توضیحات

Horwood Publishing
Chichester

DR N.A. SEINEYDOR
Neryahu A. Shneydor was born in Jerusalcm, then Palestine, now Israel, in 1932.
His secondary education was interrupted by the 1948 Independence War and the
siege of Jerusalem. He was then 16 years old and became a junior member of the
Haganah (the semi-legal military organisation) and joined the minuscule Signal
Group of the city. He manned a signal station which used Morse-key operated
lamps and, in daytime, heliographs, most of the equipment being of World War I
vintage. This may have aroused his interest in electrical engineering. He studied
Electrical Engineering in 1950-54 at the Technion – Israel Institute of Technology,
Haifa, Israel, where he obtained his BSc. and Dipl. Ingknieur degrees. The latter
was a relic from the time when Technion was under German influence: most of the
founding professors being immigrants from Germany, some escapees from Nazism.
There followed four years of military service, mostly with the navy where he
specialised in servo and in gunnery- and totpedo-fire control. Interest in these
topics led to studi’es in control theory and the Master’s degree. Dr Shneydor joined
RAFAEL, Israel Armament Development Authority, in 1960. A few years before, it
was a secret ‘military unit called HEMED, Hebrew acronym for Science Corps.
Among the early achievements of HEMED-RAFAEL were a radio-guided boat
which became operational in 1955, and a sea-to-sea guided missile which evolved
to the well-known Gabriel. Dr Shneydor joined the servo group of RAFAEL, which
specialised in mechanisms for controlling antennas, gimbals, actuators and other
devices. He later participated in the development of Shafrir and Python air-to-air
missiles. For his contribution to the development of the former’s guidance system,
he was awarded the Security Prize, Israel’s highest token of appreciation

۲۷۶صفحه فونت ۱۴

پس از پرداخت آنلاین میتوانید فایل کامل این پروژه را دانلود کنید

In 1972-75 RAFAEL enabled him to study for a Doctoral degree, again at the Haifa
Technion, under the supervision of the late Professor George Zames. The thesis
was in nonlinear feedback control theory. In 1970 he had started to lecture on
guidance and navigation at the Technion Department of Aeronautical Engineering
(now the Faculty of Aerospace Engineering) and later on nonlinear control at the
Department of Electrical Engineering, as Adjunct Assistant Professor, being
promoted to Adjunct Associate Professorship in 1979.
Since 1975 Dr Shneydor was occupied with research and development projects at
RAFAEL. In 1982-87 and 1992-94 he was R&D Deputy Director of the Missile
Division. During his professional activity he published many reports, papers and
texts on guidance. Retired from RAFAEL, he continues lecturing on guidance and
control and is a consulting engineer in these areas.
First published in 1998 by
HORWOOD PUBLISHING LJMITED
International Publishers
Coll House, Westergate, Chichester, West Sussex, PO20 6QL
England
COPYRIGHT NOTICE
All Rights Reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording, or otherwise, without the permission of
Homood Publishng, International Publishers, Coll House, Westergate, Chchester,
West Sussex, England
O N.A. Shneydor, 1998
British Library Cataloguing in Publication Data
A catalogue record of this book is available from the British Library
ISBN 1-898563-43-8
Printed in Great Britain by Martins Printing Group, Bodmin, Comwall
Preface
Navigation has been with the human race from time immemorial. It is not surprising,
therefore, that a very great number of books have been published on this
ancient art. Guidance, on the other hand, has been first implemented, by building
a remotely-guided unmanned boat for military purposes, in the beginning of this
century. The technical literature on it is immense – articles, conference papers,
reviews, bibliographies. However, surprisingly few books have been published that
deal with guidance. If we do not count texts that are mainly descriptive, most
of which appeared in the first decennary after World War 11, we have less than
half a dozen books in English. During my professional career as a research-anddevelopment
(R&D) engineer I also taught at a technical university and lectured
for various industry and military audiences. I naturally used the existing texts,
but gradually developed an approach which is different from theirs. Encouraged by
colleagues and students, I eventually turned my lecture notes and transparencies
into this book.
