18th annual conference on manual control.pdf - Acgsc.org

B. Minimum Information Storage Trajectories
We now consider the amount of information it takes %o specify a trajectory.
If the machine control is to be computer driven then this determines
the number of instructions required. If information storage or the time required
to input this storage are important constraints on operation iJ_ may become
desirable to minimize (to some degree) the required instructions.
If a trajectory consists of straight line segments then the breakpoints
must be given and the required slopes can then be determined. The initial and
final configuration points are required, but are common to all tr'ajectories.
Comparing the trajectories of Figure 12 we see that trajectories 1 and 2 require
less information than trajectory 3,vv£_ two line segments to the latter's four.
Could we do better perhaps with a smooth curve from the initialconfiguration
point to the final configuration point. The minimum we we would require to
avoid the collision zone is a quadratic curve, specified by three points, the
initialand finalpoints being two. This is equivalent, in information, to the
two line segment trajectory and is therefore also a minimum information trajectory.
We might note that the quadratic passing through the corner point,
Xo -q'Yo = q' is alsoa minimum time trajectoryas well.
III.An Example with Rotational and Translational Motion
Figure 14 indicates an initialand finalconfiguration for the machine of
Figure 6, and indicates three different trajectories. The scales are measured
in units of d, according to the scaling concept p reviously defined. Assuming
again some scaled maximum speed, Smax, we find that for
Trajectory i Ti_ (('_o'_i-_.@_ . (_,_ _,1)2_+ (3._-_,_>2_;/%,, _'_._0_]_,_
Wr jeotory3 (( i + 2.1)i = 3,q
(,ggJza
Ctl(\ .
',
I
0 d zd _d _.a .sd
(_;) 0o) (,s) _2o3 (2_)
Figure 14. Trajectories
Machine with
in a Two
RotationaI
Dimensional
Motion
Configuration Space:
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