of a general linear system of ordinary differential equations with a bound on the magnitude of the applied thrust is presented. By allowing the bound to become arbitrarily large, we include the usual linear power-limited rendezvous problem. The accumulation of the inaccuracies caused by the linear approximation can be alleviated by repeatedly reinitializing the thrusting function. There are two distinct versions of the primer vector that appear in this problem These primer vectors are shown to be closely related to the concept of controllability of the linear system. The work is applied to the problem of rendezvous of a spacecraft with a satellite in general Keplerian orbit. It the orbit is circular, the unbounded-thrust problem can be solved in closed form, and the optimal thrusting function presented as a feedback law.
*Professor, Department of Mathematics and Computer Science. Eastern Connecticut State University, Willimantic, Connecticut 06226: and Visiting Professor, Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609-2280.