Optimal terminal-time determination for the ZEM/ZEV feedback guidance law with generalized performance index

Abstract

This paper investigates a problem of determining the optimal terminal-time or time-to-go of the ZEM/ZEV (Zero-Effort-Miss/Zero-Effort-Velocity) feedback guidance law for a variety of orbital intercept or rendezvous maneuvers. A generalized ZEM/ZEV guidance problem, whose objective is to minimize a combination of the control energy and terminal time, is examined. Algebraic equations whose solution provides the optimal terminal-time of the orbital intercept/rendezvous problems are derived based on the optimal control theory. The effectiveness of the proposed approach is demonstrated for various orbital maneuver problems.