Control, Navigation, and Guidance**

Transcription

1 quality control theory conference has reached an enviable state of maturity which clearly is in demand as annual attendance approaches 600. Nevertheless, we do need additional technical -meetings to provide a forum for control engineers whose interest is more in applications and the practice of control engineering and technology. Small, specialized workshops held throughout the world on a variety of topics seem appropriate. Why not have CSS a sponsored workshop at a highly automated steel making plant with a theme of automation in the steel industry? How about an automation workshop at an automobile manufacturer who has a highly automated car assembly line in operation? The mind boggles at the number of such exciting small meetings which could be professionally rewarding for our members. Special publications could result and a whole new spectrum of technical activities could emerge. My proposal for reorganization would facilitate such activities. I should state here that as a future regular member of the CSS I eagerly await the expansion of the CSS technical activities. Of course there are many problems in our profession not directly related to the CSS. Our academic colleagues are facing very difficultimes. Salaries are low. Equipment is obsolete. Leadership is lacking. Graduate student enrollments are down and undergraduate enrollments up. are Industrial colleagues face problems of underutilization, needs for additional continuing education opportunities, portable pension problems (recently relieved in part by the LERA bill in the U.S.), confusion about the role of automation in industry, and others. There are plenty of challenges and opportunities for the CSS to serve and lead the profession. I anticipate that it will rise to the occasion and play a leading role in many of these areas. I close this commentary with a quote from John Kennedy: From those of us who have more, more is expected. Each of us has an opportunity to serve our profession, from which we derive professional and personal rewards. Let me once again encourage each of us to work within and without the Control Systems Society to create and apply the science and technology of control systems for the benefit of society. I hope to see many of you in San Diego. Stephen Kahne President Control, Navigation, and Guidance** Charles Stark Draper* The Charles Stark Draper Laboratory, Inc. Cambridge, Massachusetts Abstract Self-contained systems providing control and navigation for vehicles of all kinds use gyroscopic elements to maintain reference directions with respect to inertial space. Sensors for resultant gravity field and inertial reaction forces along input axes determine the vertical and also linear velocities with respect to inertial space. These components divided by an equivalent Earth radius transfer the motion to Earth coordinates in which integration gives location. Corrections for Earth s rotation projected in and perpendicular to the horizontal plane are made as computed cosine and sine projections of Earth s angular velocity. Current systems result with the order of fractional miles per hour performance. 1. Background Travel for persons and transportation for loads are activities that have been *Senior Scientist, The Charles Stark Draper Laboratory, Inc., 555 Technology Square, Cambridge, MA 02139, U.S.A. **Received July IO, Accepted by Associate Editor N. B. Nichols. 4 pursued by the human race since the beginnings the of long climb from primitive origins. Means with strength and power to move cargo have always been necessary but never, by themselves, adequate for delivering items to chosen locations. Useful overall results have required, as an additional factor, ability for the generation and use of sensed information to realize effective control and direction for the entities of strength. With one notable exception, components of strengthave lacked the general ability to sense, process, and apply information for carrying out successful missions. The exception is that of human beings whose bones and muscles may carry loads while their bodies include nervous systems, sensors, and brains that give them unique capabilities for acquiring and using information to provide control and direction. Figure 1 is an idealized functional diagram that suggests how various entities in the chain of nervous system activities may be associated with actions of muscles and bones as loads are carried. The senses, primarily the eyes, have visual contacts with near and far features of the Earth to provide indica /81/ $00.75%1981 IEEE tions of orientation and location of the body with respect to external references. This information interpreted by thought based on background knowledge and judgment, gives Actual Situations of the body. Comparison to Actual Situations with Desired Situations leads to position and motion Corrections transmitted by the nervous system to the muscles for changing positions and forces on the bones. Responses of the muscles to the Correction signals causes Actual Situations to change in ways leading to success for the mission associated with the desired situations. II. Control and Direction by Human Pilots As tlme went on, the desirability for carrying ever-greater loads led to the use of animals, carts, wagons, boats, ships, trains, automobiles, and within the last century, to aircraft and space vehicles. In general, these Effectors of increasing load capacities and more successful missions did not include within themselves means for sensing, processing and applying information to the purposes of Control and Direction. These basic functions always required complement- control systems magazine

2 @ r LOAD SUPPORT AND MOVEMENT IBONES AND MUKLESI CORRECTION FORCES I r----- PLANS, I I CORRECTION ACTION DEMANDS ACTUAL SITUATION lnfowator ie DESIRED CORRECTION ESTIMATING INTERPRETING RESULTS I I - - JUDGEMENT AND KNOWLEDGE DESIRED SITUATION I SENSE0. ISTABLE- I 4SITUATION NERVOUSSYSTMI SENSING MOTION ANDMUSCLES) INFORMATION IEYES,BODYS TOWARD _j OBJECTIVE) I VISUAL CONTACTS ~ *r A&E%:5)NI r GEOMETRICAL I ing entities that may be called Informators, to provide Corrections for actually existing Situations of Effectors to produce Desired Results. From the standpoint of functional diagrams, the essential change from Fig. 1 is that the Informator became a separate arrangement not associated with the Effector as an integral functional component. The diagram for any working combination with the Informator and the Effector as separate operational entities would be generally similar to functional diagrams associated with other systems of the same kind. For this reason, the particularly interesting example chosen to illustrate the ideal functional relationships involved uses Fig. 2 for the Wright Brothers Airplane with, of course, a human pilot having only his senses, brain, and body for controlling and directing flight of the vehicle. In Fig. 2, eyes, with perhapsome help from body force acceleration, having visual contacts to external surface features, sense orientations and locations of the airplane with respect to Earth References. Knowledge, judgment, and skill are applied to estimate meanings for this information in terms of Actual Airplane Situations. These are compared december 7981 with Desired Airplane Situations required during planned missions to determine Corrections needed to ensure successful results. These Corrections are interpreted in terms of actions by the pilot as he uses his hands, feet, and arms actuated by nerve impulses to apply proper inputs of force to the aircraft control members. This process continues during the progress of missions to keep the airplane continuously in stable flight and moving over the Earth effectively on paths required for reaching desired destinations. With unaided-by-instruments human pilots flying aircraft, troubles of two kinds appeared when effects such as terrain, fog, clouds, and darkness eliminated visual contacts with Earth. One very serious difficulty was that of maintaining safe control of flight when lost visibility cut off short-term Earth orientational references. Other problems came from the lack of good information on location, direction, and ground track because of poor visibility. At the beginning of the 1920s, the absence of continuous, moderate accuracy but very reliable, independent-of-visud-references information on orientation adequate for safety in aircraft was an especially important handicap to the progress of aviation. This importance came from the fact that out of control, too-large aircraft angles with respect to Earth accompanied by erratic angular velocities could result in tail spins or other forms of out-of-stable motion that tended to produce catastrophic results. Other troubles beyond control difficulties that were associated with poor visibility came from the loss of Earth References suitable for use in judging Corrections required following for courses that effectively led to Desired Destinations Self-contained Systems for Control During the last years of the 1920s, difficulties with aircraft control that depended on visual contacts Earth to points, appearing under conditions of poor or zero visibility came to be recognized as major stumbling blocks in the path of aviation development. Support for developing practical ways to eliminate visibility limitations to aircraft control was provided by the Guggenheim Foundation during the late 1920s. The necessary instruments were designed by the Sperry Gyroscope Company under 5