I believe this text differs from other ones in the field in several respects. Here
are some of its key features. * Although it necessarilly emphasizes military applications of guidance, i.e.,
guided weapons, it also pays attention to guidance in nature: some real, some anecdotic,
some invented by recreational mathematicians. * This book does not purport to be a history. However, it does try to give credit
to pioneering scientists and to early developments and inventions.
* In the theory of guidance one often has to solve differential and other equations.
Wherever practical I present an analytic solution rather than resort to numerical
ones: very often, the analytic solution enables one to discover interesting properties
which would otherwise be obscured by lines of code and numerical data. Furthermore,
most of the engineers and scientists among the readers, especially the younger
ones, could easily make their own computer code wherever they wish to deepen their
quantitative understanding of a problem studied.
* Geometrical rules and guidance laws are stated in three-dimensional vector
terms as well as the usual planar ones, and several examples have to do with threevi
PREFACE
dimensional guidance situations.
* Many graphical illustrations are given of trajectories, launch zones and intercept
zones, as well as of time histories of maneuver acceleration and other important
variables. This should be of practical value for many readers.
This text is intended for people — students, engineers, analysts, physicists, prcgrammers
-involved or interested in any of the various aspects of guidance systems:
use, development, design, manufacture, marketing, analysis, operational research.
Mathematics at a first-year university level is the only prerequisite. However, for
comprehending some portions of the text, acquaintance with feedback control theory
would be helpful.
Acknowledgements
I would like to thank the director of the Ecole des Mines de Paris, France, Dr.
Jacques B. Levy, who made it possible for me to spend a sabbatical at the institute,
when most of the work on this text was done, and Prof. Jean LGvine of the Centre
Automatique et Sfitkmes of the Ecole des Mines for his invaluable aid during various
stages of the work. I also wish to thank Prof. Aviv Etosen, Dean of the Faculty
of Aerospace ~h~ineeriTne~ch,n ion – Israel Institute of Technology, where I spent
the last semester of the sabbatical. I was very fortunate to have the manuscript
reviewed by several colleagues. The comments and suggestions made by Oded Golan
and Ilan Rusnak of RAFAEL are gratefully acknowledged. I am especially indebted
to Uri Reychav, also of RAFAEL, who devoted many long hours of his time during
his sabbatical in the United States to going over the manuscript while it was being
written in France. Particular thanks are extended to Rachel Weissbrod and Sarah
Segev of RAFAEL library at Leshem and to Dr. Guy Shaviv of the Technion for
their patient aid. Finally, I express my gratitude and love for my wife Na’ama,
without whose support and encouragement this undertaking would not be pmsible.
N. A. Shneydor
Haifa, Israel
February 4, 1998
Contents
Preface v
Introduction xiii
۱ Terminology and Definitions 1
۱٫۱ The Three Levels of the Guidance Process . . . . . . . . . . . . . . . 1
۱٫۱٫۱ Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
