guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
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only line-of-sight thrusting is used, the velocity perpendicular to the line of<br />
sight will become 103v Thus, unless v is zero (initially), rendezvous<br />
is not possible with &%-of-sight thrusti R g. For.the more accurate approximation<br />
of linear terms in the equations of motion, the same situation pertains<br />
except that some sets of initial conditions would reduce the effect <strong>and</strong> others<br />
would magnify it. In either case, it is clear that a technique for managing<br />
the relative velocity perpendicular to the line of sight <strong>and</strong> for reducing it to<br />
zero as range <strong>and</strong> range-rate are reduced to zero is essential for rendezvous.<br />
Further, though an astronaut could learn to make the necessary corrections by<br />
trial <strong>and</strong> error, techniques for optimal <strong>and</strong> for automatic control are needed.<br />
The rendezvous operation may be described as the overall solution to the<br />
following set of interrelated problems:<br />
a. The state determination problem.<br />
b. The <strong>trajectory</strong> determination <strong>and</strong> prediction problem.<br />
C. The <strong>trajectory</strong> control problem.<br />
Each of these problems is discussed briefly here:<br />
a. The state determination problem - Before making a course correction,<br />
the current conditions (i.e., the orbit of the target vehicle <strong>and</strong> the<br />
relative position <strong>and</strong> velocity of the active vehicle), must be deter-<br />
mined. It is assumed in this monograph that this information, which<br />
is taken to include error estimation, is available at the start of the<br />
problem, as well as at later times as it may be needed.<br />
b. The <strong>trajectory</strong> determination <strong>and</strong> prediction problem - the future sepa-<br />
ration of the two vehicles must be predictable in some fashion in order<br />
that changes of velocity can be determined which will cause the<br />
separation to be reduced to zero at the same time the velocity differ-<br />
ence is nulled. The degree of sophistication required in the equations<br />
of motion will depend on the time to make the maneuver <strong>and</strong> the levels<br />
of thrust that may be used. For times which are short compared to the<br />
period of the motion <strong>and</strong> for thrust accelerations which are consider-<br />
ably larger than the differences in the gravitational or other<br />
perturbation accelerations between the two satellites, the motion of<br />
the two vehicles approximates completely the field free space problem.<br />
On the other h<strong>and</strong>, if the time to rendezvous is of the order of a<br />
quarter of a revolution or longer, the equations must contain peri-<br />
odic effects <strong>and</strong> secular effects produced by the dynamics of the two<br />
bodies. However, since the object of the maneuver is to effect a<br />
reduction of the relative motion to zero, it is to be expected that<br />
approximate representations will be satisfactory as long as errors in<br />
the rendezvous caused by poor representation at large values of the<br />
relative coordinates can be corrected by subsequent thrusting as the<br />
rendezvous is approached. In fact, this capability for error compen-<br />
sation is required since noise <strong>and</strong> measurement errors in the data<br />
sensed must be taken into consideration. Both the model errors <strong>and</strong>