3 direction of Elmer Sperry, Jr. The actual flight testing and proofs for successful results were carried out by General Jimmy Doolittle, aided by Professor Bill Brown and Ben Kelsey of MIT. The basic requirement for means to eliminate dependence on visual contacts with Earth for aircraft control was selfcontained mechanization to provide continuous and reliable Earth orientational references for aircraft roll, pitch, and yaw. The situation was more complicated than that of balance wheel escapements for clocks, chronometers, and watches, but was generally analogous to the timekeeping problem in that it could be attacked by applying the principles of mass reaction to acceleration for realizing directions without rotation with respecto inertial space. This fact was understooduring the 1920s and provided the principles that were applied in practical instruments. Inertial reaction effects for maintaining orientational references may be realized by using rapidly-spinning-atconstant-angular-velocity well-balanced rotors supported for angular motion by effectively friction-free bearings. Arrangements of this kind may be made to hold angular directions of their spin axes 6 with relatively small drift changes as time goes on. The primarily important feature of Gyroscopic Elements (as symmetrical spinning rotors are usually called) is Angular Momentum, the vector aligned with the positive right-hand direction of the spin axis and equal in magnitude to the product of the Moment of Inertia of the rotor, multiplied by its angular velocity in radians per second. From the standpoint of activity, the behavior of a gyroscopic element is that its spin axis precesses (i.e., turns) toward the axis of an applied torque at an angular velocity with respect to inertial space that is directly proportional to the magnitude of applied torque and inversely proportional to the magnitude of the angular momentum. It was feasible to mechanize slowly changing reference directions by means of gyro rotors and supporting gimbals of reasonable size so that useful orientational references could be realized in practical instruments. Horizontal plane identications could be based on twodegree-of-freedom gimbal arrangements. The required orientation for the airplane could be generated by torque components from gravity acting on pendulous elements and applied to establish proper directions for a gyro spin axis with the instrument involved stationary or not moving too rapidly with respect to the Earth. Accelerations at right angles to the direction of gravity would cause pendulums to move away from the vertical and thus change orientations of gyro indications from the horizontal. However, in practice, horizontal acceleration components continued for only short times in the same direction and, with slow rates of gyro response, errors of indications for control could be kept so small that they would not be significant for purposes of low performance aircraft. The first systems that supplied orientational references for control without visual contacts to external points used instrument-type indications the for always-necessary human pilot. Bank and Climb angles with respect to the horizontal plane were given by the twodegree-of-freedom gyro of one instrument, while azimuth was indicated by another unit based on a second independent gyro. The indications were visual for the pilot who applied them in the same ways he used his eyes as he judged situations with respect to the Earth. Angular inaccuracies and drift control systems magazine

4 rates of the gyro units generally remained at levels that caused no difficulties for control. In summary, it can be said that inertial technology applied to aircraft control has been effective for the last forty years. Longer-term greater-distance and aspects of aircraft operations, which usually presented no major problems when carried out under conditions of unrestricted visibility to Earth references, and which became difficult or impossible without visibility, have been under strong attack for over half a century. The methods applied have often involved replacing visual contacts to external points by artificially generated radiation of various kinds and wavelengths with improved ability to penetrate paths between aircraft and external stations. External sources are required, covering the regions from ground-based stations to groups of satellites in earth orbits. Arrangements have varied from equipments requiring close attention from human operators primarily automatic systems that need only monitoring supervision. Fields of operation for artificial radiation contact equipments include short range, highly accurate arrangements for safe, low or zero visibility airport conditions and long distance, open oceanavigation, and guidance that is useful for air travel over regions that do not have systems of ground stations. Even a brief summary of the changes in arrangements for transportation from the single human being, through various modifications of composite human beingautomatic technology combinations would require more space than is available in this paper. It is hoped that essential concepts may be suggested by, in effect, putting together functional patterns of airplane-human pilot systems completely to automatic equipments, always with possible monitoring by human operators, some feeling may be gained for the kind of developments that are likely to appear in the future. IV. Aircraft Inertial Control with Artificial Radiation Navigation and Guidance Fig. 3 is an idealized functional diagram for aircraft as Effectors with matching Informators that include an Inertial Space Reference Control Subsystem and an Artificial Radiation Earth Reference Navigation and Guidance Subsystem. The diagrams do not explicitly show human operator links in either subsystem. It is understood that visual indicators adapted for use by human pilots and means for introducing control actions may be included in one or both of the Informator Subsystem chains. In Fig. 3, physical quantities that determine Effector Situations are received by sensors of the Control Subsystem which provide orientational references with respect to inertial space without the ned for radiation contacts to external points. From the standpoint of practice, orientation references for sensing control angle deviation must be related to the Earth, which rotates about its polar axis with respecto inertial space. This means that the indicated horizontal plane, which should be perpendicular to the direction of gravity and contains the reference roll and pitch axes, must be rotated about the direction of north so that it moves away from a fixed inertial space orientation and stays with the Earth. The required result is achieved by giving a gravitygenerated pendulum torque the level needed for keeping the indicating axes close enough to the correct Earth axes for indications without unacceptably great Control Reference inaccuracies. Attention of the same kind is required to keep the azimuth-sensing gyro element properly aligned with Earth direction as it rotates. Pendulous action is not useful for precessing the inertial reference for azimuth so the behavior of staying with the rotating Earth must be provided by a special action feature of the means for driving the rotor. This may be provided by a special magnetic compass arrangement. Fig. 3 is an idealized functional diagram that suggests an inner Inertial Reference Control Loop in combination with an outer Radiation Contact Reference Navigation and Guidance Loop. The inertial reference arrangement shown, based on automatic mechanization, may also provide the basis for control by human pilots to ensure that flight will be independent of visibility conditions. Radiation contact references for the outer loop means that navigation and guidance will be reliable without visible references. The Actual Control Situation Reference Sensor represented as a component of the control subsystem in the idealized functional diagram of Fig. 3 receives physical quantities produces and geometrical information on the existing orientations of the Effector with respect to Inertial References, which in turn are related to Earth by Gravity and Magnetic Field Monitors. This information is supplied to the Actual Situation Computer which processes it to generate information on the Actual Control Situation. This knowledge is one of the basic inputs for the Desired-Actual Situation Correction Computer which compares the Actual Control Situation with the independently available Desired Control Situation to generate Correction Information for the Effector Situation. This information combined with Navigation and Guidance Corrections, generates Inputs for the Control Drive to the Effector which applies the forces and torques needed to cause the Actual Situation to approach circumstances that result in the Effector s achieving the Desired Situation. For Fig. 3, the Navigation and Guidance Subsystem is assumed to use visibility-insensitive radiation links with external stations, fields of facilities, satellite systems, etc., to acquire References for Actual Situations of the Effector. This information is processed by computer to generate information on Actual Navigation and Guidance Situations which is applied as an essential input to the Correction Computer. This component also receives information on Desired Situations with which Actual Situations compared to generate Corrections for the Situation of the Effector. These components are integrated with Control Corrections and applied as Correction Commands to the Control Drive which changes the actual Navigation and Guidance Situation so that the Effector accomplishes Desired Results. V. Self-contained Systems On Earth, circumstances exist where adequate coverage by stations based on artificial radiation not affected by visibility conditions is not available, and for which malfunctioning of external equipment by accident or deliberate actions would surely interfere with operations. These considerations suggest the desirability of self-contained, rugged, reliable equipment with performance of high quality. The Control Loop arrangement of Fig. 3 has performance adequate for control of effector orientational purposes and is self-contained in the sense that it does not require any links to external references by radiation of any kind. Inertial principles mechanized by Gyroscopic Elements with symmetrical rotors spinning constant at speed provide orientational references and stabilization under gravity acting through pendulous elements. december