۱٫۱٫۲ An Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
۱٫۱٫۳ Scope of this Book . . . . . . . . . . . . . . . . . . . . . . . . 3
۱٫۲ Terminology Related to Implementation ……………. 3
۱٫۲٫۱ Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
۱٫۲٫۲ Examples ……………………….. 4
۱٫۳ Geometry and Kinematics . . . . . . . . . . . . . . . . . . . . . . . . 6
۱٫۳٫۱ Basic Definitions and Notations …………….. 6
۱٫۳٫۲ Kinematics of Planar Motion ……………… 7
۱٫۴ References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
۲ Line-of-Sight Guidance 11
۲٫۱ Background and Definitions ………………….. 11
۲٫۲ A Little History ………………………… 12
۲٫۳ Kinematics ………………………….. 14
۲٫۳٫۱ Analysis of the Planar Case ………………. 14
۲٫۳٫۲ Examples for the Planar Case ……………… 16
۲٫۳٫۳ R.emarks Concerning Practical Applications ………. 23
۲٫۳٫۴ Kinematics in 3-D Vector Terms ……………. 25
۲٫۳٫۵ Kinematics of Modified LOS Guidance …………. 29
۲٫۴ Guidance Laws ………………………… 31
۲٫۴٫۱ Time-Domain Approach . . . . . . . . . . . . . . . . . . . . . 33
۲٫۴٫۲ Classical-Control Approach ………………. 36
۲٫۴٫۳ Optimal-Control Approach ………………. 38
…
VIII CONTENTS
۲٫۵ Mechanization of LOS Guidance . . . . . . . . . . . . . . . . . . . . 39
۲٫۵٫۱ CLOSvs. Beam-RidingGuidance …………… 39
۲٫۵٫۲ On Tracking and Seekers ……………….. 41
۲٫۵٫۳ Mechanization in Practice . . . . . . . . . . . . . . . . . . . . 43
۲٫۶ References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
۳ Pure Pursuit 47
۳٫۱ Background and Definitions . . . . . . . . . . . . . . . . . . . . . . . 47
۳٫۲ Some of the Long History …………………… 48
۳٫۳ Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
۳٫۳٫۱ The Planar Case, Nonmaneuvering T …………. 49
۳٫۳٫۲ The Planar Case, Maneuvering T ……………. 57
۳٫۳٫۳ Other Interesting Planar Pursuits …………… 58
۳٫۳٫۴ Deviated Pure Pursuit …………………. 59
۳٫۳٫۵ Examples ……………………….. 67
۳٫۴ Guidance Laws for Pure Pursuit ……………….. 69
۳٫۴٫۱ Velocity Pursuit vs. Attitude Pursuit …………. 70
۳٫۴٫۲ A Simple Velocity-Pursuit Guidance Law . . . . . . . . . . . 71
۳٫۴٫۳ ‘A Simple Attitude-Pursuit Guidance Law . . . . . . . . . . . 73
۳٫۵ On the Mechanization of Pursuit Guidance . . . . . . . . . . . . . . 74
۳٫۶ References …………………………… 74
۴ Parallel Navigation 77
۴٫۱ Background and Definitions ………………….. 77
۴٫۲ Kinematics of Planar Engagements ………………. 78
۴٫۲٫۱ Nonmaneuvering Target . . . . . . . . . . . . . . . . . . . . . 78
۴٫۲٫۲ Maneuvering Target . . . . . . . . . . . . . . . . . . . . . . . 82
۴٫۲٫۳ Variable Speed . . . . . . . . . . . . . . . . . . . . . . . . . . 86
۴٫۳ Nonplanar Engagements . . . . . . . . . . . . . . . . . . . . . . . . . 87
۴٫۳٫۱ Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
۴٫۳٫۲ Three properties ……………………. 87
۴٫۳٫۳ Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
۴٫۴ Guidance Laws for Parallel Navigation . . . . . . . . . . . . . . . . . 92
۴٫۴٫۱ Proportional Navigation . . . . . . . . . . . . . . . . . . . . . 92
۴٫۴٫۲ A Non-Feedback Law …………………. 93
۴٫۵ Rules Related to Parallel Navigation . . . . . . . . . . . . . . . . . . 95
۴٫۵٫۱ Constant Aspect Navigation . . . . . . . . . . . . . . . . . . . 95
۴٫۵٫۲ Constant Projected Line . . . . . . . . . . . . . . . . . . . . . 96
۴٫۶ References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
CONTENTS ix
۵ Proportional Navigation 101
۵٫۱ Background and Definitions . . . . . . . . . . . . . . . . . . . . . . . 101
