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A number of observations can be made from these graphs and the corresponding animations:

1. Not all choices of Q^dwork.

Successful trials fall within a "nominal range" of Q^d

2. Choice of sampling strategy noticeably affects the appearance of the walks. Somewhat

surprisingly, no one strategy is demonstrably superior.

3. Walks are not of uniform quality.

Some walks initially appear stable but then fall

over.

Other walks appear chaotic but don't fall.

Choices of Q^dtoward the centre of

the nominal ranges give the most consistent walks in terms of stability and appearance.

4. One walk begins moving forward, slows to

a

stop

and

then

moves

backwards

chaotically for about 15 steps before finally falling. The fact that such a walk emerges

from a base

PCG

designed

to

produce

forward

walking

motions

illustrates

the

Figure 4.4 through Figure 4.6 show the end-of-cycle components of the reduced state vector, Q_i^*,

over time, for the walks of Figure 4.3 (b), (d) and (f).

The sampled points are joined by lines to

better visualize oscillations.

The lines do not represent the continuous motion of the RV during

each stride. Q^dis indicated by a dotted line.

A number of qualitative observations can be made about the behaviour of Q_i^*:

1. A startup phase is clearly evident. The number of steps required to reach a steady-state

response varies from 5 to over 20, with 10 being most typical.

Q^din the middle of nominal range stabilize most quickly.

Trials using values of

2. The desired value, Q^d
   , is not always achieved, but a limit cycle is still attained in many

such cases.

3. No particular sampling strategy appears superior with respect to steady state error or

rate of stabilization.