5 ~ ~~ ~ ~~~ ~~ ~~ ~ OVERALL SYSTEM INFORMATION INDICATOR I Fig. 3. Idealized overall functional diagram for Effector subsystem matched with Informator subsystem including an inertial control subsystem and a radiation contact navigation and guidance subsystem. Angular indications have uncertainties in the magnitude range of one degree. Angular Drift Rates are in the range of some 12 degrees per hour. That is, Drift is about One Earth s Rate (symbol em) of rotation, which is 15 degrees per hour. In terms of distance on the surface of the Earth, one eru is about 900 nautical miles per hour at the equator, so that one Milli- Earth s-rate-unit, which is one thousandth of Earth s Rate (symbol meru) corresponds to about one nautical mile per hour. If it is assumed that Inertial Systems for Navigation and Guidance should give indications of location on the Earth that have inaccuracies at about one tenth of a nautical mile per hour, the acceptable drift rate is about 0.1 meru. One minute or arc between vertical directions at two points on the equator corresponds to a change in location of one nautical mile, which is about 6000 feet. If interest is in resolution of distances between points some six feet apart on the Earth s surface, the resolution must be about minute of arc. This angular uncertainty corresponds to approximately 0.06 arc second. 8 If more modest performance levels are accepted, say resolutions of about 600 feet and drift rates of about 0.5 nautical mile per hour, the angularesolution required is 6 arc seconds and the Drift is approximately 0.5 meru. Using these numbers as goals and taking the sensor performance realized in aircraft control systems of about 1945 as starting levels, the existing technology has to be improved by a factor of 100 for resolution and about 2000 from the standpoint of drift. Some years of development, production, and operation of gyroscopic aircraft control systems starting in 1930 has been largely directed toward gyro rotors and gimbal pivots all based on ball bearings. Results achieved had reached situations that did not offer the orders of magnitude improvements needed consistently to achieve completely self-contained instruments for inertial control, navigation, and guidance systems with 500 foot resolution and 0.5 nautical mile per hour drift levels of performance. These circumstances were clearly understood when work on the first completely inertial control, navigation, and guidance system for aircraft wa started during It was decided that friction levels of mechanical parts such as gimbals would always be too great for direct control actions to be taken as torque components directly from gyroscopic rotors. For this reason, all sensor designs were directed toward generating output signals suitable for use as inputs to servo-motor drive systems positioning for mechanical members without imposing significant output torque requirements the on physical quantity receiving instruments. This meant that the sensor outputs could be used only to establish and maintain inertial references for orientation and location of servo-controlled mechanical parts. By including in the sensors means for accepting Command Signal Inputs, orientations and locations of these parts could be driven to change as required to follow computed or mechanism gener- ated changes. VI. Control, Navigation, and Guidance Systems Sensors of two kinds are requlred implement inertial control, navigation, to control systems magazine

6 and guidance systems. Instruments of the first kind are sensitive to angular deviations from reference orientations about input axes fixed to their cases. Sensors of this kind are called Angular Deviation Receivers (Symbol ADR). They are also designed to accept Command Signals as Inputs that cause the Instruments to change orientations of the Reference Directions about their Input Axes. Sensors of the second kind are sensitive to specific force as the components per output gives linear velocity change. In practice, velocity is a generally desired output so that sensors for specific force are often designed to have integration included as an internal function. Instruments of this kind are called Specific Force Integrating Receivers and represented in symbols by (SFIR). In practice, initial settings of reference orientations are made to match externally available information that provides Indicated North and Indicated East orientations of Computer which operates to generate the Actual Situation. Indications of Actual Situation are compared with Desired Control Situations and desired Navigation and Guidance Situations by the Correction Computer which generates correction information. This information is processed by the Effector Control Command Computer to produce Correction Commands for the Effector Drive Control Subsystem. The actions that follow the Correction Command Inputs OVERALL EFFECTOR SYSTEM EFFECTOR SUBSYSTEM INTERACTIONS wlm ENVIRONMENT r---f I r EFFECTOR CONTROL DRIVE SUBSYSTEM L- 1 SENSOR SUBSYSTEM L SYSTEM INFORMATION _ _ _- - J OVERALL SYSTEM INFORMATION INDICATOR Fig. 4. Overall Effector system with complete inertial Control, Navigation and Guidance. I unit mass of gravity force and inertial reaction force components along input axis directions fixed to their cases. The effective input is the resultant sum of gravity and acceleration with respect to inertial space which cannot be separated except by making sure that the Input Axis is at right angles to the direction of the undesired input. Under circumstances for which the input is pure inertial reaction force without any "contamination" by gravity, a single integration of instrument Instrument Input axes fixed parallel to the indicated Horizontal Plane which is perpendicular to the direction of gravity. The Inertial Sensor Subsystem of Fig. 4 contains components for sensing Orientational Situations of the Effector with respect to Inertial Orientational Situation References. Another component senses Actual Linear Locations of the Effector in terms of Inertial Location References. Information of Actual Orientational and Locational Situations is transferred to the close the operating loop by causing the Effector to move so that it produces Desired Results by completing trips over selected courses to chosen objectives. Positions on Earth for the purposes of navigation are determined by local directions of gravity with respect to a geometrical system associated with the Earth. The coordinates usually chosen are conventional Latitude and Longitude Indications as initial reference settings by Angular Deviation Receivers that rotate december

7 with respect to the references as they respond to computer commands based on information from Specific Force Integrating Receivers. The Angular Deviation Receivers also rotate with respect to inertial space under computer commands that depend on requirements for compensating out the motion associated with the horizontal and vertical components of Earth s rotation. These components are in at right angles to the horizontal plane and have magnitudes that are functions of latitude. Corrections for Earth s rotation combined with required rotations of the Indicated Horizontal Plane depend on magnitude of the horizontal linear indications that greatly exceed the performance requirements for Control System operations. This means that Control System Activity may be based on theory and mechanization that is already provided within Inertial Systems for Navigation, and Guidance, so that separate equipment for the purposes of aircraft control is not necessary. This function may be drawn from components and subsystems that are already present as information elements required to serve the general purposes of satisfactory Effector operation. In general, Fig. 4 shows three subsystems as essential parts of the In- the Desired-Actual Situation Correction Computer to generate Correction Information. This information is processed by the Effector Control Command Computer to produce Correction Commands for the Effector Control Drive Subsystem. Diagrams representing means for carrying out all functions required in an operating inertial system would involve generally conventional resolver subsystems and other arrangements that would essential be for the realization of satisfactory results. The necessary complexity is not used here because it could tend to interfere with explanations of basic principles. The representations of Fig. 5. Mechano-pictorial diagram for local level control, navigation. and guidance sensor subsystem with single-degree-of-freedom instruments. velocity components divided by the Effective Radius of the Earth. The rotation components resulting keep two of the SFIR Input Axes at right angles to the direction of gravity so thatheir inputs will contain only accelerationgenerated farce without contamination by effects from gravity. Conections to compensate for deviations of plumb bob gravity that act when indications are taken from stationary platform observations are also accounted for in the computations. It is important to note that the Actual Orientational Situation Sensors represented in Fig. 4 must have accuracies of 10 formator Subsystem. These three are: (1) Control, Navigation, and Guidance Sensor Subsystem, (2) Actual Situation Computer, and (3) Correction Computing Subsystem. The second subsystem receives Actual Situation Orientational Information and Actual Situation Locational Information and produces Actual Situation Information. This information is one input for the Desired-Actual Situation Computer which also receives arbitrary information from outside the overall system on the Desired Control System Situation and Desired the Navigation and Guidance Situation. This information on Desired Situations enters instruments in Fig. 5 are simplified to stress the behavior of sensors that have special characteristics required for satisfactory operation of the Inertial System Control Drive Subsystem by causing the Effector to change its Actual Situations - _ toward -- the Desired Situations...- VII. Sensor Subsystem Components to form Computer Subsystems and Correction Computing Subsystems may have performance capabilities that are similar to or identical with those available for almost universal service in many applications of technology. The situation is quite different control systems magazine