۵٫۲ A Little History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
۵٫۳ Kinematics of A Few Special Cases ………………. 104
۵٫۳٫۱ Two Special Values of N ……………….. 104
۵٫۳٫۲ Stationary Target, Any N ……………….. 104
۵٫۳٫۳ N = 2, Nonstationary, Nonmaneuvering Target …….. 105
۵٫۴ Kinematics of PN, Approximative Approach ………….. 106
۵٫۴٫۱ True PN (TPN) ……………………. 107
۵٫۴٫۲ Use of Range-Rate in TPN …….. : ………. 109
۵٫۴٫۳ Pure PN (PPN) ……………………. 109
۵٫۴٫۴ Some Results ……………………… 112
۵٫۵ Kinematics of PN, Exact Approach ………………. 113
۵٫۵٫۱ TPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
۵٫۵٫۲ PPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
۵٫۵٫۳ TPN vs. PPN ……………………… 117
۵٫۶ PPN and TPN in 3-D Vector Terms ……………… 118
۵٫۶٫۱ Definitions and Some Properties ……………. 118
۵٫۶٫۲ An Example ……………………… 119
۵٫۷ Other Laws that Implement Parallel Navigation ………… 121
۵٫۷٫۱ Ideal PN ……………………….. 122
۵٫۷٫۲ Prediction Guidance Law ……………….. 123
۵٫۷٫۳ Schoen’s Laws …………………….. 123
۵٫۸ References …………………………… 124
۶ Mechanization of Proportional Navigation 129
۶٫۱ Background ………………………….. 129
۶٫۲ On the Structure of PN Systems ……………….. 129
۶٫۳ The Effects of Dynamics ……………………. 131
۶٫۳٫۱ Single-Lag Dynamics ………………….. 132
۶٫۳٫۲ Two-Lag Dynamics …………………… 134
۶٫۳٫۳ Higher-Order Dynamics ………………… 135
۶٫۳٫۴ The Stability Problem …………………. 135
۶٫۳٫۵ Conclusions ………………………. 140
۶٫۴ Effects of Nonlinearities in the Guidance Loop ………… 140
۶٫۴٫۱ Variable Missile Speed …………………. 141
۶٫۴٫۲ Saturation of Lateral Acceleration …………… 144
۶٫۴٫۳ Saturations at the Seeker ……………….. 145
۶٫۴٫۴ Radome Refraction Error ……………….. 149
۶٫۴٫۵ Imperfect Stabilization of the Seeker ………….. 155
۶٫۵ Noise ……………………………… 156
۶٫۵٫۱ Angular Noise …………………….. 156
x CONTENTS
۶٫۵٫۲ Glint Noise ………………………. 158
۶٫۵٫۳ Target Maneuver ……………………. 158
۶٫۵٫۴ Conclusions ………………………. 159
۶٫۵٫۵ Remark …………………………. 160
۶٫۶ References …………………………… 160
۷ Guidance Laws Related to Prop . Navigation 165
۷٫۱ Background ………………………….. 165
۷٫۲ PN Modified by Bias ……………………… 166
۷٫۲٫۱ Augmented PN (APN) …………………. 166
۷٫۲٫۲ The Guidance-to-Collision Law …………….. 168
۷٫۳ Guidance Laws for Low LOS Rates ………………. 170
۷٫۳٫۱ Biased PN (BPN) …………………… 170
۷٫۳٫۲ Dead-Space PN …………………….. 171
۷٫۴ Proportional Lead Guidance (PLG) ……………… 172
۷٫۵ Guided Weapons with Strapdown Seekers …………… 172
۷٫۵٫۱ An Integral Form of PN ………………… 173
۷٫۵٫۲ Dpamic Lead Guidance (DLG) ……………. 174
۷٫۶ Mixed Guidance Laws …………………….. 175
۷٫۶٫۱ ,Mixed Guidance: PP and Parallel Navigation (or PN) …. 175
۷٫۶٫۲ Mixed Guidance: LOS Guidance and Other Laws ……. 176
۷٫۶٫۳ Combining Midcourse Guidance and PN ………… 177
۷٫۷ References …………………………… 178
۸ Modern Guidance Laws 181
۸٫۱ Background ………………………….. 181
۸٫۲ Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
۸٫۳ Principles of OCG, and Basic Examples ……………. 183
۸٫۳٫۱ Guidance and Optimal Control …………….. 183
۸٫۳٫۲ OCG Laws for a Maneuvering Target …………. 185
۸٫۳٫۳ Laws for Systems with 1st Order Dynamics ………. 187
۸٫۳٫۴ Laws for Systems with 2nd Order Dynamics ………. 189
۸٫۳٫۵ Laws for Systems with High-Order Dynamics ……… 191
۸٫۳٫۶ A Short Summary . . . . . . . . . . . . . . . . . . . . . . . . 192
۸٫۴ A More General Approach to OCG ………………. 194
۸٫۴٫۱ Definitions, and Statement of the Problem ……….. 194
۸٫۴٫۲ The LQ Problem . . . . . . . . . . . . . . . . . . . . . . . . . 195
