Computer-controlled steering of the Apollo spacecraft.

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Abstract
The digital guidance computer is the central control element in the 'Apollo control, guid- ante, and navigation system. Efficient operation of the guidance computer during any mission phase requires the performance of many different functions occurring at approxi- mately the same time. Some examples are the processing of input data in the form of ve- locity increments, gimbal angles, system status signals, astronaut keyboard commands, and ground commands, and producing output such as steering commands, control of mode and caution lamps, digital display updating, and digital telemetry transmission. To illustrate the diversity of requirements with which this computer must cope, a specific phase of the Apollo mission is described in detail, i.e., the control of the spacecraft to accomplish a pow- ered maneuver. OR position and velocity determination (navigation) the Apollo system includes inertial instruments capable of measuring thrust accelerations along three mutually orthogo- nal axes which are nonrotating. A computer performs accurate integrations and gravity calculations on a real-time basis. Incremental outputs from inertially stabilized integrating accelerometers, together with components of gravitational acceleration computed as functions of inertial position in a feedback loop, are summed to give the components of inertial velocity. The gravity calculations may be performed in a straightfor- ward manner. In Fig. 1, the equations of motion for a vehicle moving in a spherical gravitational field are given together with a simple computation algorithm by means of which posi- tion and velocity are obtained as a first-order difference equation calculation. Since velocity is updated by means of the average effective gravity over the interval of one time step, this technique has been termed the "average g" method. The task of providing steering commands (guidance) for major thrusting maneuvers is a boundary value problem subject to a variety of constraints of which fuel conservation, vehicle maneuverability, and time are examples. Explicit solutions to the problem of guidance during periods of major thrusting require relatively complex calculations to be per- formed in flight on a time-critical basis. Many of the major orbital transfer maneuvers can be ac- complished conceptually by a single impulsive velocity change. For these cases an instantaneous velocity-to-be-gained vector based on conic orbits can be defined and the vehicle steered to null this vector. Refer to Fig. 2 and let a vector v, be defined, corresponding to the present vehicle location r, as the in- stantaneous velocity required to satisfy a set of stated mis- sion objectives. The velocity difference v, between v, and the present vehicle velocity v is then the instantaneous veloc-

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