8 for the Angular Deviation Receivers, the signals are received and properly dis- Specific Force Integrating Receivers, tributed to the servomotors by resolvers and the servo-driven supporting Geometrical Gimbal arrangements with their required resolvers and signal generators. acting to generate proper components for maintaining the axis of the Inner Gimbal aligned to the direction of gravity and the Representation in terms of single-degree- orientation abouthis direction of the of-freedo mechanization for the six Gimbal itself matched to Earth refersensors involved is used as a way to ences. Signal generators are also placed simplify the diagram of Fig. 5 and clearly on each axis of the support system to direct attention toward the physical provide information on the orientation in principles and geometrical relationships yaw, pitch, and roll of the airplane. that are associated with control, navi- These signals supply indications that are gation, and guidance from self-contained systems working within regions near the effectively perfect of angular situations for the purposes of aircraft control. Earth for which gravity force is sig- Vlll. Sensor Subsystem for nificant. The procedure first is to Inertial Control, Navigation, establish accurate and maintained-forand Guidance significantly long time periods geometrical references with respect to inertial Sensors for inertial systems are despace by means of instruments and then signed to have performance with two to use sensed information for modifying characteristics: (1) accurate definition, output situations so that desired results and (2) effectively unchanging for sigare indicated in terms of Earth co- nificant periods of time. Indications of ordinates. The geometrical entity in- reference orientations are given by volved is a platform-like unit having its Angular Deviation Receivers (ADRs). primary axis of angular freedom per- Indications of reference locations are pendicular to the Indicated Horizontal made available by Specific Force In- Plane. A second axis is attached to the tegrating Receivers (SFIRs). In addition plane of the platform that rotates within bearings carried by an enclosing gimbal to providing signals that depend Deviations from set angular and locaupon (the middle gimbal) to provide angular tional references, ADRs and SFIRs each motion about a platform direction on a must have capabilities for accurately rotationally free axis at right angles to the primary axis. The Outer Gimbal pivoted changing the geometrical situations of their cases that physically represent these to the structure of the vehicle and rotating references in response to quantitatively with respect to the Middle Gimbal about a direction at right angles to this axis and defined Input Command Signals. This means that output signals from instrualso to the Inner Platform axis, gives the ments accurately describe situation Inertial System angular freedom over changes associated with physical parts of wide limits with respect to the base by the entities involved. Computer proceswhich it is supported from the vehicle. sing of such signals gives Information on This means that the axis directly fixed to the Inner Gimbal can remain effectively vertical as the vehicle involved rotates Actual Situations of the Effector that compared with Desired Situations leads to Control Commands for the Effector. through relatively large arbitrary angles The usefulness of an Inertial Sensor in azimuth and with respect to the Subsystem composed of instruments and horizontal plane. It is possible to entirely eliminate angle magnitude restrictions, other components with the basic features suggested in Fig. 5 depends upon sensors but description of the essential details with high resolutions and accurate rewould complicate the present discussion sponses to Command Input signals. If ofundamentals. For this reason, the resolution of about one foot is taken as a simple gimbal and axis arrangements reasonable goal for the overall system, suggested by Fig. 5 will be considered as Angular Deviations should be effectively adequately suggesting means for provid- indicated for the region of 0.01 arc ing isolation of the Inertial System second. A drift accompany to this Functional Entities from angular motions resolution might be in the region of 1 of the supporting vehicles. millimeru that is, IOp6 Earth s Rate Unit Information included in Fig. 5 notes which is about 0.06 arc second per hour. that each one of the axes in the ar- SFIF resolution might be taken as 0.1 rangement that carries the Inner Gimbal milligal, that Earth is gravity. is fitted with a servo-drive motor between With sensor performance levels of this the supported member and the supporting kind, good inertial navigation and member. Input signals for these servo- guidance results might be obtained by drives originate in the six sensors. These assuming that the inertial-instrument- december 1981 established references are unvaryingly useful for indication purposes and available during reasonably long periods of time. Applying such references to establish coordinate points and to compute navigation and guidance information during the progress of missions would make it possible to generate satisfactory results. The important matter to be noted is that system operation depends only on internally store datand information generated by self-contained mechanisms. It is also true that these situations must be established by settings to match chosen initial conditions. Simple circumstances may be associated with the system to be started in operation when it is supplied with power and located base on a mounted so that it is satisfactory with respect to the Earth. One of the working functions for the Inner Gimbal in Fig. 5 is to carry six sensors in orientations that have their Input Axes associated in definite ways with the direction of gravity. The Input Axis of one (ADR) with subscript (u-d), that is up-to-down and the Input Axis of one (SFIR) with the same (u-d) subscript are both parallel the Indicated to Vertical. The other two (ADR s), (ADR)(,-,) and (ADR)(,,., are mounted with their Input Axes at right angles to each other and both perpendicular to the Indicated Vertical. In the same pattern, (SFIR)(,,) is mounted with its Input directed Axis West-to-East, and (SFIR)(,,) has its Input Axis directed South-to-North. Both of the (ADRs) and both of the (SFIRs) with Input Axes perpendicular to the Indicated Vertical have their Input Axes located in the same plane at the level of the center line of the Middle Gimbal Axis. This plane is called the Indicatd Horizontal Plane. To make an initial setting with the system located on the base stationary with respect to the Earth, the Inner Gimbal and the support gimbals may be arranged so that the Indicated Vertical is roughly aligned with gravity and servodrive power turned on with (SFIRs) having their Input Axes in the Indicated Horizontal Plane connected to the associated gimbals. Under these circumstances, the overall servodrive action is to level the Indicated Horizontal Plane at right angles to gravity. Without (ADR) sensors in operation the system does not respond to angular velocity. Leveling operation depends upon having the (SRR) Input average no projections of gravity because then the input axes will right be at angles gravity to (the direction, a plum bob, would in- 11