۸٫۴٫۳ On the Solution to the LQ Problem . . . . . . . . . . . . . . 196
۸٫۴٫۴ Two Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 197
۸٫۵ Laws Based on LQG Theory . . . . . . . . . . . . . . . . . . . . . . 200
۸٫۵٫۱ Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
۸٫۵٫۲ The LQG Problem . . . . . . . . . . . . . . . . . . . . . . . . 201
CONTENTS xi
۸٫۶ On the Mechanization of OCG Laws . . . . . . . . . . . . . . . . . . 202
۸٫۶٫۱ Control Acceleration . . . . . . . . . . . . . . . . . . . . . . . 203
۸٫۶٫۲ Control Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 204
۸٫۶٫۳ Radome Refraction Error . . . . . . . . . . . . . . . . . . . . 205
۸٫۶٫۴ Estimating the Time-to-Go . . . . . . . . . . . . . . . . . . . 205
۸٫۶٫۵ Estimating the System State . . . . . . . . . . . . . . . . . . 206
۸٫۷ Comparison with Other Guidance Laws . . . . . . . . . . . . . . . . 208
۸٫۷٫۱ OCG and Proportional Navigation . . . . . . . . . . . . . . . 208
۸٫۷٫۲ OCG and Other Modern Laws . . . . . . . . . . . . . . . . . 209
۸٫۸ References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 11
A Equations of Motion 217
A. l General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 17
A.2 A Rotating FOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
A.3 Coplanar Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
A.4 Examples . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . . . . 221
B Angular Transformations 225
C A Few Concepts from Aerodynamics 229
C. l Skid-to-turn (STT) Configuration . . . . . . . . . . . . . . . . . . . . 229
C.2 Bank-to-turn (BTT) Configuration . . . . . . . . . . . . . . . . . . . 231
C.3 On Angle of Attack and Sideslip . . . . . . . . . . . . . . . . . . . . 231
C.4 Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
D Derivations of Several Equations 235
D.1 The Graphs of the Kh Plane. Sec . 2.3.2 ……………. 235
D.2 Derivation of (2.21) ………………………. 237
D.3 Proofs for (3.8) and (3.9) . . . . . . . . . . . . . . . . . . . . . . . . 237
D.4 On the tf-Isochrones of Sec . 3.3.l(c) ……………… 238
D.5 Definition of DPP (Sec . 3.3.4) in Vector Terms ………… 239
D.6 A Proof for (4.11) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
D.7 A Proof for Inequality (4.13) …………………. 240
D.8 Derivation of (4.15) of Sec . 4.2.2(a) ………………. 241
D.9 Derivation Of (4.34) and (4.35) ………………… 242
D.10 Vector Rcpresentation for Sec . 5.4.1 ……………… 243
D. l l On Equivalent Noise Bandwidth . . . . . . . . . . . . . . . . . . . . 244
D.12 APN Law in Vector Terms . . . . . . . . . . . . . . . . . . . . . . . . 244
D.13 Derivation of (8.14) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
D.14Referenccs ………………………. 245
List of Symbols and Abbreviations
Index
Introduction
According to the dictionary, ‘guidance’ is “the process for guiding the path of an
object towards a given point, which in general may be moving.” If the given point,
which we will call the taryet, is fixed, e.g., a sea port, or its path in the future is
known with sufficient accuracy, e.g., planet Mars, then the process is usually called
navigation. If the target moves in a way that is not quite predictable – for example,
a prey escaping its predator, an aircraft evading ground-to-air missiles – then the
process is guidance in its narrower sense, which is the sense we will give it in this
text.
