OPTIMAL STEERING FOR REQUIRED-VELOCITY GUIDANCE

Dr. Howard M. Robbins

Peer Reviewed

Abstract: For many of the powered phases of a space mission, the trajectory conditions to be satisfied at cutoff can be specified by a "required velocity", which is a function of position and time. Then, satisfaction of the trajectory conditions can be ensured by directing the vehicle's thrust vector parallel to the velocity difference vector (velocity-to-be-gained vector). However, this simple steering law is, in general, nonoptimal. Therefore, it is of interest to seek approximately optimal steering laws for required-velocity guidance. This has been done by analysis based on the calculus of variations and on certain approximations valid for "short" burns. The analysis shows that the optimal steering policy gives an approximately constant turning rate of the thrust direction with respect to inertial space, and can be realized by directing the thrust acceleration parallel to a, modified velocity-difference vector Vd* which includes certain extra terms that ensure a nearly optimal turning rate of the thrust direction. The relation between steering laws, turning rates, and fuel-optimality is discussed at some length. In a wide class of cases, the approximately optimal steering laws turn out to be essentially equivalent to the powered-flight guidance law previously proposed by R. H. Battin
Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 12, Number 4
Pages: 355 - 363
Cite this article: Robbins, Dr. Howard M., "OPTIMAL STEERING FOR REQUIRED-VELOCITY GUIDANCE", NAVIGATION, Journal of The Institute of Navigation, Vol. 12, No. 4, Winter 1965-1966, pp. 355-363.
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