9 dicate on a stationary base). With the inner platform horizontal under (SFIR) control alone, the sensor input axes in the plane may have any direction with respect to the projection of Earth Rotation Angular Velocity on the plane. If the Angular Deviation Sensors with their Input Axes in the plane are placed in operation, connected to receive angular deviations aboutheir Input Axes and driving servomotors, the (ADRs) without Command Inputs will cause the Inner Gimbal to have zero angular velocity with respect to inertial space about these axes. As the Earth rotates carrying the system, this Gimbal, which, except for its no-angular-velocity-with-respect-toinertial-space situation, moves with the Earth, will not hold Indicated Horizontal Plane orientation which it must finally maintain at right angles to the direction of gravity. A step in achieving this normal-togravity situation may be accomplished by connecting one of the (ADRs) in the direction-seeking mode to search out the direction of its Input Axis that is at right angles to the projection of Earth s angular velocity on the plane at right angles to the direction of gravity. For this purpose, the (ADR) is connected to drive the servo-motor that rotates the structure associated with the Indicated Horizontal Plane about the Indicated Vertical Axis. The direction about which the plane has zero angular velocity is taken as Indicated East. When this direction has been determined, the direction at right angles counterclockwise is Indicated North. With Indicated North identified, Indicated East at right angles to this direction and the Indicated Horizontal Plane at right angles to the direction of Indicated Gravity, the plane rotates about Earth s Angular Velocity horizontal component along Indicated North with an angular velocity magnitude equal tothe magnitude of Earth rotation multiplied by the cosine of the angle of latitude. In order for the Indicated Horizontal Plane to remain at right angles to the Indicated Vertical, the (ADR) with its Input Axis south to north must be given a Command Signal that calls for an angular velocity equal to (Earth s rotation magnitude) X (cosine latitude) about Indicated North that causes the (ADR) involved to drive its associated servomotor so that the platform moves with the Earth as far as projection of Earth s angular velocity rotation about the direction of Indicated North is concerned. In addition to the component of Earth rotation that causes the platform to rotate 12 about an axis in the Indicated Horizontal force commonly identified with the Plane, there is a second component about direction and magnitude of gravity the Indicated Vertical axis that corre- force on a pendulum suspended from a sponds to the sine of latitude component of Earth rotation. This component stationary platform. This combined action of the gravitational field and Earth must be computed and sent as a command rotation centrifugal force gives the input to the (ADR) with its Input Axis up direction of gravity indicated on a to down which provides control signals stationary platform. for power to the vertical axis servomotor. When an Inertial Guidance System This motor causes the Indicated Hori- with the direction of gravity initially zontal Plane platform to rotate about the set on a stationary platform begins to vertical with the magnitude of (Earth angular velocity) X (sine of latitude). move with respect to the Earth vehicle, centrifugal force as in a a separate With the Indicated Horizontal Plane component no longer acts directly. The properly leveled at right angles to the system is accelerated by forces driving Actual Direction of Gravity as indicated the vehicle by which the guidance system by specific force sensed on a stationary is carried. Centrifugal force due to Earth platform, with Indicated East and In- rotation is no longer a separate identidicated North Directions established and fiable input component. It becomes being maintained by (ADR) signals important that the Input Axes of Specific supplied to servodrives, with the In- Force Receivers involved remain at right dicated Horizontal Plane satisfactorily leveled about both Indicated East and angles to the make sure direction of gravitation to thathe active input com- Indicated North and with Earth Rotation ponents are associated, not at all with Components, horizontal and vertical, properly compensated by computations based on Earth rotation magnitude and trigonometric functions of latitude, an Inertial Guidance System may be con- sidered as functionally prepared for operation. It remains, of course, to place information on Initial Location and Programs for Desired Operations in the Memory and Situation Recording and Indicating Facilities Inertial an on Navigation System. One situation that must be given attention is that all matter reacts to acceleration with respect to inertial space and is subjected to force from gravitational fields that involve body mass in actions equivalent to and not distinguishable from each other as output force components due to different physical inputs. The physical facts stressed in the last paragraph are important for indications of gravity by pendulous massesuspended from pivots or strings on platforms stationary with respect to the Earth. Force from the gravitational field acting on a pendulous mass may certainly be a major effect in many situations. In addition, rotation of the Earth acting at a point on the surface which must be at some distance from the axis forces any mass to travel in a circle. This path causes the mass to be subjected to an outward-acting centrifugal force proportional to the radius from the axis and the square of the magnitude of Earth Rota- tion. The centrifugal force action combines with the gravitational field effect at the same point to produce the resultant gravitation, but entirely with linear acceleration. This result may be accomplished by rotating the (SFIR) Input Axes on the Indicated Horizontal Plane so that they become perpendicular to gravitation immediately when vehicle acceleration starts and thathisituation continues until movement with respect to the Earth is stopped. When the vehicle comes to rest with respect to the Earth s surface, a computed component to compensate for centrifugal force should immediately be combined with acceleration input only effects to give conventional Pendulum Indications. With provisions made to compensate for effects of Earth-rotation centrifugal force on stationary platform initial settings, it remains to make sure that the two (SFIRs) whose Input Axes should remain at right angles to the direction of the gravitational field, do actually have this orientation during operation of the overall system. When these two Input Axes are at right angles to the gravitational field, the only physical quantity effective as their inputs are linear accelerations along (SFIR) Input Axes in the Indicated Horizontal Plane. This means that the single integrations carried out by the instruments give Horizontal Linear Velocity Indications. Because of the direction-holding-with-respect-toinertial-space characteristics of the inner platform, effectively applied to mechanism, the (SFIR) Input Axes could have incorrect directions for inputs, and gravitational field inputs could begin to contaminate linear acceleration inputs. These difficulties may both be control systems magazine

10 ~ ~~~ ~ overcome by dividing the (SFIR) linear velocity indications by an effective radius of the Earth to compute the angular velocity components needed by the inner platform so that it remains perpendicular to the direction of the gravitational field, and the active (SFIR) Input Axes are always parallel to horizontal components of linear moving vehicle accelerations. The mechanism and computer functions that have been discussed above for the inner platform and all but two of the sensors that it carries, operate to give indications satisfactory for control and with onexception, with results for navigation and guidance in primarily horizontal directions. The exceptions are one (ADR) and one (SFIR) with their Input Axes parallel to each other and aligned with the Indicated Vertical Axis. The (ADR) is important for all Control, Navigation, and Guidance initial settings and operations. It is the sensor that holds the direction of Indicated North (and also Indicated East) while accepting conections for orientation of the platform about the Indicated Vertical associated with the sine component of Earth s rotation. The (SFIR) with its input axis vertical may be used with a chosen constant computer output sequence of pulses to balance out the Indication Level corresponding to 1000 gal for establishing a gravitation field reference of, say, Earth s, one gravity, G level. (By using the actual output of the (SFIR) in comparison with the constant reference signal to determine the diffence between the reference and the sensed output, inertial indications of altitude may be achieved.) IX. Functions of Sensors and Associated Entities Combined to Form a Local Level Inertial Control, Navigation, and Guidance System Control, navigation, and guidance systems for vehicles supply indications of orientation and linear positions, velocities, and accelerations with respecto generally useful geometrical references. When these references are provided by the operation of self-contained mechanisms without visual or other radiation links to external sources, by physical interactions with gravitational fields and G factor is used to indicate the acceleration due to the attraction of Earth. The gal (a unit named after Galileo) is equal to one G factor X IO- or 1 G = 1000 gals. The practically useful unit is the milligal = gal X 10-~ accelerations with respect to inertial space, the equipments involved are generally called Inertial Navigation Systems. This name is applied because the necessary geometrical references can be made to depend upon the behavior of force- and torque-free masses as they hold linear velocities accurately controlled with respect to inertial space and the reactions of balanced, spinning gyro rotors as they maintain orientational references with respect to inertial space. In addition to providing angular and linear geometrical references, sensors must react to applied Signals which Command accurate deviations from the inertial angular references and the inertial linear references. It is essential that the instruments be able to use Command Signals from computer operations on inputs of all kinds required for the processes of generating inertial system output indications. Sensors of two basic kinds are required for realizing Inertial Systems. Angular Deviation Receivers, Symbol (ADR), establish Orientational Reference Directions and generate output signals that indicate deviations the physical of reference directions associated with the instrument cases. The sensors also accept Orientational Deviation Command Signals and in cooperation with servomotor actions translate these signals into angular displacements about (ADR) Input Axes. Specific Force Integrating Receivers, Symbol (SFIR), establish Linear Geometrical References along the directions of their Input Axes and receive as direct physical inputs, linear accelerations with respect to inertial space. Indications of acceleration along the Input Axes are integrated once within the instrument mechanisms to generate signals that represent linear velocities with respect to the Linear Reference as outputs. A second integration within the associated computer represents changes in location. Fig. 5 is an idealized mechano-geometrical diagram that suggests the combination of three Angular Deviation Receivers (ADRs), three Specific Force Integrating Receivers (SFIRs), and other essential entities to form an illustrative LOC~~ Control, Inertial Navigation and Guidance System. ance System. 2The configuration chosen for representation uses Local Earth Coordinates, that is, Earth Latitude and Earth Longitude for locational geometrical references by inertial means to be applied in generating system outputs. Basically, Fig. 5 shows an Indicated Horizontal Plane, Symbol (IHP), member carried by an axis that in operation remains effectively aligned with the Indicated Vertical, direction along which the Gravitational Field acts on the system. The structure of the IHP has 360 degrees of rotational freedom about the Indicated Vertical with servomotor drive and signals resolvers acting about the associated axis. The Indicated Vertical is carried3 in bearings (only one of which is represented in the figure) which system operation drives toward alignment with the direction of gravity. The Indicated Vertical Axis is fitted with a servomotor, resolvers, signal generators, and slip rings for handling the circuits and signals required for system operation. The bearings that carry the Inner Gimbal with the Indicated Horizontal Plane are, in turn, on bearings in the Middle Gimbal which has its A jtis carried by the Outer Gimbal which in turn has its Axis with the base perpendicular to the Middle Gimbal Axis. Each of the Axes is fitted with a servomotor, resolvers, and signal generators. arrangement The supporting of gimbals shown in Fig. 5 allows the vehicle which carries the system considerable angular freedom without disturbing the Indicated Horizontal Plane Member. Signals from the Angular Deviation Sensors respond to Deviations from Reference Orientations by generating output signals, that, applied as inputs to the servomotors, cause the gimbal angles have to orientations needed to keeparts of the system aligned to commanded angles. These orientations change as the Deviation Commands to the sensors alter their patterns. In all cases, relative gimbal angles shift keep to the Indicated Horizontal Plane Member free from mechanical interference as the supporting vehicle changes its orientation. X. Geometrical Relationships Location on the Earth is generally associated with the direction of gravity as this physical quantity is indicated by a plumb bob carried by a support on a stationary platform. This direction is determined by the force of the gravitational field acting directly on the plumb 3All of the gimbal components of an inertial navigation system are actually complete forms with two carefully aligned bearings. In Fig. 5, each gimbal would, if complete, impair visibility as shown in the diagram. In practice the other bearing is generally present. december