The guided object may be a vehicle (a car, a boat, a missile, a spacecraft), a
robot or, in fact, a living being. The process of guidance is based on the position
and the velocity of the target relative to the guided object. The participants in
the guidance process are also referred to in the literature as the evader and the
pursuer, respectively. In nature, the ways predators catch their prey and some
insects rendezvous their mates are certainly guidance processes. In human history,
it is said that seamen, especially those who excercised the ignoble art of sea piracy,
practised the rule we now call ‘parallel navigation’ (the ‘navigation’ part of the term
being of course a misnomer) or ‘collision course’. Mariners in general have known
the inverse rule, which they apply in order to avoid collision at sea.
Modern, i.e., analytic, approach to guidance problems dates from the eighteenth
century, when several mathematicians studied what we now call ‘pure pursuit’ or
‘hound and hare pursuit’. This pursuit follows a very straightforward geometrical
rule: run (or fly, or sail, as the case may be) where you see your target. Both this
simple rule and the aforementioned parallel-navigation are tu~o-pointg uidnnce rules,
called so because only the pursuer and the target are involved in their respective
definitions.
A family of geometrical rules for three-point guidance exists as well; the name
derives from the fact that a third, reference point is required for the statement of
the rule. In the most basic three-point geometrical rule, the pursuer is required to
be on the line between the reference point and the target. For obvious reasons, this
type of guidance is called ‘line-of-sight guidance’.
xiv INTRODUCTION
Most of the applications for the theory of guidance are in weaponry. History
for this kind of application begins in 1870, when Werner von Siemens submitted a
proposal for “the destruction of enemy vessels by guided torpedos” to the Prussian
ministry of war. Although not specifically said so by Siemens, the guidance of his
proposed torpedo would have been of the line-of-sight type. We shall describe this
proposal briefly later on; suffice it to mention now that by 1916 it had materialized
into the first operational guided-weapon system in history.
The pure-pursuit rule was first applied to weapon systems in the early 19401s,
during the second world war, when most of the basic relevant theory had in fact
been known for two centuries and technical means for detecting targets and for
conrolling guided vehicles had been developed. Towards the end of the war, a more
sophisticated type of twepoint guidance, called ‘proportional navigation’ for historical
reasons, was studied. The basic theory of proportional navigation (PN) was
first formulated in the United States in 1943. Some steps towards implementing
a variant of PN in missile systems were taken in 1944 or 1945 by German scientists,
who presumably did not know that the theory had already been developed
elsewhere. The vast majority of two-point guided weapon systems existing today
utilize PN in one of- its numerous variants. There are nonmilitary applications of
PN, too; for example, in space travel, extraterrestrial landing, and robotics.
PN has its limitations, though. In particular one should mention sensitivity to
noise and to maneuvers carried out by the evader when the pursuer is approaching
it. (To ‘maneuver’ means here to make abrupt changes in the direction of motion,
i.e., execute high-acceleration turns; in pilots’ parlance, to ‘jink’, and in mariners’
one, to ‘zigzag’.) A family of so-called ‘modern guidance laws’ has been developing
since the early 1960’s that do not suffer from these limitations or suffer much less.
These laws are based on several recently developed techniques, in particular optimalcontrol
theory and optimal-estimation theory, hence the often used terms ‘optimalcontrol
guidance’ or just ‘optimal guidance’.
This family of laws can be regarded as the most recent stage of the evolution
process that started with Siemens’s proposal. It seems that in spite of the maturity
of the theory and the availability of the necessary technology, mostly microelectronics
and computer science, practical application is still somewhat rare, probably
due to economical reasons. Needless to say, however, the secrecy that prevails over
armament development issues makes up-to-date, reliable information inacessible,
and therefore statements on recent developments are uncertain.
This is about as far as we go in this book. The next evolutionary stage would
probably consist of laws based on differential-game theory. Although papers regarding
this approach to guidance have been appearing since the 19701s, it seems that
it is not ripe enough for inclusion in an introductory text like the present one.