11 ~~ ~~ ~~ bob combined with a component due to centrifugal force as the stationary mass moves in a circle about the Earth s axis of rotation because of its location on the surface. The resultant of gravitational field force and centrifugal force is always present (when latitude is less than 90 ) and is the resultant that determined the Geoid. When the situation considered is one in which a system is canied by an accelerating vehicle so that it does not receive any specifically identifiable acceleration component that may be associated with centrifugal force, it is not possible to separate out any special effect from the complex of sensor inputs. Acceleration is an input, that from its instrumental outputs, cannot be separated into components. -This means that, for vehicles motion in following not tracks over the Earth s surface, it is impossible to identify the effect of centrifugal force due to rotation of the Earth. The force due to gravity in direction and in magnitude is due entirely to interactions of mass with the gravitational field. This means that gravity force acting alone masses in moving vehicies identifies Locations at certain points with respect to the Earth s surface that are different from those indicated for the same points by pendulum actions on a stationary base. For this reason, locations indicated in flight by inertial systems will not agree with data mapped on Geoid Surfaces. Discrepancies from Geoidal data on locations indicated by inertial systems should not, in general, bevery great and can be computed with reasonable accuracy from available information. Corrections determined in this way may be computer-generated and applied to inertial navigation system results. Fig. 5 shows the Inner Gimbal which is effectively carried by the servodriven Middle Gimbal and Outer Gimbal to have three degrees of angular freedom under complex the of angular-deviationcontrolling signals from the Angular Deviation Receivers that have their Input Axes mutually at right angles to each other on the Indicated Horizontal Plane. This triad of Sensors is fixed to the Inner Gimbal Structure which supports the Instruments so that two of their Input Axes are in the Indicated Horizontal Plane at right angles to the third Input Axis which, in operation, is aligned with the direction of gravity to establish the Indicated Vertical about which the Inner Gimbal has complete rotational freedom. 14 In operation, one of the (ADR) Input Axes that lies in the Indicated Horizontal Plane is aligned with the projection of the Earth s Axis of Rotation on this plane to give the direction of Indicated North. The Input Axis of the second (ADR) is fixed to the Inner Gimbal at right angles to Indicated North so that it has the direction of Indicated East. A Specific Force Integrating Receiver is associated with each of the Angular Deviation Receivers. The match-up of the sensors with their Input Axes along the Indicated Vertical has already been discussed. The other two (SFIRs) have their Input Axes at right angles to the Input Angles of the (ADRs) with which they are associateduring operation. Thus the (SFIR) with its Input Axis directed south-to-north forms an operating pair with the (ADR) that has its Input Axis directed west-to-east. The remaining (SFIR) which has its Input Axis directed west-to-east combines its functions with those of the (ADR) with its Input Axis south-to-north....- ~ XI. Component Functions with System on Stationary Base Preparation of an Inertial System for serving Control, Navigation, and Guidance requirements of a carrying vehicle which moves in regions near the Earth requires an adequate continuous supply of operating power, knowledge of Starting Location, introduction of complete computer programs and other information together with correct initial settings of all essential instrument and other mechanism situations. The desired stationary platform situation is for the Indicated Vertical to be aligned with the plumb bob direction of gravity so that the Indicated Horizontal Plane is truly level. Indicated North must have the direction of the projection of Earth s Rotation on this plane. Indicated East is the direction at right angles to Indicated North on the Indicated Horizontal Plane. Adequate orientational references may be provided by the Indicated Horizontal Plane, leveled to be perpendicular to the direction of Indicated Gravity and with its (ADR) Input Axes assigned to Indicated East and Indicated North, respectively. The gravitational signals that are nulled to level the plane are provided by the (SFIR) with its Input Axisouth-to-north acting through the (ADR) with its Input Axis west-to-east and the (SFIR) with its Input Axis westto-east acting through the (ADR) with Input Axis south-to-north. The plumb bob direction of gravity is physically determined as the resultant on test masses within instruments of gravitational field force and inertial reaction force from linear acceleration associated with the circular path movement about the Earth s axis of rotation imposed on this mass at its location on the surface by the angular velocity of Earth with respect to inertial space. Because all matter useful for sensing gravity and acceleration has, under Einstein s Principle of Equivalence, exactly the same Mass for reactions to these two effects, it is impossible to separate a resultant input formed by any mixture from the two sources into components identified with their origin. The only way that the output signal from an (SFIR) may be associated exclusively with the gravitational field as input completely to is exclude any component of acceleration with respect to inertial space from action along the Input Axis of the Instrument. This sensor characteristic means that in regions for which gravitational fields of significant magnitudes exist, the only way that accurate indications of acceleration can be achieved, is to align (SFIR) Input Axes so that they remain always effectively at right angles to the existing gravitational field, while acceleration inputs are substantially at right angles to gravity. For the diagram of Fig. 5, the plumb bob orientation of Indicated the Horizontal Plane is inclined to the force of the gravitational field because of the centrifugal force component due to Earth rotation. If this inclination is allowed to continue during flight, (SFIR) Input Axes will be tipped so that gravity effects are mixed in with vehicle acceleration inputs. This may be avoided by using computer data to automatically correct out the Earth rotation centrifugal force effect on the inertial reference orientation immediately when the system starts to move after stationary base equipment has been completed and starting conditions have been introduced in terms of initial Latitude, Longitude, Destination, Path, Flight Program, etc. XII. Indicated Horizontal Plane Compensation for Rotation of the Earth With the Indicated Horizontal Plane leveled to perpendicularity with the direction of plumb bob gravity under control of the (ADR) having its Input Axis west-to-east, the (ADR) with its Input Axis south-to-north, and the (ADR) control systems magazine

12 with its Input Axis up-to-down, the plane carried by a stationary platform on the Earth would rotate with respecto an inertially stabilized reference during the passage of each day. This action appears because the (ADR) signals command that the mechanism parts of the platform remain nonrotating with respect to inertial space, while the Earth rotates continuously within this space. This motion of the Indicated Horizontal Plane may be eliminated by aligning the proper (ADR) Input Axes with Indicated North, Indicated East, and the Indicated Vertical, and applying to the (ADR) with its Input Axis south-tonorth Command a Signal equal in magnitude (Magnitude of Earth Angular Velocity) to X cosine (Latitude) in the proper sense about the Axis. The effect of this input is to cause the Indicated Horizontal Plane to rotate about the Indicated North Axis with an angular velocity component of the proper magnitude and sense to drive the Indicated Vertical so that it stays aligned with the Actual Vertical. The sine component of Earth s rotation must be compensated in the same way as the cosine component with angular velocity requiredetermined by computer and the corresponding result applied as the Angular Deviation Command Signal to the (ADR) with its up-to-down Input Axis aligned to the direction of the gravity. The Earth s angular velocity sine component rotates the Indicated Horizontal Plane structure so that it keeps up with the surface as the inertiallyreferred direction of east changes due to the rotation of the Earth. XIII. System Moving Over Surface of Earth-Rotation of Indicated Horizontal Plane for Maintaining Alignment Perpendicular to Direction of Gravitational Field When an inertial system with proper initial settings to inertial references and alignment of the Indicated Vertical to the direction of the gravitational field with the effect of Earth rotation centrifugal force removed starts to move in directions at right angles to the direction of gravity the Indicated Horizontal Plane including the south-to-north and west-toeast (SFIR) Input Axes will have inputs due entirely to horizontal linear acceleration without any component due to gravity. For this situation, the (SFIR s) will start to generate linear velocity outputs along Indicated North and Indicated East. If these references maintain their initial orientations with respect to inertial space, two error-generating effects operate. The (SFIR) Input Axes begin to accept components due to the gravitational field, an action that leads to inaccuracies of linear velocity indications. In addition, failure of the Indicated Vertical to maintain its alignment with the direction of the gravitational field leads to errors in estimated location based on field directions. These inaccuracy-generating effects may be controlled by rotating the Indicated Horizontal Plane about Indicated North and Indicated East with components equal to the corresponding (SFIR) linear velocity signal outputs divided by a proper Equivalent Radius of the Earth. These computer operations generate command signals for the two (ADR s) that, applied to the servodrives about Indicated North and Indicated East rotate the Indicated Horizontal Plane about these two axes so that for significant perids of time the Plane remains under control of inertial references, as the vehicle moves at right angles to the direction of the Gravitational Field. This situation, by accurate sensor indications of angular deviations about Indicated East and Indicated North gives information on changes on Indicated Latitude and of Indicated Longitude from Initial Reference Settings. Similar results may be achieved by computer integrations of (SFIR) Indication Outputs corresponding the Indicated to North Direction and the Indicated East Direction. These outputs generally are displayed by Readout systems designed to provide information on Mission Programs, Deviations of Actual Situations from Desired Situations, currently useful control corrections and other matters of importance to the achievement of satisfactory results. In general, control by human monitors may be applied with automatic adjustments of system parameters, or pilots may electo substitute themselves for one or more components of the operating loop component chains. In all cases, it is likely that information from sensing instruments will be used as the basis for generating information and judging system responses. Note-by Dr. Walter W. Wrigley, Consultant: In discussing the effect of centrifugal acceleration due to Earth s daily rotation on interpreting the output of the (SFIR) with a north-south input axis, the author clearly shows the problems encountered in attempting to separate the inertial reaction components of specific force from the mass attraction (gravitational) components. The method discussed involves use the of direction of the gravitational field as the reference for an indicated vertical. This technique effectively removes mass attraction from the inputs to the horizontal (SFIRs) once the initial conditions are known from alignment on a base stationary relative to Earth. An alternative approach is to use plumb bob gravity (the combined effect of mass attraction and daily centrifugal acceleration) as the reference for an indicated vertical. While incorporating a small component of mass attraction in the inputs to the horizontal (SFIRs), this technique permits indication of change in vehicle velocity with little computed aid. XIV. Summary Vehicle-carried, self-contained systems to provide the functions of Control, Navigation, and Guidance with acceptable performance and good reliability from equipment of reasonable size and cost have attracted much attention and support during the past few decades. The desired results have been and still remain those of high accuracy operation without cooperation from off-vehicle complexes of radiation contact stations on Earth or moving with carriers in the sky. If this basic requirement is fulfilled, navigation of good quality becomes possible in all land and water areas of Earth while underwater voyages of significant length are routine for submarines. Navigation is no longer vulnerable to accidents or deliberate damage affecting external radiation linkages and is subject to troubles from enemy actions only by destruction of essential onboard system components. In addition to the factors that have been mentioned, installations of inertial navigation equipment integrated with other vehicle systems provide enhanced convenience and operating capabilities. Benefits of this kind to many airplanes, coupled with special advantages for military vehicles have provided motivation for a number of industrial firms to build and provide hundreds of inertial navigation systems. It has been a general procedure for each manufacturer to design its own system. Several different mechanizations have been used with operational results that apparently lie in the same general region of performance. december