The very fast progress of guided weaponry in the past fifty years would not
be possible without advances in many technologies. One should mention internalcombustion
engines, rocket motors, inertial instrumentation (especially gyroscopes),
aeronautics, electronics (especially microelectronics and radar), electro-optics, and
computer engineering. These and some other technological disciplines relevant to
guidance are beyond the scope of this text, except where they have direct implications
regarding its main topics. There are two reasons for this exclusuion. Firstly,
including even some of the relevant disciplines would have made the book much
weightier than what the author had in mind; secondly, an abundant literature is
available that deals with most of the said technologies.
This book regards guidance from the point of view of the pursuer, i.e., how to
arrive at the target, or intercept it. The inverse problem, that of avoidance, is not
dealt with. Guidance is treated from the viewpoints of kinematics, dynamics, and
control. In other words, we study trajectories, zones of interception, required maneuver
effort, launch envelopes, stability of the guidance process, and related topics.
Furthermore, technical problems involved with implementation and mechanization
are discussed when they may affect accuracy, energy expenditure, and structural
limits, hence, finally, costs.
The book is organized as follows. Following Chapter 1, which presents basic
definitions and terminology, Chapters 2-7 deal with what have come to be called
the classical guidance laws, namely
* Line-of-sight guidance (Chapter 2),
* Pure pursuit. (Chapter 3),
* Parallel navigation (Chapter 4),
* Proportional navigation (Chapters 5 and 6),
* Several guidance laws related to proportional navigation (Chapter 7).
Chapter 8 is dedicated to optimal-control guidance.
REFERENCES
Ross Jr., Frank, Guided Mzssiles: Rockets and Torpedos, New York, Lathrop, Lee
& Shepard, 1951.
Weyl, A. R., Engins te’le’guidi.s, Paris, Dunod, 1952; a translation of Guided Missiles,
London, Temple Press, 1949.
Gatland, Kenneth W., Development of the guided missile, 2nd ed., London, Iliffe,
۱۹۵۴٫
Benecke, Th. and A. W. Quick (eds.), History of German Guided Missile Development,
AGARD First Guided Missile Seminar, Munich, April 1956.
xvi INTRODUCTION
Ordway, Frederick and Ronald C. Wakeford, International Missile and Spacecraft
Guide, McGraw-Hill, 1960.
Clemow, J., Missile Guidance, London, Temple Press, 1962.
Smith, J. R. and A. L. Kay, Geman Aircmft of the Second World War, Putnam,
۱۹۷۲, pp. 645-712.
Spearman, M. Leroy, Historical Development of Worldwide Guided Missiles, NASA
Technical Memorandum 85658, June 1983.
Benecke, Theodor et al., Die Deutsche Luftfahrt-Flugkorper und Lenkraketen,
Koblenz, Bernard und Graefe, 1987.
Trenkle, Fritz, Die Deutschen Fvnklenkverfahren bis 1945, Heidelberg, Alfred Hiithig,
۱۹۸۷٫
Chapter 1
Terminology and Definitions
This chapter is dedicated to definitions of several concepts and terms used in the
study of guidance. Some of these definitions are not universal, there being differ-.
ences between British and American usage as well as between individual authors.
We shall use the terminology that seems most accepted, giving alternatives where
relevant.
۱٫۱ The Three Levels of the Guidance Process
>
‘Guidance’ is the process for guiding the path of an object towards a given point,
which in general may be moving. If the given point is fixed and the guided object
is ‘manned’ (or is, for example, a migrating bird), then the process is simply
navigation.’ Thus, although navigation can be said to be a subclass of guidance, in
this book we give the term ‘guidance’ a narrower meaning, which excludes navigation.
This specific meaning will now be explained.
۱٫۱٫۱ Definitions
Guidance is a hierarchical process which may be said to consist of three levels.
(a) In the highest one, a geometrical rule is stated in terms of a line-of-sight
that passes through the objective of the guidance. We shall henceforth refer to this
objective as the target T, and to the guided object as M. This definition serves to
distinguish between guidance in the meaning given to it in this book and marine
navigation, for example, or inertial guidance.
‘~ometimes a narrower definition is given for navigation, according to which it is merely the
art or science of finding the exact location of an observer

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