13 This already-too-long paper does not have space for discussion of the considerable range of design features that have been applied. For this reason, attention concentrated is here on the fundamental physical and geometrical performance needed from instruments to meet requirements of generalized inertial systems. Because single-degree-offreedom sensors provide simple relationships of physical inputs for corresponding outputs and contribute to overall system operating by easy-toexplain interactions with other components, instruments of this kind are used to illustrate basic principles for the figures of this paper. Inertial navigation employs the unqiue feature of geometrical references generated by internal mechanisms without radiation links external to points. References with this general characteristic using inertial reactions on mass component escapement parts have been basic elements in clocks, chronometers, and other time-keeping devices for hundreds of years. Improvements have been slow in coming, but today wrist watches with crystal oscillators give time indications of excellent reliability and high performance. The essential action is that of vibration with its period accurately controlled by inertial reactions of accelerated mass. With all periods in a sequence escapement of oscillations equal to all other periods, any cycle may be chosen and used as the reference for time indicated by a chain of uninterrupted cycles. Inertial navigation requires service from basic functions that are, in general, similar to the function that mechanical escapements provide for time keepers. These functions are first, a reference instant to which time measurements may be referenced and second, an indefinitely long sequence accurately of equal periods that may be counted for the measurement of time intervals. The same general philosophy is useful for representations of geometrical situations in terms of components associated with operations of single-degree-of-freedom sensors. Each of the three degrees of geometrical freedom that are characteristic of the physical world inwhichwe live may be associated with a straight line directed at right angles to each of two other similar directions. In addition to three straight-line displacement degrees of freedom, there are three other degrees of freedom that exist as rotations about the linear directions. This general geometrical situation requires instruments able to provide three single-degree-of-freedom references for linear motion and three single-degree-offreedom references for rotation. The linear input instruments must be able to produce indications of physical displacements from linear references or commanded-by-signal changes from these references. Angular deviation sensors receive mechanical rotations with respect to inertial space about input axis directions and produce output signals for control of servodrives. These instruments also receive angular deviation command signals and generate corresponding changes in angular outputs about reference directions. The sensors dealing with angular inputs are called Angular Deviation Receivers, Symbol (ADR). Other instruments sensitive to specific force, which is the resultant per unit mass of gravitational field force and inertial reaction force acting along their input axes may include means for integration of information within their mechanisms and for this reason are called Specific Force Integrating Receivers. Symbol (SFIR). These sensors are designed to accept command signals that may be used to change the inertialineareference along the input axis direction. Functional requirements for sensor subsystems of inertial guidance systems may be provided by three angular deviation receivers with input axes mutually at right angles and three specific force integrating receivers also with their input axes at right angles. The sensors are arranged in three pairs, each pair including one angular deviation receiver and one specific force receiver. These instruments and their mechanical support to an axis with 360 degrees of angular freedom form Sensor the Package. In one pair of instruments both input axes are along the indicated vertical. All of the units in the other two pairs have their input axes perpendicular tu the indicated vertical. The angular deviation receiver input axes are at right angles to each other. The input axes of the specific force receivers are at right angles to the associated angular deviation receiver input axes. With the inertial system in place and energized on a stationary base to transmit servqmotor input signals from the specific force integrating receiver units with their input axes free to align themselves at right angles to the direction of gravity, the middle support gimbal and the outer support gimbal may be moved to bring the inner gimbal axis into alignment with the direction of gravity, an action that levels the indicated horizontal plane without any particular orientation about the vertical. If the angular deviation receivers with their input axes at right angles to the indicated vertical are activated, the instruments receive the Earth s angular velocity projection on the horizontal plane that has components along the angular deviation receiver input axes that may be used to rotate one of these input axes so that it becomes perpendicular to the horizontal projection of Earth s rate. This input axis becomes indicated east and the other angular deviation receiver input axis becomes indicated north, which has the horizontal component of Earth s angular velocity along its direction. As the system sits nonmoving on an Earth-stationary base, the Earth rotates with respect to inertial space. Under signals that represent zero angular deviations from inertial space orientational references, the indicated horizontal plane would rotate with respect to the Earth. Because navigation and guidance are geometrical operations carried out with respect to the Earth, it is necessary to remove Earth s rotation as a motion of the sensor package. This result is achieved by applying a command signal that causes the angular deviation receiver with its input axis along indicated north to rotate the inner gimbal about this direction with an angular velocity magnitude equal to Earth s angular velocity multiplied by the cosine of latitude. In addition to providing compensation for the horizontal projection Earth s of angular velocity, it is necessary to apply an angular velocity correction to the sensor package about the indicated vertical that is proportional in magnitude to Earth s angular velocity multiplied by the sine of latitude. When the system is started into motion from a stationary base, a compensation may be introduced fur the effect of centrifugal force due to rotation of the Earth that is associated with fixed a location. This correction removes all horizontal linear acceleration forces from the vertical axis instrument input so that the force direction and magnitude depends only upon gravitational field effects, a situation accounted for in geodetic relationships between locations and gravitational field force directions. When the system has the indicated horizontal plane leveled, and indicated 16 control systems magazine

14 north aligned actual to north (and, therefore, indicated east aligned with actual east), mechanical requirements for beginning flight are fulfilled. In addition, mission objectives together with flight programs, initial conditions, etc., set into computers, readouts and monitoring systems, complete preparations for travel. Initial geometrical references are provided by the leveled orientation of the indicated horizontal plane, the physical direction of the input axis along indicated north and the direction of the input axis along indicated east. The maintenance of level about indicated north and indicated east shows that compensation for Earth s rotation is correct. Indications of zero gravity force by the specific force indicating receivers with centrifugal force from Earth s rotation properly taken into account, having their input axes in the indicated horizontal plane, shows that this plane perpendicular is to the gravitational field. This situation, coupled with indicated north and indicated east both aligned with their correct directions are the initial inertially provided geometrical references. The corresponding initial situation for linear references is associated with the specific force integrating receivers having their input axes perpendicular to the gravitational field input and arbitrarily set output readings. When the vehicle carrying the inertial system starts in substantially horizontal motion, the physical effects acting along their input axes, which start at right angles to the direction of the gravitational field, begin as purely linear acceleration components. Each of the two specific integrating receivers receives its particular internal mechanization to generate an output signal that represents linear velocity along the input axis. At the start of motion the specific force integrating receiver input axes are perpendicular to the direction of the gravitational field and hold this direction with respect to inertial space as internally controlled reference directions. If the situation of horizontal linear acceleration components continues, the sensor input axes deviate from being perpendicular to the direction of the gravitational field so that projections of gravity combine with inertial reaction force components and acto contaminate the acceleration inputs. An additional important consideration is that geometrical outputs from complete systems in terms of locations, velocities, directions, etc., must be based on gravitational field directions with respect to Earth coordinates. In actual systems, the essential gravitational field directions are associated with situations of the indicated horizontal plane. It is operationally useful to keep the plane perpendicular the to direction the of gravitational field. With a system involved in horizontal motion over the Earth, this continued leveling of the indicated horizontal plane with linear velocity motion along, say, the direction of indicated north would be accompanied by a rate of change in latitude that requires a corresponding change in angular velocity with respect to inertial space about the direction the of angular deviation receiver input axis along the west-to-east direction. The magnitude of the required additional angular velocity component for south-to-north motion may be computer-generated as the magnitude of the linear velocity component divided by a proper effective radius of the Earth. The introduction of this angular velocity compensation for south-to-north linear velocity serves to keep the indicated horizontal plane level about the west-to-east angular deviation receiver input axis. West-to-east linear acceleration input to the active specific force integrating receiver and division of the result by the equivalent radius of Earth may be used to generate a correcting angular velocity component for application to south-tonorth angular deviation receiver input axis. This angular velocity adds its effect about the indicated north direction that combines with the computer-generated command signals already present to compensate for Earth s rotation and complete leveling the indicated of horizontal plane. Ideal mechanization for the inertial system arrangements that have been assumed are discussed from the standpoint of functional interactions involved. The sensing instruments must have functional characteristics of two kinds. First they must be capable of initially accepting and then maintaining for significantly long periods of time, the accurately defined configurations required as geometrical references. Second, they must be capable receiving of and generating accurate responses to command signals for indefinitely extensive sequences of inputs directed toward physically changing numerically or measuring input deviations. All instruments must provide indications with electrical signal forms usable by computers, readout systems and servodrives. These requirements apply to angular deviation receivers as they provide orientation references about their input axes and generate angular deviations to match command input signals. The characteristics are also those needed by specific force integrating receivers as they establish indications corresponding to linear reference positions along their input axes and,their generated output signals that accurately represent integrations of acceleration along their input axes. It is an interesting fact that the theory of inertial navigation systems isubstantially complete except for empirical results providing information on the proper magnitude of the equivalent radius of Earth for compensating indicated horizontal plane orientations for linear velocity of vehicles. The angular deviation receiver with 5s input axis along the indicated vertical has the important function receiving of signals from the angular deviation receivers, having their input axes in the indicated horizontal plane, and supplying drive signals to the servomotor acting about the indicated vertical axis to rotate the sensor package so that the angular deviation receivers on the plane have their input axes properly along indicated north and indicated east. The angular deviation receiver with its input axis upto-down also acts to receive the command signal that corresponds to the sine component of Earth s angular velocity and applies its driving effect about the indicated vertical axis of the sensor package. A specific force integrating receiver is shown in one of the figures of the paper to suggest a requirement of completeness. Instrumentation with the performance needed for this position has not been generally available so that discussion of it is omitted here. It is interesting to note that the performance achieved by inertial systems has in the past been limited primarily by the behavior of sensors. Certainly many contributions have improved system performance during the past quarter century; however, opportunities of many kinds continue to exist and it is to be expected that ever-improving technology will provide capabilities that are probably not even ideas at the present time. For a biography of the author. please see the Awards section of this issue. december